Merge pull request #2 from dhuth/master

Moved omega into chill.

279 files changed, 8926 insertions, 0 deletions

diff --git a/omega/examples/old_test/affineClosure b/omega/examples/old_test/affineClosure
new file mode 100644
index 0000000..1039856
--- /dev/null
+++ b/omega/examples/old_test/affineClosure
@@ -0,0 +1,19 @@
+
+symbolic n;
+symbolic c;
+
+R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+R;
+ac := approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+	0 <= lambda0, lambda1,lambda2,lambda3,lambda4
+	&& c = lambda0-lambda1+ 10 lambda2 - lambda3
+	&& i = lambda1-lambda2
+	&& j = lambda3-lambda4
+	&& n = lambda4)};
+ac;
+
+#ac intersection {[i,j] : i = 1 && c = -1}		;
+#ac intersection {[i,j] : i = -1 && c = 10}		;
+#ac intersection {[i,j] :  j = 1 && c = -1 }		;
+#ac intersection {[i,j] : j = -1 && n = 1}		;
+	
diff --git a/omega/examples/old_test/affineClosure.oc-rt b/omega/examples/old_test/affineClosure.oc-rt
new file mode 100644
index 0000000..fbf8bf9
--- /dev/null
+++ b/omega/examples/old_test/affineClosure.oc-rt
@@ -0,0 +1,32 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# symbolic n;
+# 
+# symbolic c;
+# 
+# 
+# R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+# 
+# R;
+
+{[i,j]: 1 <= i <= 10 && 1 <= j <= n}
+
+# 
+# ac := approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# 	0 <= lambda0, lambda1,lambda2,lambda3,lambda4
+# 	&& c = lambda0-lambda1+ 10 lambda2 - lambda3
+# 	&& i = lambda1-lambda2
+# 	&& j = lambda3-lambda4
+# 	&& n = lambda4)};
+# 
+# ac;
+
+{[i,j]: 0 <= n && 0 <= n+c+i+j && 0 <= n+c+10i+j && 0 <= n+j}
+
+# 
+# 
+# #ac intersection {[i,j] : i = 1 && c = -1}		;
+# #ac intersection {[i,j] : i = -1 && c = 10}		;
+# #ac intersection {[i,j] :  j = 1 && c = -1 }		;
+# #ac intersection {[i,j] : j = -1 && n = 1}		;
+# 	
diff --git a/omega/examples/old_test/affineClosure2 b/omega/examples/old_test/affineClosure2
new file mode 100644
index 0000000..35ae0e1
--- /dev/null
+++ b/omega/examples/old_test/affineClosure2
@@ -0,0 +1,55 @@
+symbolic n;
+symbolic c;
+# # Omega Calculator [v1.00, Mar 96]:
+# # 
+# # 
+# # 
+# # R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+# # 
+# # R;
+# 
+# {[i,j]: 1 <= i <= 10 && 1 <= j <= n}
+# 
+# # 
+# # ac := approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# # 	0 <= lambda0, lambda1,lambda2,lambda3,lambda4
+# # 	&& c = lambda0-lambda1+ 10 lambda2 - lambda3
+# # 	&& i = lambda1-lambda2
+# # 	&& j = lambda3-lambda4
+# # 	&& n = lambda4)};
+# # 
+# # ac;
+# 
+# {[i,j]: 0 <= n && 0 <= n+c+i+j && 0 <= n+c+10i+j && 0 <= n+j}
+# 
+# # 
+# # 
+# # #ac intersection {[i,j] : i = 1 && c = -1}		;
+# # #ac intersection {[i,j] : i = -1 && c = 10}		;
+# # #ac intersection {[i,j] :  j = 1 && c = -1 }		;
+# # #ac intersection {[i,j] : j = -1 && n = 1}		;
+# # 	
+
+approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+	0 <= lambda0,lambda1,lambda2,lambda3,lambda4
+	&& n = lambda1+lambda2+lambda3+lambda4
+	&& i = lambda2+10lambda3
+	&& j = lambda2+lambda3+lambda4
+	&& c = lambda0+lambda2+lambda3
+	&& c = 1
+	)};
+approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+	0 <= lambda1,lambda2,lambda3,lambda4
+	&& n = lambda1+lambda2+lambda3+lambda4
+	&& i = lambda2+10lambda3
+	&& j = lambda2+lambda3+lambda4
+	&& c = lambda2+lambda3
+	&& c = 1
+	)};
+approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+	0 <= lambda1,lambda2,lambda3,lambda4
+	&& n = lambda1+lambda2+lambda3+lambda4
+	&& i = lambda2+10lambda3
+	&& j = lambda2+lambda3+lambda4
+	&& c = lambda2+lambda3
+	)};
diff --git a/omega/examples/old_test/affineClosure2.oc-rt b/omega/examples/old_test/affineClosure2.oc-rt
new file mode 100644
index 0000000..b4c1fd7
--- /dev/null
+++ b/omega/examples/old_test/affineClosure2.oc-rt
@@ -0,0 +1,70 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# symbolic c;
+# 
+# # # Omega Calculator [v1.00, Mar 96]:
+# # # 
+# # # 
+# # # 
+# # # R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+# # # 
+# # # R;
+# # 
+# # {[i,j]: 1 <= i <= 10 && 1 <= j <= n}
+# # 
+# # # 
+# # # ac := approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# # # 	0 <= lambda0, lambda1,lambda2,lambda3,lambda4
+# # # 	&& c = lambda0-lambda1+ 10 lambda2 - lambda3
+# # # 	&& i = lambda1-lambda2
+# # # 	&& j = lambda3-lambda4
+# # # 	&& n = lambda4)};
+# # # 
+# # # ac;
+# # 
+# # {[i,j]: 0 <= n && 0 <= n+c+i+j && 0 <= n+c+10i+j && 0 <= n+j}
+# # 
+# # # 
+# # # 
+# # # #ac intersection {[i,j] : i = 1 && c = -1}		;
+# # # #ac intersection {[i,j] : i = -1 && c = 10}		;
+# # # #ac intersection {[i,j] :  j = 1 && c = -1 }		;
+# # # #ac intersection {[i,j] : j = -1 && n = 1}		;
+# # # 	
+# 
+# approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# 	0 <= lambda0,lambda1,lambda2,lambda3,lambda4
+# 	&& n = lambda1+lambda2+lambda3+lambda4
+# 	&& i = lambda2+10lambda3
+# 	&& j = lambda2+lambda3+lambda4
+# 	&& c = lambda0+lambda2+lambda3
+# 	&& c = 1
+# 	)};
+
+{[i,j]: c = 1 && 0 <= i <= 10j, 10 && j <= n}
+
+# 
+# approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# 	0 <= lambda1,lambda2,lambda3,lambda4
+# 	&& n = lambda1+lambda2+lambda3+lambda4
+# 	&& i = lambda2+10lambda3
+# 	&& j = lambda2+lambda3+lambda4
+# 	&& c = lambda2+lambda3
+# 	&& c = 1
+# 	)};
+
+{[i,j]: c = 1 && 1 <= i <= 10 && 1 <= j <= n}
+
+# 
+# approximate {[i,j] : exists (lambda0, lambda1,lambda2,lambda3,lambda4 :
+# 	0 <= lambda1,lambda2,lambda3,lambda4
+# 	&& n = lambda1+lambda2+lambda3+lambda4
+# 	&& i = lambda2+10lambda3
+# 	&& j = lambda2+lambda3+lambda4
+# 	&& c = lambda2+lambda3
+# 	)};
+
+{[i,j]: c <= i <= 10c && c <= j <= n}
+
+# 
diff --git a/omega/examples/old_test/beatrice2 b/omega/examples/old_test/beatrice2
new file mode 100644
index 0000000..7b425fd
--- /dev/null
+++ b/omega/examples/old_test/beatrice2
@@ -0,0 +1,51 @@
+#    do i = 1, np {
+#	do j = 1, i {
+#	    ij = ia(i) + j
+#	    a = 1. / (i + j)
+#	    do k = 1, i {
+#		maxl = k
+#		if (k == i) then
+#		    maxl = j
+#		endif
+#		do l = 1, maxl {
+#		    kl = ia(k) + l
+#		    b = 1. / (k + l)
+#		    val = a + b
+#		    if (i == j) then
+#			val = val * .5
+#		    endif
+#		    if (k == l) then
+#			val = val * .5
+#		    endif
+#		    x(ij,kl) = val
+#		    x(kl,ij) = val
+#		}
+#	    }
+#	}
+#    }
+#! 
+#
+# 
+# As far as I remember it was the dependence test between X(IJ,KL) and X(IJ,KL).
+# 
+# Pips discovered the following precondition:
+# 
+
+{[d1,d2,d3,d4] : exists ( NP,
+			I,J,K,L,IJ,KJ,MAXL,
+			I',J',K',L',IJ',KJ',MAXL' :
+			I' = I+d1 &&
+			J' = J+d2 &&
+			K' = K+d3 &&
+			L' = L+d4 
+	&& 1<=L &&  1<=J &&  MAXL<=K &&  I<=NP &&  NP<=40 &&  10<=NP 
+	&& 10+8K+MAXL<=NP+8I+J &&  38K+MAXL<=38I+J 
+	&&  J+K<=I+MAXL &&  L<=MAXL
+	&& 1 <= J,K <= I <= NP && 1 <=L <= MAXL
+
+	&& 1<=L' &&  1<=J' &&  MAXL'<=K' &&  I'<=NP &&  NP<=40 &&  10<=NP 
+	&& 10+8K'+MAXL'<=NP+8I'+J' &&  38K'+MAXL'<=38I'+J' 
+	&&  J'+K'<=I'+MAXL' &&  L'<=MAXL'
+	&& 1 <= J',K' <= I' <= NP && 1 <=L' <= MAXL'
+	)};
+
diff --git a/omega/examples/old_test/beatrice2.oc-rt b/omega/examples/old_test/beatrice2.oc-rt
new file mode 100644
index 0000000..7952859
--- /dev/null
+++ b/omega/examples/old_test/beatrice2.oc-rt
@@ -0,0 +1,56 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #    do i = 1, np {
+# #	do j = 1, i {
+# #	    ij = ia(i) + j
+# #	    a = 1. / (i + j)
+# #	    do k = 1, i {
+# #		maxl = k
+# #		if (k == i) then
+# #		    maxl = j
+# #		endif
+# #		do l = 1, maxl {
+# #		    kl = ia(k) + l
+# #		    b = 1. / (k + l)
+# #		    val = a + b
+# #		    if (i == j) then
+# #			val = val * .5
+# #		    endif
+# #		    if (k == l) then
+# #			val = val * .5
+# #		    endif
+# #		    x(ij,kl) = val
+# #		    x(kl,ij) = val
+# #		}
+# #	    }
+# #	}
+# #    }
+# #! 
+# #
+# # 
+# # As far as I remember it was the dependence test between X(IJ,KL) and X(IJ,KL).
+# # 
+# # Pips discovered the following precondition:
+# # 
+# 
+# {[d1,d2,d3,d4] : exists ( NP,
+# 			I,J,K,L,IJ,KJ,MAXL,
+# 			I',J',K',L',IJ',KJ',MAXL' :
+# 			I' = I+d1 &&
+# 			J' = J+d2 &&
+# 			K' = K+d3 &&
+# 			L' = L+d4 
+# 	&& 1<=L &&  1<=J &&  MAXL<=K &&  I<=NP &&  NP<=40 &&  10<=NP 
+# 	&& 10+8K+MAXL<=NP+8I+J &&  38K+MAXL<=38I+J 
+# 	&&  J+K<=I+MAXL &&  L<=MAXL
+# 	&& 1 <= J,K <= I <= NP && 1 <=L <= MAXL
+# 
+# 	&& 1<=L' &&  1<=J' &&  MAXL'<=K' &&  I'<=NP &&  NP<=40 &&  10<=NP 
+# 	&& 10+8K'+MAXL'<=NP+8I'+J' &&  38K'+MAXL'<=38I'+J' 
+# 	&&  J'+K'<=I'+MAXL' &&  L'<=MAXL'
+# 	&& 1 <= J',K' <= I' <= NP && 1 <=L' <= MAXL'
+# 	)};
+
+{[d1,d2,d3,d4]: d2-39, -39, d4-39, d3-39 <= d1 <= d3+39, d2+39, d4+39, 39 && d4-39, -39 <= d3 <= 39, d4+39 && -39 <= d2 <= 39 && 39d4 <= 1521+38d1+d2 && d3 <= 39+d1+d4 && d2 <= 1521+d1+38d3+d4 && 38d1+d2 <= 1521+39d4 && 38d1+d2 <= 1521+38d3+d4 && d2 <= 1521+d1+39d4 && d1+38d3+d4 <= 1521+d2 && d1+d4 <= 39+d3 && 38d3+d4 <= 1521+38d1+d2 && d1+39d4 <= 1521+d2}
+
+# 
+# 
diff --git a/omega/examples/old_test/blume1.w b/omega/examples/old_test/blume1.w
new file mode 100644
index 0000000..14d7329
--- /dev/null
+++ b/omega/examples/old_test/blume1.w
@@ -0,0 +1,6 @@
+symbolic n, line5expr(2);
+
+$$
+\{ [i,j] -> [i',j'] \mid line5expr(In) = line5expr(Out) && 2 <= j <= 1 && 1 <= i <= n && 2 <= j' <= 1 && 1 <= i' <= n \};
+$$
+
diff --git a/omega/examples/old_test/blume1.w.oc-rt b/omega/examples/old_test/blume1.w.oc-rt
new file mode 100644
index 0000000..68d6aad
--- /dev/null
+++ b/omega/examples/old_test/blume1.w.oc-rt
@@ -0,0 +1,12 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Symbolic n, line5expr(2);
+# 
+# 
+# $$
+# \{ [i,j] -> [i',j'] \mid line5expr(In) = line5expr(Out) && 2 <= j <= 1 && 1 <= i <= n && 2 <= j' <= 1 && 1 <= i' <= n \};
+
+{[i,j] -> [i',j']  : FALSE }
+
+# 
+# $$
+# 
diff --git a/omega/examples/old_test/cfft2d1 b/omega/examples/old_test/cfft2d1
new file mode 100644
index 0000000..8b59f29
--- /dev/null
+++ b/omega/examples/old_test/cfft2d1
@@ -0,0 +1,21 @@
+#
+# A (memory-based!) data dependence relation from a greatly simplified
+# cfft2d1.t that was causing us trouble.
+#
+
+symbolic line22(1), im_1(2);
+
+flow := { [iii_w,jj_w] -> [iii_r,jj_r] :
+	   im_1(In) = im_1(Out)
+	&& 1 <= jj_w
+	&& jj_w <= line22(In)
+	&& 1 <= iii_w
+	&& iii_w <= 200
+	&& 1 <= jj_r
+	&& jj_r <= line22(Out)
+	&& 1 <= iii_r
+	&& iii_r <= 200 };
+
+zero_plus := { [i1,j1] -> [i2,j2] : i1 = i2 && j1 < j2 };
+
+flow intersection zero_plus;
diff --git a/omega/examples/old_test/cfft2d1.oc-rt b/omega/examples/old_test/cfft2d1.oc-rt
new file mode 100644
index 0000000..8f8dd27
--- /dev/null
+++ b/omega/examples/old_test/cfft2d1.oc-rt
@@ -0,0 +1,29 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #
+# # A (memory-based!) data dependence relation from a greatly simplified
+# # cfft2d1.t that was causing us trouble.
+# #
+# 
+# Symbolic line22(1), im_1(2);
+# 
+# 
+# flow := { [iii_w,jj_w] -> [iii_r,jj_r] :
+# 	   im_1(In) = im_1(Out)
+# 	&& 1 <= jj_w
+# 	&& jj_w <= line22(In)
+# 	&& 1 <= iii_w
+# 	&& iii_w <= 200
+# 	&& 1 <= jj_r
+# 	&& jj_r <= line22(Out)
+# 	&& 1 <= iii_r
+# 	&& iii_r <= 200 };
+# 
+# 
+# zero_plus := { [i1,j1] -> [i2,j2] : i1 = i2 && j1 < j2 };
+# 
+# 
+# flow intersection zero_plus;
+
+{[In_1,In_2] -> [Out_1,Out_2] : im_1(In_1,In_2) = im_1(Out_1,Out_2) && Out_1 = In_1 && 1 <= In_2 < Out_2 <= line22(In_1) && 1 <= In_1 <= 200}
+
+# 
diff --git a/omega/examples/old_test/chosol b/omega/examples/old_test/chosol
new file mode 100644
index 0000000..134172c
--- /dev/null
+++ b/omega/examples/old_test/chosol
@@ -0,0 +1,11 @@
+T10:={[i] -> [0,i,0,0]};
+T20:={[i,j] -> [1,j,0,i]};
+T30:={[i] -> [1,i-1,1,0]};
+
+symbolic n;
+IS10 := {[i]: 2 <= i <= n};
+IS20 := {[i,j]: 2 <= i <= n && 1 <= j <= i-1};
+IS30 := IS10;
+
+codegen T10:IS10,T20:IS20,T30:IS30;
+codegen 2 T10:IS10,T20:IS20,T30:IS30;
diff --git a/omega/examples/old_test/chosol.oc-rt b/omega/examples/old_test/chosol.oc-rt
new file mode 100644
index 0000000..8fa3b38
--- /dev/null
+++ b/omega/examples/old_test/chosol.oc-rt
@@ -0,0 +1,32 @@
+>>> T10:={[i] -> [0,i,0,0]};
+>>> T20:={[i,j] -> [1,j,0,i]};
+>>> T30:={[i] -> [1,i-1,1,0]};
+>>> 
+>>> Symbolic n;
+>>> IS10 := {[i]: 2 <= i <= n};
+>>> IS20 := {[i,j]: 2 <= i <= n && 1 <= j <= i-1};
+>>> IS30 := IS10;
+>>> 
+>>> codegen T10:IS10,T20:IS20,T30:IS30;
+for(t2 = 2; t2 <= n; t2++) {
+  s1(t2);
+}
+for(t2 = 1; t2 <= n-1; t2++) {
+  for(t4 = t2+1; t4 <= n; t4++) {
+    s2(t4,t2);
+  }
+  s3(t2+1);
+}
+
+>>> codegen 2 T10:IS10,T20:IS20,T30:IS30;
+for(t2 = 2; t2 <= n; t2++) {
+  s1(t2);
+}
+for(t2 = 1; t2 <= n-1; t2++) {
+  for(t4 = t2+1; t4 <= n; t4++) {
+    s2(t4,t2);
+  }
+  s3(t2+1);
+}
+
+
diff --git a/omega/examples/old_test/closure1 b/omega/examples/old_test/closure1
new file mode 100644
index 0000000..0e4c541
--- /dev/null
+++ b/omega/examples/old_test/closure1
@@ -0,0 +1,8 @@
+({[i] -> [i+2]} union {[i] -> [i+3]})+;
+R := ({[i] -> [i'] : i'=i+3} union {[i] -> [i'] : i'=i+5} union {[i] -> [i'] : i'=i+7})+;
+R;
+notR := {[i] -> [i'] : i' >= i+3} - R;
+notR;
+{[i] -> [i'] : i' >= i+3} - notR;
+
+
diff --git a/omega/examples/old_test/closure1.oc-rt b/omega/examples/old_test/closure1.oc-rt
new file mode 100644
index 0000000..93ecda0
--- /dev/null
+++ b/omega/examples/old_test/closure1.oc-rt
@@ -0,0 +1,31 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# ({[i] -> [i+2]} union {[i] -> [i+3]})+;
+
+{[i] -> [Out_1] : Exists ( alpha : 2alpha = i+Out_1 && i <= Out_1-2)} union
+ {[i] -> [Out_1] : Exists ( alpha : i < Out_1+2alpha && Out_1+3alpha <= i)}
+
+# 
+# R := ({[i] -> [i'] : i'=i+3} union {[i] -> [i'] : i'=i+5} union {[i] -> [i'] : i'=i+7})+;
+# 
+# R;
+
+{[i] -> [i'] : Exists ( alpha : i+3alpha = i' && i <= i'-3)} union
+ {[i] -> [i'] : Exists ( alpha : i < i'+3alpha && 2i'+7alpha <= 2i)} union
+ {[i] -> [i'] : Exists ( alpha : i'+3alpha < i && 2i <= 2i'+5alpha)}
+
+# 
+# notR := {[i] -> [i'] : i' >= i+3} - R;
+# 
+# notR;
+
+{[i] -> [i+4] }
+
+# 
+# {[i] -> [i'] : i' >= i+3} - notR;
+
+{[i] -> [i+3] } union
+ {[i] -> [i'] : i <= i'-5}
+
+# 
+# 
+# 
diff --git a/omega/examples/old_test/closure2 b/omega/examples/old_test/closure2
new file mode 100644
index 0000000..1cfcefd
--- /dev/null
+++ b/omega/examples/old_test/closure2
@@ -0,0 +1,4 @@
+R := {[i,j] -> [i+3,j]} union {[i,j] -> [i+2,j-1]} union {[i,j] -> [i+1,j+1]};
+R+;
+R+ compose R;
+R - (R+ compose R);
diff --git a/omega/examples/old_test/closure2.oc-rt b/omega/examples/old_test/closure2.oc-rt
new file mode 100644
index 0000000..e10a428
--- /dev/null
+++ b/omega/examples/old_test/closure2.oc-rt
@@ -0,0 +1,22 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := {[i,j] -> [i+3,j]} union {[i,j] -> [i+2,j-1]} union {[i,j] -> [i+1,j+1]};
+# 
+# R+;
+
+{[i,j] -> [Out_1,j'] : Out_1+2j' = i+2j && j' < j} union
+ {[i,j] -> [Out_1,j'] : Exists ( alpha : i+j' = j+Out_1+3alpha && 3+i+2j <= Out_1+2j' && i+j' <= j+Out_1)}
+
+# 
+# R+ compose R;
+
+{[i,j] -> [Out_1,j'] : Out_1+2j' = i+2j && j' <= j-2} union
+ {[i,j] -> [Out_1,j'] : Exists ( alpha : i+j' = j+Out_1+3alpha && 3+i+2j <= Out_1+2j' && 3+i+j' <= j+Out_1)} union
+ {[i,j] -> [Out_1,j'] : Exists ( alpha : i+j' = j+Out_1+3alpha && 6+i+2j <= Out_1+2j' && i+j' <= j+Out_1)}
+
+# 
+# R - (R+ compose R);
+
+{[i,j] -> [i+2,j-1] } union
+ {[i,j] -> [i+1,j+1] }
+
+# 
diff --git a/omega/examples/old_test/closure3 b/omega/examples/old_test/closure3
new file mode 100644
index 0000000..4fdc022
--- /dev/null
+++ b/omega/examples/old_test/closure3
@@ -0,0 +1,10 @@
+symbolic n,m;
+d11 := {[i,j] -> [i,2i+j] : 1 <= i <= n && 1 <= j,2i+j <= m};
+d12 := {[i,j] -> [i,j+4] : 1 <= i <= n && 1 <= j,j+4 <= m};
+d := d11 union d12;
+d+;
+d+ compose d;
+d11 - (d+ compose d);
+gist d11 - (d+ compose d) given d11;
+d12 - (d+ compose d);
+gist d12 - (d+ compose d) given d12;
diff --git a/omega/examples/old_test/closure3.oc-rt b/omega/examples/old_test/closure3.oc-rt
new file mode 100644
index 0000000..4d99b34
--- /dev/null
+++ b/omega/examples/old_test/closure3.oc-rt
@@ -0,0 +1,48 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# d11 := {[i,j] -> [i,2i+j] : 1 <= i <= n && 1 <= j,2i+j <= m};
+# 
+# d12 := {[i,j] -> [i,j+4] : 1 <= i <= n && 1 <= j,j+4 <= m};
+# 
+# d := d11 union d12;
+# 
+# d+;
+
+{[1,j] -> [1,j+2] : j+2 <= m <= 4 && 1 <= n && 1 <= j} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = j+4alpha && Out_2+4 <= m <= 2i && 1 <= j <= Out_2-4 && i <= n)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = 2i+j+4alpha && 1 <= i <= n && Out_2 <= m && 1 <= j && 5 <= m && 2i+j <= Out_2)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha,beta : Out_2 = j+4alpha && 1 <= i <= n && Out_2 <= m && 2i+4beta < Out_2 && 1 <= j && Out_2 <= m+2i+4beta && 4i+j <= Out_2)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = j+4alpha && 1 <= i <= n && 1 <= j <= Out_2-4 && Out_2 <= m && 2i < m)}
+
+# 
+# d+ compose d;
+
+{[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = j+4alpha && Out_2+4 <= m <= 2i && 1 <= j <= Out_2-8 && i <= n)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = j+4alpha && 1 <= i <= n && Out_2 <= m && 1 <= j && 4i+j <= Out_2)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = 2i+j+4alpha && 1 <= i <= n && Out_2 <= m && 4+2i+j <= Out_2 && 1 <= j)} union
+ {[i,j] -> [i,Out_2] : Exists ( alpha : Out_2 = j+4alpha && 1 <= i <= n && 1 <= j <= Out_2-8 && Out_2 <= m && 2i < m)}
+
+# 
+# d11 - (d+ compose d);
+
+{[i,j] -> [i,2i+j] : 1 <= i <= 3, n && 1 <= j && 2i+j <= m} union
+ {[i,j] -> [i,2i+j] : Exists ( alpha : 2alpha = 1+i && 5 <= i <= n && 2i+j <= m && 1 <= j)}
+
+# 
+# gist d11 - (d+ compose d) given d11;
+
+{[i,j] -> [i',Out_2] : i' <= 3} union
+ {[i,j] -> [i',Out_2] : Exists ( alpha : 0 = 1+i'+2alpha && 5 <= i)}
+
+# 
+# d12 - (d+ compose d);
+
+{[i,j] -> [i,j+4] : 2 <= i <= n && 1 <= j <= m-4}
+
+# 
+# gist d12 - (d+ compose d) given d12;
+
+{[i,j] -> [i',Out_2] : 2 <= i'}
+
+# 
diff --git a/omega/examples/old_test/closure4 b/omega/examples/old_test/closure4
new file mode 100644
index 0000000..e5adb13
--- /dev/null
+++ b/omega/examples/old_test/closure4
@@ -0,0 +1,8 @@
+symbolic n,m;
+R1 := {[x,y] -> [x,y+1] : 1 <= x,y <= 10};
+R2 := {[x,y] -> [x+1,y] : 1 <= x <= 20 && 5 <= y <= 15};
+R12 := R1 union R2;
+R12c := R12+;
+R12c;
+(R12c compose R12c) - R12c;
+(R12c compose R12) - R12c;
diff --git a/omega/examples/old_test/closure4.oc-rt b/omega/examples/old_test/closure4.oc-rt
new file mode 100644
index 0000000..d208cce
--- /dev/null
+++ b/omega/examples/old_test/closure4.oc-rt
@@ -0,0 +1,28 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# R1 := {[x,y] -> [x,y+1] : 1 <= x,y <= 10};
+# 
+# R2 := {[x,y] -> [x+1,y] : 1 <= x <= 20 && 5 <= y <= 15};
+# 
+# R12 := R1 union R2;
+# 
+# R12c := R12+;
+# 
+# R12c;
+
+{[x,y] -> [x,y'] : 1 <= y < y' <= 11 && 1 <= x <= 10} union
+ {[x,y] -> [x',y] : 1 <= x < x' <= 21 && 5 <= y <= 15} union
+ {[x,y] -> [x',y'] : 1 <= x < x' <= 21 && 1 <= y < y' <= 11 && x <= 10 && 5 <= y'}
+
+# 
+# (R12c compose R12c) - R12c;
+
+{[x,y] -> [x',y']  : FALSE }
+
+# 
+# (R12c compose R12) - R12c;
+
+{[x,y] -> [x',y']  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/closure5 b/omega/examples/old_test/closure5
new file mode 100644
index 0000000..2792806
--- /dev/null
+++ b/omega/examples/old_test/closure5
@@ -0,0 +1,6 @@
+symbolic n,m;
+d11 := {[i,j] -> [i,2i+j] : 1 <= i <= n && 1 <= j,2i+j <= m};
+d12 := {[i,j] -> [i,j+4] : 1 <= i <= n && 1 <= j,j+4 <= m};
+d := d11 union d12;
+e := d - (d+ compose d);
+gist e given d;
diff --git a/omega/examples/old_test/closure5.oc-rt b/omega/examples/old_test/closure5.oc-rt
new file mode 100644
index 0000000..62ade41
--- /dev/null
+++ b/omega/examples/old_test/closure5.oc-rt
@@ -0,0 +1,18 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# d11 := {[i,j] -> [i,2i+j] : 1 <= i <= n && 1 <= j,2i+j <= m};
+# 
+# d12 := {[i,j] -> [i,j+4] : 1 <= i <= n && 1 <= j,j+4 <= m};
+# 
+# d := d11 union d12;
+# 
+# e := d - (d+ compose d);
+# 
+# gist e given d;
+
+{[i,j] -> [i,2i+j] : 1 <= i <= 3, n && 1 <= j && 2i+j <= m} union
+ {[i,j] -> [i,2i+j] : Exists ( alpha : 2alpha = 1+i && 5 <= i <= n && 2i+j <= m && 1 <= j)} union
+ {[i,j] -> [i,j+4] : 2 <= i <= n && 1 <= j <= m-4}
+
+# 
diff --git a/omega/examples/old_test/closure6 b/omega/examples/old_test/closure6
new file mode 100644
index 0000000..777fbba
--- /dev/null
+++ b/omega/examples/old_test/closure6
@@ -0,0 +1,13 @@
+
+T1 := {[k,i,j] -> [k',i,j] : 1 <= k < k' < j <= i <= 1024};
+
+T2 := {[k,i,i] -> [i,i',j'] : 1 <= k < i < j' <= i' <= 1024};
+
+T3 := {[k,i,j] -> [j,i',i] : 1 <= k < j < i <= i' <= 1024};
+
+T  := T1 union T2 union T3;
+
+B  := {[k,i,j]: 1 <= k < j <= i <= 1024};
+
+T + within B;
+
diff --git a/omega/examples/old_test/closure6.oc-rt b/omega/examples/old_test/closure6.oc-rt
new file mode 100644
index 0000000..0eefdaa
--- /dev/null
+++ b/omega/examples/old_test/closure6.oc-rt
@@ -0,0 +1,29 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# T1 := {[k,i,j] -> [k',i,j] : 1 <= k < k' < j <= i <= 1024};
+# 
+# 
+# T2 := {[k,i,i] -> [i,i',j'] : 1 <= k < i < j' <= i' <= 1024};
+# 
+# 
+# T3 := {[k,i,j] -> [j,i',i] : 1 <= k < j < i <= i' <= 1024};
+# 
+# 
+# T  := T1 union T2 union T3;
+# 
+# 
+# B  := {[k,i,j]: 1 <= k < j <= i <= 1024};
+# 
+# 
+# T + within B;
+
+{[k,i,j] -> [j',i,j] : 1 <= k < j' < j <= i <= 1024} union
+ {[k,i,j] -> [j',i',Out_3] : 1 <= k < j < i < j' < Out_3 <= i' <= 1024} union
+ {[k,i,i] -> [j',i',Out_3] : 1 <= k < i < j' < Out_3 <= i' <= 1024} union
+ {[k,i,i] -> [i,i',Out_3] : 1 <= k < i < Out_3 <= i' <= 1024} union
+ {[k,i,j] -> [j,i',i] : 1 <= k < j < i <= i' <= 1024} union
+ {[k,i,j] -> [j',i',i] : 1 <= k < j < j' < i <= i' <= 1024} union
+ {[k,i,j] -> [i,i',Out_3] : 1 <= k < j < i < Out_3 <= i' <= 1024}
+
+# 
+# 
diff --git a/omega/examples/old_test/closure7 b/omega/examples/old_test/closure7
new file mode 100644
index 0000000..6ba2e1d
--- /dev/null
+++ b/omega/examples/old_test/closure7
@@ -0,0 +1,12 @@
+
+R := {[t,s] -> [t+1,s] } union
+ {[t,s] -> [t,s] } union
+ {[t,s] -> [t,s+1] };
+
+R;
+R+;
+
+S := {[t,s] -> [t+1,s] } union {[t,s] -> [t,s+1] };
+
+S;
+S+;
diff --git a/omega/examples/old_test/closure7.oc-rt b/omega/examples/old_test/closure7.oc-rt
new file mode 100644
index 0000000..0de9745
--- /dev/null
+++ b/omega/examples/old_test/closure7.oc-rt
@@ -0,0 +1,36 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# R := {[t,s] -> [t+1,s] } union
+#  {[t,s] -> [t,s] } union
+#  {[t,s] -> [t,s+1] };
+# 
+# 
+# R;
+
+{[t,s] -> [t+1,s] } union
+ {[t,s] -> [t,s] } union
+ {[t,s] -> [t,s+1] }
+
+# 
+# R+;
+
+{[t,s] -> [t,s'] : s <= s'} union
+ {[t,s] -> [t',s'] : t < t' && s <= s'}
+
+# 
+# 
+# S := {[t,s] -> [t+1,s] } union {[t,s] -> [t,s+1] };
+# 
+# 
+# S;
+
+{[t,s] -> [t+1,s] } union
+ {[t,s] -> [t,s+1] }
+
+# 
+# S+;
+
+{[t,s] -> [t,s'] : s < s'} union
+ {[t,s] -> [t',s'] : t < t' && s <= s'}
+
+# 
diff --git a/omega/examples/old_test/closure8 b/omega/examples/old_test/closure8
new file mode 100644
index 0000000..b1f9b9b
--- /dev/null
+++ b/omega/examples/old_test/closure8
@@ -0,0 +1 @@
+{[i] -> [i]}+;
diff --git a/omega/examples/old_test/closure8.oc-rt b/omega/examples/old_test/closure8.oc-rt
new file mode 100644
index 0000000..90d5282
--- /dev/null
+++ b/omega/examples/old_test/closure8.oc-rt
@@ -0,0 +1,6 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# {[i] -> [i]}+;
+
+{[i] -> [i] }
+
+# 
diff --git a/omega/examples/old_test/collard b/omega/examples/old_test/collard
new file mode 100644
index 0000000..0fb4ee4
--- /dev/null
+++ b/omega/examples/old_test/collard
@@ -0,0 +1,16 @@
+symbolic n;
+
+I1 := {[i,j] : 1 <= i < j <= n};
+I2 := {[i,j,K] : 1 <= i < j,K <= n};
+I3 := {[i] : 1 <=  i <= n};
+I4 := {[i,j] : 1 <= j < i <= n};
+I5 := {[i] : 1 <= i <= n};
+
+T1 := {[i,j]   -> [1,i,0,n-i,n-j]};
+T2 := {[i,j,k] -> [1,i,1,n-j,k]};
+T3 := {[i]     -> [0,0,0,0,i]};
+T4 := {[i,j]   -> [2,j,1,i,j]};
+T5 := {[i]     -> [2,i,0,0,0]};
+
+
+codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
diff --git a/omega/examples/old_test/collard.oc-rt b/omega/examples/old_test/collard.oc-rt
new file mode 100644
index 0000000..9d2c8c0
--- /dev/null
+++ b/omega/examples/old_test/collard.oc-rt
@@ -0,0 +1,49 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# 
+# I1 := {[i,j] : 1 <= i < j <= n};
+# 
+# I2 := {[i,j,K] : 1 <= i < j,K <= n};
+# 
+# I3 := {[i] : 1 <=  i <= n};
+# 
+# I4 := {[i,j] : 1 <= j < i <= n};
+# 
+# I5 := {[i] : 1 <= i <= n};
+# 
+# 
+# T1 := {[i,j]   -> [1,i,0,n-i,n-j]};
+# 
+# T2 := {[i,j,k] -> [1,i,1,n-j,k]};
+# 
+# T3 := {[i]     -> [0,0,0,0,i]};
+# 
+# T4 := {[i,j]   -> [2,j,1,i,j]};
+# 
+# T5 := {[i]     -> [2,i,0,0,0]};
+# 
+# 
+# 
+# codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+for(t5 = 1; t5 <= n; t5++) {
+  s3(t5);
+}
+for(t2 = 1; t2 <= n-1; t2++) {
+  for(t5 = 0; t5 <= n-t2-1; t5++) {
+    s1(t2,n-t5);
+  }
+  for(t4 = 0; t4 <= n-t2-1; t4++) {
+    for(t5 = t2+1; t5 <= n; t5++) {
+      s2(t2,n-t4,t5);
+    }
+  }
+}
+for(t2 = 1; t2 <= n; t2++) {
+  s5(t2);
+  for(t4 = t2+1; t4 <= n; t4++) {
+    s4(t4,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/cover b/omega/examples/old_test/cover
new file mode 100644
index 0000000..2cfdacf
--- /dev/null
+++ b/omega/examples/old_test/cover
@@ -0,0 +1,6 @@
+symbolic p(2), n, m;
+R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m };
+W1 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) >= 0 };
+W2 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) <  0 };
+Exposed := R intersection complement ( W1 union W2 );
+Exposed;
diff --git a/omega/examples/old_test/cover.oc-rt b/omega/examples/old_test/cover.oc-rt
new file mode 100644
index 0000000..1d25c6e
--- /dev/null
+++ b/omega/examples/old_test/cover.oc-rt
@@ -0,0 +1,16 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic p(2), n, m;
+# 
+# R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m };
+# 
+# W1 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) >= 0 };
+# 
+# W2 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(Set) <  0 };
+# 
+# Exposed := R intersection complement ( W1 union W2 );
+# 
+# Exposed;
+
+{[In_1,In_2]  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/dagstuhl1 b/omega/examples/old_test/dagstuhl1
new file mode 100644
index 0000000..56f1a4e
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl1
@@ -0,0 +1,7 @@
+T := {[i,j] -> [i+10j]};
+I := {[0:9,0:9]};
+# Version 1.0.0 incorrectly generates references to i and j
+codegen T:I;
+
+# Version 1.0.0 doesn't generate an assignment for t2
+codegen {[p,i,j] : 0 <= i,j <= 9 && p = i+10j};
diff --git a/omega/examples/old_test/dagstuhl1.oc-rt b/omega/examples/old_test/dagstuhl1.oc-rt
new file mode 100644
index 0000000..7c3f019
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl1.oc-rt
@@ -0,0 +1,23 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# T := {[i,j] -> [i+10j]};
+# 
+# I := {[0:9,0:9]};
+# 
+# # Version 1.0.0 incorrectly generates references to i and j
+# codegen T:I;
+for(t1 = 0; t1 <= 99; t1++) {
+  s1(intDiv(t1+-10*j,1),intDiv(t1-i,10));
+}
+
+# 
+# 
+# # Version 1.0.0 doesn't generate an assignment for t2
+# codegen {[p,i,j] : 0 <= i,j <= 9 && p = i+10j};
+for(t1 = 0; t1 <= 99; t1++) {
+  for(t2 = intMod(t1,10); t2 <= 9; t2 += 10) {
+    t3=intDiv((-t2+t1+9),10);
+    s1(t2+10*t3,t2,t3);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/dagstuhl2 b/omega/examples/old_test/dagstuhl2
new file mode 100644
index 0000000..4cc3758
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl2
@@ -0,0 +1,6 @@
+{[i,j] : 
+	2i+6j>=9
+	&& 5i-3j >= 0
+	&& 2i-10j >= -15
+	&& -2i+6j >= 3
+	&& -2i-6j >= -17};
diff --git a/omega/examples/old_test/dagstuhl2.oc-rt b/omega/examples/old_test/dagstuhl2.oc-rt
new file mode 100644
index 0000000..2cf1f8c
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl2.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# {[i,j] : 
+# 	2i+6j>=9
+# 	&& 5i-3j >= 0
+# 	&& 2i-10j >= -15
+# 	&& -2i+6j >= 3
+# 	&& -2i-6j >= -17};
+
+{[i,j]  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/dagstuhl3 b/omega/examples/old_test/dagstuhl3
new file mode 100644
index 0000000..c63fdf8
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl3
@@ -0,0 +1,4 @@
+# In verify, we now prefer to eliminate wildcards last
+# This gives us an improved chance of finding equality
+# constraints on wildcards. 
+{[i,j] : 0 <= i,j <= 4 && exists(a:i=j+5a)};
diff --git a/omega/examples/old_test/dagstuhl3.oc-rt b/omega/examples/old_test/dagstuhl3.oc-rt
new file mode 100644
index 0000000..6dbb128
--- /dev/null
+++ b/omega/examples/old_test/dagstuhl3.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # In verify, we now prefer to eliminate wildcards last
+# # This gives us an improved chance of finding equality
+# # constraints on wildcards. 
+# {[i,j] : 0 <= i,j <= 4 && exists(a:i=j+5a)};
+
+{[i,i]: 0 <= i <= 4}
+
+# 
diff --git a/omega/examples/old_test/davew1 b/omega/examples/old_test/davew1
new file mode 100644
index 0000000..2d8d907
--- /dev/null
+++ b/omega/examples/old_test/davew1
@@ -0,0 +1,25 @@
+#
+# A one point, we couldn't handling this analysis of value-based dependences.
+# Now we can :-)
+#
+
+Pos := {[In_1,In_2] -> [i,j] :	1 <= i,j <= 100 &&
+				In_1 = 1+2j+i && 2i+In_2 = 1 };
+
+ko := {[In_1,In_2] -> [i,j] :	1+In_1+2j = 4i && In_2+i+2j = 0 &&
+				1 <= i <= 100 && 1 <= j <= 100};
+
+kf := {[i,j] -> [i',j'] :	1 <= i,i',j,j' <= 100 && i < i' &&
+				4i = 2+2j+2j'+i' && 2i' = 1+2j+i };
+
+k := ko join kf;
+
+k intersection Pos;
+example (k intersection Pos);
+Pos;
+Pos - (ko join kf);
+Pos - k;
+answer := Pos - k;
+answer;
+answer intersection {[7,-7] -> [4,1]};
+gist answer given Pos;
diff --git a/omega/examples/old_test/davew1.oc-rt b/omega/examples/old_test/davew1.oc-rt
new file mode 100644
index 0000000..bc9844c
--- /dev/null
+++ b/omega/examples/old_test/davew1.oc-rt
@@ -0,0 +1,67 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #
+# # A one point, we couldn't handling this analysis of value-based dependences.
+# # Now we can :-)
+# #
+# 
+# Pos := {[In_1,In_2] -> [i,j] :	1 <= i,j <= 100 &&
+# 				In_1 = 1+2j+i && 2i+In_2 = 1 };
+# 
+# 
+# ko := {[In_1,In_2] -> [i,j] :	1+In_1+2j = 4i && In_2+i+2j = 0 &&
+# 				1 <= i <= 100 && 1 <= j <= 100};
+# 
+# 
+# kf := {[i,j] -> [i',j'] :	1 <= i,i',j,j' <= 100 && i < i' &&
+# 				4i = 2+2j+2j'+i' && 2i' = 1+2j+i };
+# 
+# 
+# k := ko join kf;
+# 
+# 
+# k intersection Pos;
+
+{[In_1,In_2] -> [i,j] : Exists ( alpha : In_2+2i = 1 && 2In_1+In_2 = 3+4j && In_2 = 5+8j+20alpha && -199 <= In_2 <= -2j-5 && 1 <= j)}
+
+# 
+# example (k intersection Pos);
+
+{[7,-7] -> [4,1] }
+
+# 
+# Pos;
+
+{[In_1,In_2] -> [i,j] : In_1 = 1+i+2j && In_2+2i = 1 && 1 <= i <= 100 && 1 <= j <= 100}
+
+# 
+# Pos - (ko join kf);
+
+{[In_1,In_2] -> [i,j] : In_1 = 1+i+2j && In_2+2i = 1 && 1 <= i <= j+2, 100 && 1 <= j <= 100} union
+ {[In_1,In_2] -> [i,j] : Exists ( alpha : In_1 = 1+i+2j && In_2+2i = 1 && j+3 <= i <= 100 && 5+10alpha <= 3i+2j && 3i+2j <= 13+10alpha && 1 <= j)}
+
+# 
+# Pos - k;
+
+{[In_1,In_2] -> [i,j] : 1+i+2j = In_1 && 2In_1+In_2 = 3+4j && 2j+2 <= In_1 <= 3j+3, 2j+101 && 1 <= j <= 100} union
+ {[In_1,In_2] -> [i,j] : Exists ( alpha : 1+i+2j = In_1 && 2In_1+In_2 = 3+4j && 3j+4 <= In_1 <= 2j+101 && 8+4j+10alpha <= 3In_1 && 3In_1 <= 16+4j+10alpha && 1 <= j)}
+
+# 
+# answer := Pos - k;
+# 
+# answer;
+
+{[In_1,In_2] -> [i,j] : 1+i+2j = In_1 && 2In_1+In_2 = 3+4j && 2j+2 <= In_1 <= 3j+3, 2j+101 && 1 <= j <= 100} union
+ {[In_1,In_2] -> [i,j] : Exists ( alpha : 1+i+2j = In_1 && 2In_1+In_2 = 3+4j && 3j+4 <= In_1 <= 2j+101 && 8+4j+10alpha <= 3In_1 && 3In_1 <= 16+4j+10alpha && 1 <= j)}
+
+# 
+# answer intersection {[7,-7] -> [4,1]};
+
+{[In_1,In_2] -> [i,j]  : FALSE }
+
+# 
+# gist answer given Pos;
+
+{[In_1,In_2] -> [i,j] : i <= j+2} union
+ {[In_1,In_2] -> [i,j] : Exists ( alpha : j <= i-3 && 3i+2j <= 13+10alpha && 5+10alpha <= 3i+2j)}
+
+# 
diff --git a/omega/examples/old_test/ddtest b/omega/examples/old_test/ddtest
new file mode 100644
index 0000000..27b1ff3
--- /dev/null
+++ b/omega/examples/old_test/ddtest
@@ -0,0 +1,97 @@
+symbolic p(2), n, m1, m2, low;
+
+R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 };
+
+f1i := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+			      1 <= iw <= n && 1 <= jw <= m2 &&
+			      jw = jr &&
+			      iw = ir };
+f1f := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+			      1 <= iw <= n && 1 <= jw <= m2 &&
+			      jw = jr &&
+			      iw < ir };
+
+f3i := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+			      1 <= iw <= n && 1 < low <= jw <= m1 &&
+			      jw-1 = jr &&
+			      iw = ir };
+f3f := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+			      1 <= iw <= n && 1 < low <= jw <= m1 &&
+			      jw-1 = jr &&
+			      iw < ir };
+
+o31i := { [iw3,jw3] -> [iw1,jw1] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+				   jw1 = jw3-1 &&
+				   iw1 = iw3 };
+
+o13f := { [iw1,jw1] -> [iw3,jw3] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+				   jw1 = jw3-1 &&
+				   iw1 < iw3 };
+
+o31f := { [iw3,jw3] -> [iw1,jw1] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+				   jw1 = jw3-1 &&
+				   iw3 < iw1 };
+
+o11f := { [iw1a,jw1a] -> [iw1b,jw1b] : 1 <=iw1a<= n && 1 <=jw1a<= m2 &&
+				       1 <=iw1b<= n && 1 <=jw1b<= m2 &&
+				       jw1a = jw1b &&
+				       iw1a < iw1b };
+o33f := { [iw3a,jw3a] -> [iw3b,jw3b] : 1 <=iw3a<= n && 1 < low <=jw3a<= m1 &&
+				       1 <=iw3b<= n && 1 < low <=jw3b<= m1 &&
+				       jw3a-1 = jw3b-1 &&
+				       iw3a < iw3b };
+
+
+# FIRST GROUP - 1i and 2i (NO POSSIBLE OUTPUT DEPS. BETWEEN)
+v1i := f1i;
+v1i;
+
+Exposed12i := R intersection complement domain f1i;
+Exposed12i;
+
+# SECOND GROUP - 3i
+v3i := f3i / Exposed12i;  # / is restrictRange
+v3i;
+
+Exposed3i := R intersection complement domain f3i;
+Exposed3i;
+
+# THIRD GROUP - 1,2,3f (THERE ARE POSSIBLE OUTPUT DEPS BETWEEN THEM)
+
+v1f := ( f1f / Exposed3i )
+	intersection complement ( f3i compose o13f )
+	intersection complement ( f3f compose o13f )
+	intersection complement ( f1i compose o11f )
+	intersection complement ( f1f compose o11f );
+v1f;
+
+# WE SHOULD BE ABLE TO DO v1f WITH SOME VALUE-BASED FLOW DD'S
+
+v1f_val := ( f1f / Exposed3i )
+	intersection complement ( v3i compose o13f )
+	intersection complement ( f3f compose o13f )
+	intersection complement ( v1i compose o11f )
+	intersection complement ( f1f compose o11f );
+v1f_val;
+
+#
+# The effects of loop-independent flow have been taken out already,
+# so this should work.  But it does not.  Probably I am stupyd.
+#
+
+v1f_clever := ( f1f / Exposed3i )
+	intersection complement ( f3f compose o13f )
+	intersection complement ( f1f compose o11f );
+v1f_clever;
+
+#
+# NOW CHECK FOR EQUIVALENCES - THESE SHOULD BE TRUE
+#
+
+v1f subset v1f_val;
+v1f_val subset v1f;
+# v1f subset v1f_clever;
+# v1f_clever subset v1f;
diff --git a/omega/examples/old_test/ddtest.oc-rt b/omega/examples/old_test/ddtest.oc-rt
new file mode 100644
index 0000000..1c3e009
--- /dev/null
+++ b/omega/examples/old_test/ddtest.oc-rt
@@ -0,0 +1,152 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic p(2), n, m1, m2, low;
+# 
+# 
+# R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 };
+# 
+# 
+# f1i := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+# 			      1 <= iw <= n && 1 <= jw <= m2 &&
+# 			      jw = jr &&
+# 			      iw = ir };
+# 
+# f1f := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+# 			      1 <= iw <= n && 1 <= jw <= m2 &&
+# 			      jw = jr &&
+# 			      iw < ir };
+# 
+# 
+# f3i := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+# 			      1 <= iw <= n && 1 < low <= jw <= m1 &&
+# 			      jw-1 = jr &&
+# 			      iw = ir };
+# 
+# f3f := { [iw,jw] -> [ir,jr] : 1 <= ir <= n && 1 <= jr <= m1 &&
+# 			      1 <= iw <= n && 1 < low <= jw <= m1 &&
+# 			      jw-1 = jr &&
+# 			      iw < ir };
+# 
+# 
+# o31i := { [iw3,jw3] -> [iw1,jw1] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+# 				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+# 				   jw1 = jw3-1 &&
+# 				   iw1 = iw3 };
+# 
+# 
+# o13f := { [iw1,jw1] -> [iw3,jw3] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+# 				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+# 				   jw1 = jw3-1 &&
+# 				   iw1 < iw3 };
+# 
+# 
+# o31f := { [iw3,jw3] -> [iw1,jw1] : 1 <= iw1 <= n && 1 <= jw1 <= m2 &&
+# 				   1 <= iw3 <= n && 1 < low <= jw3 <= m1 &&
+# 				   jw1 = jw3-1 &&
+# 				   iw3 < iw1 };
+# 
+# 
+# o11f := { [iw1a,jw1a] -> [iw1b,jw1b] : 1 <=iw1a<= n && 1 <=jw1a<= m2 &&
+# 				       1 <=iw1b<= n && 1 <=jw1b<= m2 &&
+# 				       jw1a = jw1b &&
+# 				       iw1a < iw1b };
+# 
+# o33f := { [iw3a,jw3a] -> [iw3b,jw3b] : 1 <=iw3a<= n && 1 < low <=jw3a<= m1 &&
+# 				       1 <=iw3b<= n && 1 < low <=jw3b<= m1 &&
+# 				       jw3a-1 = jw3b-1 &&
+# 				       iw3a < iw3b };
+# 
+# 
+# 
+# # FIRST GROUP - 1i and 2i (NO POSSIBLE OUTPUT DEPS. BETWEEN)
+# v1i := f1i;
+# 
+# v1i;
+
+{[iw,jw] -> [iw,jw] : 1 <= jw <= m1, m2 && 1 <= iw <= n}
+
+# 
+# 
+# Exposed12i := R intersection complement domain f1i;
+# 
+# Exposed12i;
+
+{[In_1,In_2]: 1, m2+1 <= In_2 <= m1 && 1 <= In_1 <= n}
+
+# 
+# 
+# # SECOND GROUP - 3i
+# v3i := f3i / Exposed12i;
+#   # / is restrictRange
+# v3i;
+
+{[iw,jw] -> [iw,jw-1] : 2 <= low <= jw <= m1 && 1 <= iw <= n && m2 <= jw-2}
+
+# 
+# 
+# Exposed3i := R intersection complement domain f3i;
+# 
+# Exposed3i;
+
+{[In_1,In_2]: 1 <= In_1 <= n && 1 <= In_2 <= m1 && low <= 1} union
+ {[In_1,In_2]: 1 <= In_2 <= m1, low-1 && 1 <= In_1 <= n}
+
+# 
+# 
+# # THIRD GROUP - 1,2,3f (THERE ARE POSSIBLE OUTPUT DEPS BETWEEN THEM)
+# 
+# v1f := ( f1f / Exposed3i )
+# 	intersection complement ( f3i compose o13f )
+# 	intersection complement ( f3f compose o13f )
+# 	intersection complement ( f1i compose o11f )
+# 	intersection complement ( f1f compose o11f );
+# 
+# v1f;
+
+{[iw1a,jw1a] -> [ir,jr]  : FALSE }
+
+# 
+# 
+# # WE SHOULD BE ABLE TO DO v1f WITH SOME VALUE-BASED FLOW DD'S
+# 
+# v1f_val := ( f1f / Exposed3i )
+# 	intersection complement ( v3i compose o13f )
+# 	intersection complement ( f3f compose o13f )
+# 	intersection complement ( v1i compose o11f )
+# 	intersection complement ( f1f compose o11f );
+# 
+# v1f_val;
+
+{[iw1a,jw1a] -> [ir,jr]  : FALSE }
+
+# 
+# 
+# #
+# # The effects of loop-independent flow have been taken out already,
+# # so this should work.  But it does not.  Probably I am stupyd.
+# #
+# 
+# v1f_clever := ( f1f / Exposed3i )
+# 	intersection complement ( f3f compose o13f )
+# 	intersection complement ( f1f compose o11f );
+# 
+# v1f_clever;
+
+{[iw1a,jw1a] -> [iw1a+1,jw1a] : 1 <= jw1a <= m2, m1 && 1 <= iw1a < n && low <= 1} union
+ {[iw1a,jw1a] -> [iw1a+1,jw1a] : 1 <= jw1a <= m2, m1, low-1 && 1 <= iw1a < n}
+
+# 
+# 
+# #
+# # NOW CHECK FOR EQUIVALENCES - THESE SHOULD BE TRUE
+# #
+# 
+# v1f subset v1f_val;
+
+True
+# 
+# v1f_val subset v1f;
+
+True
+# 
+# # v1f subset v1f_clever;
+# # v1f_clever subset v1f;
diff --git a/omega/examples/old_test/emit b/omega/examples/old_test/emit
new file mode 100644
index 0000000..3b33a98
--- /dev/null
+++ b/omega/examples/old_test/emit
@@ -0,0 +1,38 @@
+#
+# A problem that arises during the analysis of emit.t
+# We are trying to find the dependences to the read 58: rhs(i)
+# There are memory-based deps from the write 58: rhs(j)
+# 			       and the write 50: rhs(i0+k)
+# Due to some screwy stuff, we do not realize that the first is
+# a partial cover for the second, and do the real kill test.
+#
+# line_49_expr is nwall(l)
+#
+
+symbolic matdim_E, i0_1(1), line_49_expr(1);
+
+is_58 := { [i,j] : i+1 <= j <= matdim_E && 1 <= i <= matdim_E };
+is_50 := { [l,k] : 1 <= k <= line_49_expr(Set) && 1 <= l <= 5 };
+
+plus_plus := { [i,j] -> [i',j'] : i < i' && j < j' };
+plus_zero := { [i,j] -> [i',j'] : i < i' && j = j' };
+plus_star := { [i,j] -> [i',j'] : i < i' };
+
+mo_50_50 := (is_50 * is_50) intersection plus_star
+		intersection { [l1,k1]->[l2,k2] : i0_1(In)+k1 = i0_1(Out)+k2 };
+mo_50_58 := (is_50 * is_58)
+		intersection { [l,k] -> [i,j] : i0_1(In)+k = j };
+mo_58_58 := (is_58 * is_58) intersection plus_zero
+		intersection { [i,j] -> [i',j'] : j = j' };
+
+mf_58_58 := (is_58 * is_58) intersection plus_plus
+		intersection { [iw,jw] -> [ir,jr] : jw = ir };
+mf_50_58 := (is_50 * is_58)
+		intersection { [l,k] -> [i,j] : i0_1(In)+k = i };
+
+vf_58_58 := mf_58_58 - (mf_58_58 compose mo_58_58);
+vf_58_58;
+
+vf_50_58 := mf_50_58 intersection ( complement (mf_58_58 compose mo_50_58) )
+		     intersection ( complement (mf_50_58 compose mo_50_50) );
+vf_50_58;
diff --git a/omega/examples/old_test/emit.oc-rt b/omega/examples/old_test/emit.oc-rt
new file mode 100644
index 0000000..1bf7d6c
--- /dev/null
+++ b/omega/examples/old_test/emit.oc-rt
@@ -0,0 +1,61 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #
+# # A problem that arises during the analysis of emit.t
+# # We are trying to find the dependences to the read 58: rhs(i)
+# # There are memory-based deps from the write 58: rhs(j)
+# # 			       and the write 50: rhs(i0+k)
+# # Due to some screwy stuff, we do not realize that the first is
+# # a partial cover for the second, and do the real kill test.
+# #
+# # line_49_expr is nwall(l)
+# #
+# 
+# Symbolic matdim_E, i0_1(1), line_49_expr(1);
+# 
+# 
+# is_58 := { [i,j] : i+1 <= j <= matdim_E && 1 <= i <= matdim_E };
+# 
+# is_50 := { [l,k] : 1 <= k <= line_49_expr(Set) && 1 <= l <= 5 };
+# 
+# 
+# plus_plus := { [i,j] -> [i',j'] : i < i' && j < j' };
+# 
+# plus_zero := { [i,j] -> [i',j'] : i < i' && j = j' };
+# 
+# plus_star := { [i,j] -> [i',j'] : i < i' };
+# 
+# 
+# mo_50_50 := (is_50 * is_50) intersection plus_star
+# 		intersection { [l1,k1]->[l2,k2] : i0_1(In)+k1 = i0_1(Out)+k2 };
+# 
+# mo_50_58 := (is_50 * is_58)
+# 		intersection { [l,k] -> [i,j] : i0_1(In)+k = j };
+# 
+# mo_58_58 := (is_58 * is_58) intersection plus_zero
+# 		intersection { [i,j] -> [i',j'] : j = j' };
+# 
+# 
+# mf_58_58 := (is_58 * is_58) intersection plus_plus
+# 		intersection { [iw,jw] -> [ir,jr] : jw = ir };
+# 
+# mf_50_58 := (is_50 * is_58)
+# 		intersection { [l,k] -> [i,j] : i0_1(In)+k = i };
+# 
+# 
+# vf_58_58 := mf_58_58 - (mf_58_58 compose mo_58_58);
+# 
+# vf_58_58;
+
+{[i,i+1] -> [i+1,Out_2] : 1 <= i <= Out_2-2 && Out_2 <= matdim_E}
+
+# 
+# 
+# vf_50_58 := mf_50_58 intersection ( complement (mf_58_58 compose mo_50_58) )
+# 		     intersection ( complement (mf_50_58 compose mo_50_50) );
+# 
+# vf_50_58;
+
+{[In_1,-i0_1(In_1)+1] -> [1,j] : -line_49_expr(In_1)+1 <= i0_1(In_1) <= 0 && 1 <= In_1 <= 4 && 2 <= j <= matdim_E && UNKNOWN} union
+ {[In_1,-i0_1(In_1)+1] -> [1,j] : In_1 = 5 && -line_49_expr(In_1)+1 <= i0_1(In_1) <= 0 && 2 <= j <= matdim_E}
+
+# 
diff --git a/omega/examples/old_test/example1 b/omega/examples/old_test/example1
new file mode 100644
index 0000000..0721b20
--- /dev/null
+++ b/omega/examples/old_test/example1
@@ -0,0 +1,4 @@
+foo := {[In_1,In_2] -> [i,j] : exists ( alpha : In_2+2i = 1 && 2In_1+In_2 = 3+4j && In_2+20alpha = 5+8j && -199 <= In_2 <= -2j-5 && 1 <= j)};
+example foo;
+
+
diff --git a/omega/examples/old_test/example1.oc-rt b/omega/examples/old_test/example1.oc-rt
new file mode 100644
index 0000000..89b2e0a
--- /dev/null
+++ b/omega/examples/old_test/example1.oc-rt
@@ -0,0 +1,10 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# foo := {[In_1,In_2] -> [i,j] : Exists ( alpha : In_2+2i = 1 && 2In_1+In_2 = 3+4j && In_2+20alpha = 5+8j && -199 <= In_2 <= -2j-5 && 1 <= j)};
+# 
+# example foo;
+
+{[7,-7] -> [4,1] }
+
+# 
+# 
+# 
diff --git a/omega/examples/old_test/farkas b/omega/examples/old_test/farkas
new file mode 100644
index 0000000..ce754fc
--- /dev/null
+++ b/omega/examples/old_test/farkas
@@ -0,0 +1,8 @@
+
+symbolic n;
+symbolic c;
+
+R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+
+ac := farkas R;
+ac;
diff --git a/omega/examples/old_test/farkas.oc-rt b/omega/examples/old_test/farkas.oc-rt
new file mode 100644
index 0000000..cd52e5e
--- /dev/null
+++ b/omega/examples/old_test/farkas.oc-rt
@@ -0,0 +1,17 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# symbolic n;
+# 
+# symbolic c;
+# 
+# 
+# R := {[i,j] : 1 <= i <= 10 && 1 <= j <= n};
+# 
+# 
+# ac := farkas R;
+# 
+# ac;
+
+{[i,j]: 0 <= constantTerm+n+i+j && 0 <= constantTerm+n+10i+j && 0 <= n+j && 0 <= n}
+
+# 
diff --git a/omega/examples/old_test/farkas2 b/omega/examples/old_test/farkas2
new file mode 100644
index 0000000..2781423
--- /dev/null
+++ b/omega/examples/old_test/farkas2
@@ -0,0 +1,6 @@
+
+R := {[1:10,1:10]} union {[5:15,11:20]};
+R;
+f := farkas R;
+f;
+Hull R;
diff --git a/omega/examples/old_test/farkas2.oc-rt b/omega/examples/old_test/farkas2.oc-rt
new file mode 100644
index 0000000..22d43cc
--- /dev/null
+++ b/omega/examples/old_test/farkas2.oc-rt
@@ -0,0 +1,22 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# R := {[1:10,1:10]} union {[5:15,11:20]};
+# 
+# R;
+
+{[In_1,In_2]: 1 <= In_1 <= 10 && 1 <= In_2 <= 10} union
+ {[In_1,In_2]: 5 <= In_1 <= 15 && 11 <= In_2 <= 20}
+
+# 
+# f := farkas R;
+# 
+# f;
+
+{[In_1,In_2]: 0 <= constantTerm+10In_1+In_2 && 0 <= constantTerm+In_1+10In_2 && 0 <= constantTerm+15In_1+20In_2 && 0 <= constantTerm+In_1+In_2 && 0 <= constantTerm+15In_1+11In_2 && 0 <= constantTerm+5In_1+20In_2}
+
+# 
+# Hull R;
+
+{[In_1,In_2]: 1, 2In_1-19 <= In_2 <= 20 && 1 <= In_1 <= 15 && 2In_2 <= 15+5In_1}
+
+# 
diff --git a/omega/examples/old_test/farkas3 b/omega/examples/old_test/farkas3
new file mode 100644
index 0000000..8adec2e
--- /dev/null
+++ b/omega/examples/old_test/farkas3
@@ -0,0 +1,3 @@
+
+R := {[1:10,1:10,1:10,1:10]};
+AffineHull R;
diff --git a/omega/examples/old_test/farkas3.oc-rt b/omega/examples/old_test/farkas3.oc-rt
new file mode 100644
index 0000000..095cb54
--- /dev/null
+++ b/omega/examples/old_test/farkas3.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# R := {[1:10,1:10,1:10,1:10]};
+# 
+# AffineHull R;
+
+{[In_1,In_2,In_3,In_4]}
+
+# 
diff --git a/omega/examples/old_test/fc1 b/omega/examples/old_test/fc1
new file mode 100644
index 0000000..66a9e90
--- /dev/null
+++ b/omega/examples/old_test/fc1
@@ -0,0 +1,23 @@
+symbolic n;
+
+I1 := {[i,j] : 1 <= i < j <= n};
+I2 := {[i,j,k] : 1 <= i < j,k <= n};
+I3 := {[i] : 1 <= i <= n};
+I4 := {[i,j] : 1 <= j < i <= n};
+I5 := {[i] : 1 <= i <= n};
+
+T1 := {[i,j] -> [i-1,0,n-i,n-j]};
+T2 := {[i,j,k] -> [i-1,1,n-i,n-j]};
+T3 := {[i] -> [0,0,0,i]};
+T4 := {[i,j] -> [j+n-1,0,i,j]};
+T5 := {[i] -> [i+n-2,1,0,0]};
+
+T1(I1);
+T2(I2);
+T3(I3);
+T4(I4);
+T5(I5);
+codegen T1:I1,T2:I2;
+codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+codegen 2 T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+
diff --git a/omega/examples/old_test/fc1.oc-rt b/omega/examples/old_test/fc1.oc-rt
new file mode 100644
index 0000000..8075f2d
--- /dev/null
+++ b/omega/examples/old_test/fc1.oc-rt
@@ -0,0 +1,89 @@
+>>> symbolic n;
+>>> 
+>>> I1 := {[i,j] : 1 <= i < j <= n};
+>>> I2 := {[i,j,k] : 1 <= i < j,k <= n};
+>>> I3 := {[i] : 1 <= i <= n};
+>>> I4 := {[i,j] : 1 <= j < i <= n};
+>>> I5 := {[i] : 1 <= i <= n};
+>>> 
+>>> T1 := {[i,j] -> [i-1,0,n-i,n-j]};
+>>> T2 := {[i,j,k] -> [i-1,1,n-i,n-j]};
+>>> T3 := {[i] -> [0,0,0,i]};
+>>> T4 := {[i,j] -> [j+n-1,0,i,j]};
+>>> T5 := {[i] -> [i+n-2,1,0,0]};
+>>> 
+>>> T1(I1);
+{[In_1,0,n-In_1-1,In_4]: 0 <= In_1 && 2+In_1+In_4 <= n && 0 <= In_4}
+>>> T2(I2);
+{[In_1,1,n-In_1-1,In_4]: 0 <= In_1 && 2+In_1+In_4 <= n && 0 <= In_4}
+>>> T3(I3);
+{[0,0,0,i]: 1 <= i <= n}
+>>> T4(I4);
+{[In_1,0,i,In_1-n+1]: i <= n <= In_1 && 2+In_1 <= n+i}
+>>> T5(I5);
+{[In_1,1,0,0]: n-1 <= In_1 <= 2n-2}
+>>> codegen T1:I1,T2:I2;
+for(t1 = 0; t1 <= n-2; t1++) {
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s1(t1+1,n-t4);
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s2(t1+1,n-t4,N/A);
+  }
+}
+
+>>> codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+for(t1 = 0; t1 <= 2*n-2; t1++) {
+  if (t1 <= 0) {
+    for(t4 = 1; t4 <= n; t4++) {
+      s3(t4);
+    }
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s1(t1+1,n-t4);
+  }
+  if (t1 >= n) {
+    for(t3 = -n+t1+2; t3 <= n; t3++) {
+      s4(t3,t1-n+1);
+    }
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s2(t1+1,n-t4,N/A);
+  }
+  if (t1 >= n-1) {
+    s5(-n+t1+2);
+  }
+}
+
+>>> codegen 2 T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+for(t4 = 1; t4 <= n; t4++) {
+  s3(t4);
+}
+for(t4 = 0; t4 <= n-2; t4++) {
+  s1(1,-t4+n);
+}
+for(t4 = 0; t4 <= n-2; t4++) {
+  s2(1,-t4+n,N/A);
+}
+if (n == 1) {
+  s5(-n+2);
+}
+for(t1 = 1; t1 <= n-2; t1++) {
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s1(t1+1,n-t4);
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s2(t1+1,n-t4,N/A);
+  }
+}
+if (n >= 2) {
+  s5(1);
+}
+for(t1 = max(n,1); t1 <= 2*n-2; t1++) {
+  for(t3 = t1-n+2; t3 <= n; t3++) {
+    s4(t3,t1-n+1);
+  }
+  s5(-n+t1+2);
+}
+
+
diff --git a/omega/examples/old_test/fc2 b/omega/examples/old_test/fc2
new file mode 100644
index 0000000..b195d72
--- /dev/null
+++ b/omega/examples/old_test/fc2
@@ -0,0 +1,29 @@
+symbolic n;
+
+I1 := {[i,j] : 1 <= i < j <= n};
+I2 := {[i,j,k] : 1 <= i < j,k <= n};
+I3 := {[i] : 1 <= i <= n};
+I4 := {[i,j] : 1 <= j < i <= n};
+I5 := {[i] : 1 <= i <= n};
+
+T1 := {[i,j] -> [i-1,0,n-i,n-j]};
+T2 := {[i,j,k] -> [i-1,1,n-i,n-j]};
+T3 := {[i] -> [0,0,0,i]};
+T4 := {[i,j] -> [j+n-1,0,i,j]};
+T5 := {[i] -> [i+n-2,1,0,0]};
+
+first := {[i,*,*,*] -> [i]};
+
+first(T1(I1));
+first(T2(I2));
+first(T3(I3));
+first(T4(I4));
+first(T5(I5));
+T1(I1);
+T2(I2);
+T3(I3);
+T4(I4);
+T5(I5);
+codegen T1:I1,T2:I2;
+codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+
diff --git a/omega/examples/old_test/fc2.oc-rt b/omega/examples/old_test/fc2.oc-rt
new file mode 100644
index 0000000..742929e
--- /dev/null
+++ b/omega/examples/old_test/fc2.oc-rt
@@ -0,0 +1,115 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# 
+# I1 := {[i,j] : 1 <= i < j <= n};
+# 
+# I2 := {[i,j,k] : 1 <= i < j,k <= n};
+# 
+# I3 := {[i] : 1 <= i <= n};
+# 
+# I4 := {[i,j] : 1 <= j < i <= n};
+# 
+# I5 := {[i] : 1 <= i <= n};
+# 
+# 
+# T1 := {[i,j] -> [i-1,0,n-i,n-j]};
+# 
+# T2 := {[i,j,k] -> [i-1,1,n-i,n-j]};
+# 
+# T3 := {[i] -> [0,0,0,i]};
+# 
+# T4 := {[i,j] -> [j+n-1,0,i,j]};
+# 
+# T5 := {[i] -> [i+n-2,1,0,0]};
+# 
+# 
+# first := {[i,*,*,*] -> [i]};
+# 
+# 
+# first(T1(I1));
+
+{[i]: 0 <= i <= n-2}
+
+# 
+# first(T2(I2));
+
+{[i]: 0 <= i <= n-2}
+
+# 
+# first(T3(I3));
+
+{[0]: 1 <= n}
+
+# 
+# first(T4(I4));
+
+{[i]: n <= i <= 2n-2}
+
+# 
+# first(T5(I5));
+
+{[i]: n-1 <= i <= 2n-2}
+
+# 
+# T1(I1);
+
+{[In_1,0,n-In_1-1,In_4]: 0 <= In_1 && 2+In_1+In_4 <= n && 0 <= In_4}
+
+# 
+# T2(I2);
+
+{[In_1,1,n-In_1-1,In_4]: 0 <= In_1 && 2+In_1+In_4 <= n && 0 <= In_4}
+
+# 
+# T3(I3);
+
+{[0,0,0,i]: 1 <= i <= n}
+
+# 
+# T4(I4);
+
+{[In_1,0,i,In_1-n+1]: i <= n <= In_1 && 2+In_1 <= n+i}
+
+# 
+# T5(I5);
+
+{[In_1,1,0,0]: n-1 <= In_1 <= 2n-2}
+
+# 
+# codegen T1:I1,T2:I2;
+for(t1 = 0; t1 <= n-2; t1++) {
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s1(t1+1,n-t4);
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s2(t1+1,n-t4);
+  }
+}
+
+# 
+# codegen T1:I1,T2:I2,T3:I3,T4:I4,T5:I5;
+for(t1 = 0; t1 <= 2*n-2; t1++) {
+  if (t1 <= 0) {
+    for(t4 = 1; t4 <= n; t4++) {
+      s3(t4);
+    }
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s1(t1+1,n-t4);
+  }
+  if (t1 >= n) {
+    for(t3 = t1-n+2; t3 <= n; t3++) {
+      s4(t3,t1-n+1);
+    }
+  }
+  for(t4 = 0; t4 <= -t1+n-2; t4++) {
+    s2(t1+1,n-t4);
+  }
+  if (t1 >= n-1) {
+    s5(t1-n+2);
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/foo b/omega/examples/old_test/foo
new file mode 100644
index 0000000..1a5ef46
--- /dev/null
+++ b/omega/examples/old_test/foo
@@ -0,0 +1,13 @@
+
+R := {[t,s] -> [t+2,s+2] : t <= s} union
+ {[t,s] -> [t+4,s+4] : t <= s} union
+ {[t,s] -> [t+3,s+3] : t <= s} union
+ {[t,s] -> [t',s-t+t'] : t <= s, t'-5} union
+ {[t,s] -> [t+1,s+1] : t <= s} union
+ {[t,s] -> [t',s-t+t'] : t <= s-1, t'-2};
+R;
+difference R;
+Hull difference R;
+
+Hull R;
+
diff --git a/omega/examples/old_test/foo.oc-rt b/omega/examples/old_test/foo.oc-rt
new file mode 100644
index 0000000..3f7f5a9
--- /dev/null
+++ b/omega/examples/old_test/foo.oc-rt
@@ -0,0 +1,37 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# R := {[t,s] -> [t+2,s+2] : t <= s} union
+#  {[t,s] -> [t+4,s+4] : t <= s} union
+#  {[t,s] -> [t+3,s+3] : t <= s} union
+#  {[t,s] -> [t',s-t+t'] : t <= s, t'-5} union
+#  {[t,s] -> [t+1,s+1] : t <= s} union
+#  {[t,s] -> [t',s-t+t'] : t <= s-1, t'-2};
+# 
+# R;
+
+{[t,s] -> [t+2,s+2] : t <= s} union
+ {[t,s] -> [t+4,s+4] : t <= s} union
+ {[t,s] -> [t+3,s+3] : t <= s} union
+ {[t,s] -> [t',s-t+t'] : t <= s, t'-5} union
+ {[t,s] -> [t+1,s+1] : t <= s} union
+ {[t,s] -> [t',s-t+t'] : t <= s-1, t'-2}
+
+# 
+# difference R;
+
+{[1,1]} union
+ {[In_1,In_1]: 2 <= In_1}
+
+# 
+# hull difference R;
+
+{[In_1,In_1]: 1 <= In_1}
+
+# 
+# 
+# Hull R;
+
+{[t,s] -> [t',s-t+t'] : t <= s, t'-1}
+
+# 
+# 
diff --git a/omega/examples/old_test/foo2 b/omega/examples/old_test/foo2
new file mode 100644
index 0000000..69a63da
--- /dev/null
+++ b/omega/examples/old_test/foo2
@@ -0,0 +1,3 @@
+Hull( {[1,1]} union
+ {[In_1,In_1]: 2 <= In_1});
+
diff --git a/omega/examples/old_test/foo2.oc-rt b/omega/examples/old_test/foo2.oc-rt
new file mode 100644
index 0000000..c8f0209
--- /dev/null
+++ b/omega/examples/old_test/foo2.oc-rt
@@ -0,0 +1,8 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# hull( {[1,1]} union
+#  {[In_1,In_1]: 2 <= In_1});
+
+{[In_1,In_1]: 1 <= In_1}
+
+# 
+# 
diff --git a/omega/examples/old_test/foo6 b/omega/examples/old_test/foo6
new file mode 100644
index 0000000..0b702cd
--- /dev/null
+++ b/omega/examples/old_test/foo6
@@ -0,0 +1 @@
+approximate  {[i,j] : exists (a,b : a,b >= 0  && i = -201a-3b && j = 103a+200b)};
diff --git a/omega/examples/old_test/foo6.oc-rt b/omega/examples/old_test/foo6.oc-rt
new file mode 100644
index 0000000..aeb1b67
--- /dev/null
+++ b/omega/examples/old_test/foo6.oc-rt
@@ -0,0 +1,6 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# approximate  {[i,j] : exists (a,b : a,b >= 0  && i = -201a-3b && j = 103a+200b)};
+
+{[i,j]: 200i+3j <= 0 && 0 <= 103i+201j}
+
+# 
diff --git a/omega/examples/old_test/forall b/omega/examples/old_test/forall
new file mode 100644
index 0000000..8b1de0a
--- /dev/null
+++ b/omega/examples/old_test/forall
@@ -0,0 +1,21 @@
+symbolic n,m,B;
+{ [max_diff] : 
+    forall (m : 
+	(not exists (z1,z2 : 0<=z1<n && z1<=z2<m+z1 && z2 = m))
+	or 
+	(forall (minX,minY :
+            (not (forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
+                  exists (x1,x2 :  0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
+                  forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
+                  exists (y1,y2 :  0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY)))
+            or 
+	    (minY-minX <= max_diff)))) &&
+    exists (m,z1,z2,minX,minY :
+	0<=z1<n && z1<=z2<=m+z1 && z2 = m &&
+        forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
+        exists (x1,x2 :  0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
+        forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
+        exists (y1,y2 :  0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY) &&
+	minY-minX = max_diff)};
+
+
diff --git a/omega/examples/old_test/forall.oc-rt b/omega/examples/old_test/forall.oc-rt
new file mode 100644
index 0000000..13f78fa
--- /dev/null
+++ b/omega/examples/old_test/forall.oc-rt
@@ -0,0 +1,28 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m,B;
+# 
+# { [max_diff] : 
+#     forall (m : 
+# 	(not exists (z1,z2 : 0<=z1<n && z1<=z2<m+z1 && z2 = m))
+# 	or 
+# 	(forall (minX,minY :
+#             (not (forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
+#                   exists (x1,x2 :  0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
+#                   forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
+#                   exists (y1,y2 :  0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY)))
+#             or 
+# 	    (minY-minX <= max_diff)))) &&
+#     exists (m,z1,z2,minX,minY :
+# 	0<=z1<n && z1<=z2<=m+z1 && z2 = m &&
+#         forall (x1,x2 : (not (0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m)) or (x1+x2 >= minX)) &&
+#         exists (x1,x2 :  0<=x1<n && x1<=x2<m+x1 && m-B+1 <= x2 <= m && x1+x2 = minX) &&
+#         forall (y1,y2 : (not (0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B)) or (y1+y2 >= minY)) &&
+#         exists (y1,y2 :  0<=y1<n && y1<=y2<=m+y1 && m+1 <= y2 <= m+B && y1+y2 = minY) &&
+# 	minY-minX = max_diff)};
+
+{[B+1]: 2 <= B && 2 <= n} union
+ {[1]: B = 1 && 2 <= n}
+
+# 
+# 
+# 
diff --git a/omega/examples/old_test/gc b/omega/examples/old_test/gc
new file mode 100644
index 0000000..932f595
--- /dev/null
+++ b/omega/examples/old_test/gc
@@ -0,0 +1,6 @@
+A := {[i] : 1 <= i <= 8};
+b := {[i] : exists (t : i=2t+1 & 0<=t<=3)};
+c := {[i] : exists (t : i=2t+2 & 0<=t<=3)};
+d := A - b;
+d;
+codegen d;
diff --git a/omega/examples/old_test/gc.oc-rt b/omega/examples/old_test/gc.oc-rt
new file mode 100644
index 0000000..6d92fa9
--- /dev/null
+++ b/omega/examples/old_test/gc.oc-rt
@@ -0,0 +1,20 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# A := {[i] : 1 <= i <= 8};
+# 
+# b := {[i] : exists (t : i=2t+1 & 0<=t<=3)};
+# 
+# c := {[i] : exists (t : i=2t+2 & 0<=t<=3)};
+# 
+# d := A - b;
+# 
+# d;
+
+{[i]: Exists ( alpha : 0 = i+2alpha && 2 <= i <= 8)}
+
+# 
+# codegen d;
+for(t1 = 2; t1 <= 8; t1 += 2) {
+  s1(t1);
+}
+
+# 
diff --git a/omega/examples/old_test/ge b/omega/examples/old_test/ge
new file mode 100644
index 0000000..e8e9e1f
--- /dev/null
+++ b/omega/examples/old_test/ge
@@ -0,0 +1,9 @@
+symbolic n;
+I1 := {[k,i] : 1 <= k < i <= n };
+I2 := {[k,i,j] : 1 <= k < i,j <= n };
+T1 := {[k,i] -> [i,k,1,0]};
+T2 := {[k,i,j] -> [i,j,0,k]};
+T1(I1);
+T2(I2);
+codegen T1:I1,T2:I2;
+codegen 2 T1:I1,T2:I2;
diff --git a/omega/examples/old_test/ge.oc-rt b/omega/examples/old_test/ge.oc-rt
new file mode 100644
index 0000000..1006fe5
--- /dev/null
+++ b/omega/examples/old_test/ge.oc-rt
@@ -0,0 +1,38 @@
+>>> symbolic n;
+>>> I1 := {[k,i] : 1 <= k < i <= n };
+>>> I2 := {[k,i,j] : 1 <= k < i,j <= n };
+>>> T1 := {[k,i] -> [i,k,1,0]};
+>>> T2 := {[k,i,j] -> [i,j,0,k]};
+>>> T1(I1);
+{[i,k,1,0]: 1 <= k < i <= n}
+>>> T2(I2);
+{[i,j,0,k]: 1 <= k < i,j <= n}
+>>> codegen T1:I1,T2:I2;
+for(t1 = 2; t1 <= n; t1++) {
+  for(t2 = 1; t2 <= n; t2++) {
+    for(t4 = 1; t4 <= min(t1-1,t2-1); t4++) {
+      s2(t4,t1,t2);
+    }
+    if (t2 <= t1-1) {
+      s1(t2,t1);
+    }
+  }
+}
+
+>>> codegen 2 T1:I1,T2:I2;
+for(t1 = 2; t1 <= n; t1++) {
+  s1(1,t1);
+  for(t2 = 2; t2 <= t1-1; t2++) {
+    for(t4 = 1; t4 <= t2-1; t4++) {
+      s2(t4,t1,t2);
+    }
+    s1(t2,t1);
+  }
+  for(t2 = t1; t2 <= n; t2++) {
+    for(t4 = 1; t4 <= t1-1; t4++) {
+      s2(t4,t1,t2);
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/givens2 b/omega/examples/old_test/givens2
new file mode 100644
index 0000000..0c6f634
--- /dev/null
+++ b/omega/examples/old_test/givens2
@@ -0,0 +1,15 @@
+#
+# an example from a slightly defective dependence relation for givens2.t
+#
+
+symbolic n, line6exp(2) ;
+
+{ [i,j,k] -> [i',j',k'] :
+       1 <=  i <= n &&
+       1 <= i' <= n &&
+  i+1 <=  j <= n &&
+ i'+1 <= j' <= n &&
+    i <=  k <= n &&
+   i' <= k' <= n  and
+ ( 1 <= line6exp(i,j) or line6exp(i,j) <= -1 ) and
+ ( 1 <= line6exp(i',j') or line6exp(i',j') <= -1 ) };
diff --git a/omega/examples/old_test/givens2.oc-rt b/omega/examples/old_test/givens2.oc-rt
new file mode 100644
index 0000000..9dfac42
--- /dev/null
+++ b/omega/examples/old_test/givens2.oc-rt
@@ -0,0 +1,38 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #
+# # an example from a slightly defective dependence relation for givens2.t
+# #
+# 
+# Symbolic n, line6exp(2) ;
+# 
+# 
+# { [i,j,k] -> [i',j',k'] :
+#        1 <=  i <= n &&
+#        1 <= i' <= n &&
+#   i+1 <=  j <= n &&
+#  i'+1 <= j' <= n &&
+#     i <=  k <= n &&
+#    i' <= k' <= n  and
+#  ( 1 <= line6exp(i,j) or line6exp(i,j) <= -1 ) and
+#  ( 1 <= line6exp(i',j') or line6exp(i',j') <= -1 ) };
+
+{[i,j,k] -> [i,j,k'] : 1 <= i <= k', j-1, k && j <= n && k <= n && k' <= n && 1 <= line6exp(i,j)} union
+ {[i,j,k] -> [i,j,k'] : 1 <= i <= k', j-1, k && line6exp(i,j) <= -1 && j <= n && k <= n && k' <= n} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i' < i < j <= n && i <= k <= n && i' < j' <= n && i' <= k' <= n && 1 <= line6exp(i,j) && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i < i' < j' <= n && i < j <= n && i <= k <= n && i' <= k' <= n && 1 <= line6exp(i,j) && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j' < j <= n && i <= k,k' <= n && 1 <= line6exp(i,j) && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j < j' <= n && i <= k,k' <= n && 1 <= line6exp(i,j) && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i' < i < j <= n && i <= k <= n && i' < j' <= n && i' <= k' <= n && line6exp(i,j) <= -1 && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i < i' < j' <= n && i < j <= n && i <= k <= n && i' <= k' <= n && line6exp(i,j) <= -1 && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j' < j <= n && i <= k,k' <= n && line6exp(i,j) <= -1 && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j < j' <= n && i <= k,k' <= n && line6exp(i,j) <= -1 && 1 <= line6exp(i',j')} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i' < i < j <= n && i <= k <= n && i' < j' <= n && i' <= k' <= n && line6exp(i',j') <= -1 && 1 <= line6exp(i,j)} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i < i' < j' <= n && i < j <= n && i <= k <= n && i' <= k' <= n && line6exp(i',j') <= -1 && 1 <= line6exp(i,j)} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j' < j <= n && i <= k,k' <= n && line6exp(i',j') <= -1 && 1 <= line6exp(i,j)} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j < j' <= n && i <= k,k' <= n && line6exp(i',j') <= -1 && 1 <= line6exp(i,j)} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i' < i < j <= n && i <= k <= n && i' < j' <= n && i' <= k' <= n && line6exp(i,j) <= -1 && line6exp(i',j') <= -1} union
+ {[i,j,k] -> [i',j',k'] : 1 <= i < i' < j' <= n && i < j <= n && i <= k <= n && i' <= k' <= n && line6exp(i,j) <= -1 && line6exp(i',j') <= -1} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j' < j <= n && i <= k,k' <= n && line6exp(i',j') <= -1 && line6exp(i,j) <= -1} union
+ {[i,j,k] -> [i',j',k'] : i' = i && 1 <= i < j < j' <= n && i <= k,k' <= n && line6exp(i',j') <= -1 && line6exp(i,j) <= -1}
+
+# 
diff --git a/omega/examples/old_test/guard1 b/omega/examples/old_test/guard1
new file mode 100644
index 0000000..0496d3b
--- /dev/null
+++ b/omega/examples/old_test/guard1
@@ -0,0 +1,11 @@
+symbolic n,m;
+incomingKnown := { [i1,i2] : exists ( alpha : i1+3alpha = 1+i2 ) && 
+                   i1 = n && i2 = m};
+
+
+codegen incomingKnown;
+incomingKnown := { [i1,i2] : exists ( alpha : i1+2alpha = 1+i2 ) &&
+                   i1 = n && i2 = m};
+
+
+codegen incomingKnown;
diff --git a/omega/examples/old_test/guard1.oc-rt b/omega/examples/old_test/guard1.oc-rt
new file mode 100644
index 0000000..db4b780
--- /dev/null
+++ b/omega/examples/old_test/guard1.oc-rt
@@ -0,0 +1,25 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# incomingKnown := { [i1,i2] : Exists ( alpha : i1+3alpha = 1+i2 ) && 
+#                    i1 = n && i2 = m};
+# 
+# 
+# 
+# codegen incomingKnown;
+if (intMod(-n+m+1,3) == 0) {
+  s1(n,m);
+}
+
+# 
+# incomingKnown := { [i1,i2] : Exists ( alpha : i1+2alpha = 1+i2 ) &&
+#                    i1 = n && i2 = m};
+# 
+# 
+# 
+# codegen incomingKnown;
+if (intMod(n+m+1,2) == 0) {
+  s1(n,m);
+}
+
+# 
diff --git a/omega/examples/old_test/hull1 b/omega/examples/old_test/hull1
new file mode 100644
index 0000000..afb18a2
--- /dev/null
+++ b/omega/examples/old_test/hull1
@@ -0,0 +1,4 @@
+R := {[1:10,1:10]} union {[-10:-1,-10:-1]} union
+	{[x,y] : -10 <= x,y <= 10 && -10 <= x-y <= 10};
+R;
+Hull R;
diff --git a/omega/examples/old_test/hull1.oc-rt b/omega/examples/old_test/hull1.oc-rt
new file mode 100644
index 0000000..f8973fa
--- /dev/null
+++ b/omega/examples/old_test/hull1.oc-rt
@@ -0,0 +1,14 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := {[1:10,1:10]} union {[-10:-1,-10:-1]} union
+# 	{[x,y] : -10 <= x,y <= 10 && -10 <= x-y <= 10};
+# 
+# R;
+
+{[x,y]: -10, y-10 <= x <= 10, y+10 && -10 <= y <= 10}
+
+# 
+# Hull R;
+
+{[x,y]: -10, y-10 <= x <= 10, y+10 && -10 <= y <= 10}
+
+# 
diff --git a/omega/examples/old_test/hull2 b/omega/examples/old_test/hull2
new file mode 100644
index 0000000..69214f8
--- /dev/null
+++ b/omega/examples/old_test/hull2
@@ -0,0 +1,3 @@
+R := {[1,1]} union {[3,3]};
+R;
+Hull R;
diff --git a/omega/examples/old_test/hull2.oc-rt b/omega/examples/old_test/hull2.oc-rt
new file mode 100644
index 0000000..f5e2e94
--- /dev/null
+++ b/omega/examples/old_test/hull2.oc-rt
@@ -0,0 +1,14 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := {[1,1]} union {[3,3]};
+# 
+# R;
+
+{[1,1]} union
+ {[3,3]}
+
+# 
+# hull R;
+
+{[In_1,In_1]: 1 <= In_1 <= 3}
+
+# 
diff --git a/omega/examples/old_test/hull3 b/omega/examples/old_test/hull3
new file mode 100644
index 0000000..22e0324
--- /dev/null
+++ b/omega/examples/old_test/hull3
@@ -0,0 +1,17 @@
+
+symbolic n;
+
+s1:={[t1, 0, 0]:1 <= t1 && 64 * t1 <= n};
+
+s2 := {[t1, t2, 0]: 1 <= t1 && 64 * t1 <= n && t2 = t1};
+
+s3 := {[t1, 0, t3]: 1 <= t1 && 64 * t1 <= n && t3 = t1};
+
+s := (s1  union s2 union s3);
+
+s;
+h := Hull s;
+
+h;
+
+h - s;
diff --git a/omega/examples/old_test/hull3.oc-rt b/omega/examples/old_test/hull3.oc-rt
new file mode 100644
index 0000000..c094288
--- /dev/null
+++ b/omega/examples/old_test/hull3.oc-rt
@@ -0,0 +1,40 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# symbolic n;
+# 
+# 
+# s1:={[t1, 0, 0]:1 <= t1 && 64 * t1 <= n};
+# 
+# 
+# s2 := {[t1, t2, 0]: 1 <= t1 && 64 * t1 <= n && t2 = t1};
+# 
+# 
+# s3 := {[t1, 0, t3]: 1 <= t1 && 64 * t1 <= n && t3 = t1};
+# 
+# 
+# s := (s1  union s2 union s3);
+# 
+# 
+# s;
+
+{[t1,0,0]: 1 <= t1 && 64t1 <= n} union
+ {[t1,t1,0]: 1 <= t1 && 64t1 <= n} union
+ {[t1,0,t1]: 1 <= t1 && 64t1 <= n}
+
+# 
+# h := hull s;
+# 
+# 
+# h;
+
+{[t1,t2,t3]: 0 <= t3 && 0 <= t2 && 64t1 <= n && 1 <= t1 && t2+t3 <= t1}
+
+# 
+# 
+# h - s;
+
+{[t1,t2,t3]: 1 <= t3 && 1 <= t2 && 64t1 <= n && t2+t3 <= t1} union
+ {[t1,t2,0]: 1 <= t2 < t1 && 64t1 <= n} union
+ {[t1,0,t3]: 1 <= t3 < t1 && 64t1 <= n}
+
+# 
diff --git a/omega/examples/old_test/ip1 b/omega/examples/old_test/ip1
new file mode 100644
index 0000000..b8cd8c4
--- /dev/null
+++ b/omega/examples/old_test/ip1
@@ -0,0 +1,13 @@
+time {[a,b,c,d,e,f] :
+	   a+b+2c+2d+e+2f >= 1
+	&& a - 3b - 2f >= 1
+	&& 3a-b >= 1
+	&& a-c >= 1
+	&& -b-3c+2e-2f >= 1
+	&& -a-2e>=1
+	&& b-2d-f >= 1
+	&& 4a+b-e >= 1
+	&& a-c+e >= 1
+	&& a >= 1
+	};
+		
diff --git a/omega/examples/old_test/ip1.oc-rt b/omega/examples/old_test/ip1.oc-rt
new file mode 100644
index 0000000..6646b8f
--- /dev/null
+++ b/omega/examples/old_test/ip1.oc-rt
@@ -0,0 +1,15 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# time {[a,b,c,d,e,f] :
+# 	   a+b+2c+2d+e+2f >= 1
+# 	&& a - 3b - 2f >= 1
+# 	&& 3a-b >= 1
+# 	&& a-c >= 1
+# 	&& -b-3c+2e-2f >= 1
+# 	&& -a-2e>=1
+# 	&& b-2d-f >= 1
+# 	&& 4a+b-e >= 1
+# 	&& a-c+e >= 1
+# 	&& a >= 1
+'time' requires getrusage, but the omega calclator was compiled with OMIT_GETRUSAGE set!
+# 	};
+# 		
diff --git a/omega/examples/old_test/ip2 b/omega/examples/old_test/ip2
new file mode 100644
index 0000000..cfef018
--- /dev/null
+++ b/omega/examples/old_test/ip2
@@ -0,0 +1,11 @@
+time {[a,b,c,d,e,f] :
+	   a+b+2c+2d+e+2f >= 1
+	&& 2a-3b-2f >= 1
+	&& 3a-2b >= 1
+	&& a-3c >= 1
+	&& -b-3c+2e-2f>=1
+	&& -a-2e >= 1
+	&& b-2d-3f >= 1
+	&& 3a+b-e >= 1
+	};
+		
diff --git a/omega/examples/old_test/ip2.oc-rt b/omega/examples/old_test/ip2.oc-rt
new file mode 100644
index 0000000..74cda4f
--- /dev/null
+++ b/omega/examples/old_test/ip2.oc-rt
@@ -0,0 +1,13 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# time {[a,b,c,d,e,f] :
+# 	   a+b+2c+2d+e+2f >= 1
+# 	&& 2a-3b-2f >= 1
+# 	&& 3a-2b >= 1
+# 	&& a-3c >= 1
+# 	&& -b-3c+2e-2f>=1
+# 	&& -a-2e >= 1
+# 	&& b-2d-3f >= 1
+# 	&& 3a+b-e >= 1
+'time' requires getrusage, but the omega calclator was compiled with OMIT_GETRUSAGE set!
+# 	};
+# 		
diff --git a/omega/examples/old_test/ip3 b/omega/examples/old_test/ip3
new file mode 100644
index 0000000..7fc0ec1
--- /dev/null
+++ b/omega/examples/old_test/ip3
@@ -0,0 +1,18 @@
+approximate {[a,b,c,d,e,f] : (
+	   a+b+2c+2d+e+2f >= 1
+	&& 2a-3b-2f >= 1
+	&& 3a-2b >= 1
+	&& a-3c >= 1
+	&& -b-3c+2e-2f>=1
+	&& -a-2e >= 1
+	&& b-2d-3f >= 1
+	&& 3a+b-e >= 1
+
+	&& a = 0
+	&& b = -1
+	&& c = -1
+	&& e = -2
+	&& d = 11
+	)
+	};
+		
diff --git a/omega/examples/old_test/ip3.oc-rt b/omega/examples/old_test/ip3.oc-rt
new file mode 100644
index 0000000..645e3f8
--- /dev/null
+++ b/omega/examples/old_test/ip3.oc-rt
@@ -0,0 +1,23 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# approximate {[a,b,c,d,e,f] : (
+# 	   a+b+2c+2d+e+2f >= 1
+# 	&& 2a-3b-2f >= 1
+# 	&& 3a-2b >= 1
+# 	&& a-3c >= 1
+# 	&& -b-3c+2e-2f>=1
+# 	&& -a-2e >= 1
+# 	&& b-2d-3f >= 1
+# 	&& 3a+b-e >= 1
+# 
+# 	&& a = 0
+# 	&& b = -1
+# 	&& c = -1
+# 	&& e = -2
+# 	&& d = 11
+# 	)
+# 	};
+
+{[0,-1,-1,11,-2,-8]}
+
+# 
+# 		
diff --git a/omega/examples/old_test/iter1 b/omega/examples/old_test/iter1
new file mode 100644
index 0000000..86ece54
--- /dev/null
+++ b/omega/examples/old_test/iter1
@@ -0,0 +1,2 @@
+R := { [i] : i < 10 && i > 1};
+codegen R;
diff --git a/omega/examples/old_test/iter1.oc-rt b/omega/examples/old_test/iter1.oc-rt
new file mode 100644
index 0000000..172ced0
--- /dev/null
+++ b/omega/examples/old_test/iter1.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i] : i < 10 && i > 1};
+# 
+# codegen R;
+for(t1 = 2; t1 <= 9; t1++) {
+  s1(t1);
+}
+
+# 
diff --git a/omega/examples/old_test/iter2 b/omega/examples/old_test/iter2
new file mode 100644
index 0000000..e3ccff1
--- /dev/null
+++ b/omega/examples/old_test/iter2
@@ -0,0 +1,2 @@
+R := { [i,j] : i <= 10 && i >= 1 && j <=100 && j >= 10};
+codegen R;
diff --git a/omega/examples/old_test/iter2.oc-rt b/omega/examples/old_test/iter2.oc-rt
new file mode 100644
index 0000000..0597426
--- /dev/null
+++ b/omega/examples/old_test/iter2.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i,j] : i <= 10 && i >= 1 && j <=100 && j >= 10};
+# 
+# codegen R;
+for(t1 = 1; t1 <= 10; t1++) {
+  for(t2 = 10; t2 <= 100; t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/iter3 b/omega/examples/old_test/iter3
new file mode 100644
index 0000000..604574b
--- /dev/null
+++ b/omega/examples/old_test/iter3
@@ -0,0 +1,2 @@
+R := { [i,j] : i < 10 && i > 1 && j < 10 && j > i};
+codegen R;
diff --git a/omega/examples/old_test/iter3.oc-rt b/omega/examples/old_test/iter3.oc-rt
new file mode 100644
index 0000000..d1288b5
--- /dev/null
+++ b/omega/examples/old_test/iter3.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i,j] : i < 10 && i > 1 && j < 10 && j > i};
+# 
+# codegen R;
+for(t1 = 2; t1 <= 8; t1++) {
+  for(t2 = t1+1; t2 <= 9; t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/iter4 b/omega/examples/old_test/iter4
new file mode 100644
index 0000000..2660d33
--- /dev/null
+++ b/omega/examples/old_test/iter4
@@ -0,0 +1,2 @@
+R := { [i,j] : i < 10 && i > 1 && j <=2i && j > i};
+codegen R;
diff --git a/omega/examples/old_test/iter4.oc-rt b/omega/examples/old_test/iter4.oc-rt
new file mode 100644
index 0000000..182cb09
--- /dev/null
+++ b/omega/examples/old_test/iter4.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i,j] : i < 10 && i > 1 && j <=2i && j > i};
+# 
+# codegen R;
+for(t1 = 2; t1 <= 9; t1++) {
+  for(t2 = t1+1; t2 <= 2*t1; t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/iter5 b/omega/examples/old_test/iter5
new file mode 100644
index 0000000..b2a973b
--- /dev/null
+++ b/omega/examples/old_test/iter5
@@ -0,0 +1,2 @@
+R := { [i,j] : i < 10 && i > 1 && j <=2i && j > i && j <= 16};
+codegen R;
diff --git a/omega/examples/old_test/iter5.oc-rt b/omega/examples/old_test/iter5.oc-rt
new file mode 100644
index 0000000..8b567d5
--- /dev/null
+++ b/omega/examples/old_test/iter5.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i,j] : i < 10 && i > 1 && j <=2i && j > i && j <= 16};
+# 
+# codegen R;
+for(t1 = 2; t1 <= 9; t1++) {
+  for(t2 = t1+1; t2 <= min(2*t1,16); t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/iter6 b/omega/examples/old_test/iter6
new file mode 100644
index 0000000..b093c0b
--- /dev/null
+++ b/omega/examples/old_test/iter6
@@ -0,0 +1,6 @@
+Y := { [i,j] : 1 <= i <= 5 and 12 <= j <= 17};
+codegen Y;
+
+X := { [i,j] : 17i-153 = 12j+17 and 1 <= i <= 100 and 1 <= j <= 100 and i < j};
+codegen X;
+
diff --git a/omega/examples/old_test/iter6.oc-rt b/omega/examples/old_test/iter6.oc-rt
new file mode 100644
index 0000000..74f06da
--- /dev/null
+++ b/omega/examples/old_test/iter6.oc-rt
@@ -0,0 +1,22 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Y := { [i,j] : 1 <= i <= 5 and 12 <= j <= 17};
+# 
+# codegen Y;
+for(t1 = 1; t1 <= 5; t1++) {
+  for(t2 = 12; t2 <= 17; t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
+# 
+# X := { [i,j] : 17i-153 = 12j+17 and 1 <= i <= 100 and 1 <= j <= 100 and i < j};
+# 
+# codegen X;
+for(t1 = 46; t1 <= 70; t1 += 12) {
+  t2=intDiv((17*t1+11),12);
+  s1(t1,intDiv(17*t1+-170,12));
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/iter7 b/omega/examples/old_test/iter7
new file mode 100644
index 0000000..3364dd7
--- /dev/null
+++ b/omega/examples/old_test/iter7
@@ -0,0 +1,3 @@
+R := {[i,j] : 3i+2j=15 && 1<=i<=j<=100};
+R;
+codegen R;
diff --git a/omega/examples/old_test/iter7.oc-rt b/omega/examples/old_test/iter7.oc-rt
new file mode 100644
index 0000000..52b7860
--- /dev/null
+++ b/omega/examples/old_test/iter7.oc-rt
@@ -0,0 +1,15 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := {[i,j] : 3i+2j=15 && 1<=i<=j<=100};
+# 
+# R;
+
+{[i,j]: 3i+2j = 15 && 3 <= j <= 6}
+
+# 
+# codegen R;
+for(t1 = 1; t1 <= 3; t1 += 2) {
+  t2=intDiv((-3*t1+15+1),2);
+  s1(t1,intDiv(-3*t1+15,2));
+}
+
+# 
diff --git a/omega/examples/old_test/iter8 b/omega/examples/old_test/iter8
new file mode 100644
index 0000000..65682bb
--- /dev/null
+++ b/omega/examples/old_test/iter8
@@ -0,0 +1,12 @@
+symbolic exprVar1;
+symbolic exprVar2;
+symbolic exprVar3;
+
+ispace := {[In_1] : exists ( alpha : In_1+8alpha = 1+exprVar2 && exprVar3 =
+0 && 1 <= exprVar1 < In_1 <= 16 && exprVar2 < In_1)};
+
+known := {[In1] : exists ( alpha : exprVar3 = 0 && exprVar2 <= 8alpha +15
+&& alpha <= 0 && 1 <= exprVar1 && exprVar1+8alpha <= exprVar2)};
+
+codegen ispace given known;
+
diff --git a/omega/examples/old_test/iter8.oc-rt b/omega/examples/old_test/iter8.oc-rt
new file mode 100644
index 0000000..ede80cb
--- /dev/null
+++ b/omega/examples/old_test/iter8.oc-rt
@@ -0,0 +1,23 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic exprVar1;
+# 
+# symbolic exprVar2;
+# 
+# symbolic exprVar3;
+# 
+# 
+# ispace := {[In_1] : Exists ( alpha : In_1+8alpha = 1+exprVar2 && exprVar3 =
+# 0 && 1 <= exprVar1 < In_1 <= 16 && exprVar2 < In_1)};
+# 
+# 
+# known := {[In1] : Exists ( alpha : exprVar3 = 0 && exprVar2 <= 8alpha +15
+# && alpha <= 0 && 1 <= exprVar1 && exprVar1+8alpha <= exprVar2)};
+# 
+# 
+# codegen ispace given known;
+for(t1 = max(exprVar2+1,exprVar1+1+intMod(((exprVar2+1)-exprVar1+1),8)); t1 <= 16; t1 += 8) {
+  s1(t1);
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/iter9 b/omega/examples/old_test/iter9
new file mode 100644
index 0000000..42724f5
--- /dev/null
+++ b/omega/examples/old_test/iter9
@@ -0,0 +1,40 @@
+
+symbolic exprVar1;
+symbolic exprVar2;
+
+ispace0 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+
+ispace1 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+
+ispace2 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+
+ispace3 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+
+ispace4 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+
+ispace5 := {[In_1] : exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+&& alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)} union
+ {[In_1] : exists ( alpha : 1+exprVar1 = In_1+8alpha && exprVar2 = 0 && 1,
+exprVar1+1 <= In_1 <= 15)};
+
+known := { [In_1] : exprVar2 = 0 && exprVar1 <= 15} union
+ {[In_1] : exprVar2 = 0 && exprVar1 <= 14} union
+ {[In_1] : exprVar2 = 0 && exprVar1 <= 15};
+
+
+k := Hull known;
+
+gist ispace0 given k;
+gist ispace1 given k;
+gist ispace2 given k;
+gist ispace3 given k;
+gist ispace4 given k;
+gist ispace5 given k;
+
+codegen ispace0, ispace1, ispace2, ispace3, ispace4, ispace5 given k;
+
diff --git a/omega/examples/old_test/iter9.oc-rt b/omega/examples/old_test/iter9.oc-rt
new file mode 100644
index 0000000..93b1c48
--- /dev/null
+++ b/omega/examples/old_test/iter9.oc-rt
@@ -0,0 +1,121 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# symbolic exprVar1;
+# 
+# symbolic exprVar2;
+# 
+# 
+# ispace0 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+# 
+# 
+# ispace1 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+# 
+# 
+# ispace2 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+# 
+# 
+# ispace3 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+# 
+# 
+# ispace4 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)};
+# 
+# 
+# ispace5 := {[In_1] : Exists ( alpha : exprVar2 = 0 && exprVar1 <= 8alpha+15
+# && alpha <= 0 && 1 <= In_1 && In_1+8alpha <= exprVar1)} union
+#  {[In_1] : Exists ( alpha : 1+exprVar1 = In_1+8alpha && exprVar2 = 0 && 1,
+# exprVar1+1 <= In_1 <= 15)};
+# 
+# 
+# known := { [In_1] : exprVar2 = 0 && exprVar1 <= 15} union
+#  {[In_1] : exprVar2 = 0 && exprVar1 <= 14} union
+#  {[In_1] : exprVar2 = 0 && exprVar1 <= 15};
+# 
+# 
+# 
+# k := Hull known;
+# 
+# 
+# gist ispace0 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)}
+
+# 
+# gist ispace1 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)}
+
+# 
+# gist ispace2 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)}
+
+# 
+# gist ispace3 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)}
+
+# 
+# gist ispace4 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)}
+
+# 
+# gist ispace5 given k;
+
+{[In_1]: Exists ( alpha : exprVar1 <= 8alpha+15 && 1 <= In_1 && In_1+8alpha <= exprVar1)} union
+ {[In_1]: Exists ( alpha : In_1+8alpha = 1+exprVar1 && 1, exprVar1+1 <= In_1 <= 15)}
+
+# 
+# 
+# codegen ispace0, ispace1, ispace2, ispace3, ispace4, ispace5 given k;
+for(t1 = 1; t1 <= 8; t1++) {
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s1(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s2(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s3(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s4(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s5(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(exprVar1-t1,8) && exprVar1-15 <= 8*intDiv(exprVar1-t1,8)) {
+    s6(t1);
+  }
+}
+for(t1 = 9; t1 <= 15; t1++) {
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s1(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s2(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s3(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s4(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s5(t1);
+  }
+  if (exprVar1-15 <= 8*intDiv(-t1+exprVar1,8)) {
+    s6(t1);
+  }
+  if (intMod(-t1+exprVar1+1,8) == 0) {
+    s6(t1);
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/lefur00 b/omega/examples/old_test/lefur00
new file mode 100644
index 0000000..061f78c
--- /dev/null
+++ b/omega/examples/old_test/lefur00
@@ -0,0 +1,15 @@
+R := { [i, j, k, l] :
+  0 <= i <= 19 &&
+  0 <= j <= 19 &&
+  1 <= k <= 1000 &&
+  -k + l >= 0 &&
+  2 k - l + 1 >= 0 &&
+  -200 i + k + l >= 0 &&
+  200 i - k - l + 199 >= 0 &&
+  -200 j - k + 2 l >= 0 &&
+  200 j + k -2 l + 199 >= 0
+} ;
+
+
+codegen R;
+
diff --git a/omega/examples/old_test/lefur00.oc-rt b/omega/examples/old_test/lefur00.oc-rt
new file mode 100644
index 0000000..3b3736f
--- /dev/null
+++ b/omega/examples/old_test/lefur00.oc-rt
@@ -0,0 +1,28 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i, j, k, l] :
+#   0 <= i <= 19 &&
+#   0 <= j <= 19 &&
+#   1 <= k <= 1000 &&
+#   -k + l >= 0 &&
+#   2 k - l + 1 >= 0 &&
+#   -200 i + k + l >= 0 &&
+#   200 i - k - l + 199 >= 0 &&
+#   -200 j - k + 2 l >= 0 &&
+#   200 j + k -2 l + 199 >= 0
+# } ;
+# 
+# 
+# 
+# codegen R;
+for(t1 = 0; t1 <= 15; t1++) {
+  for(t2 = max(2*t1-15,intDiv(t1-1+1,2)); t2 <= min(t1+1,15); t2++) {
+    for(t3 = max(intDiv(200*t1-1+2,3),intDiv(200*t2-2+2,3),intDiv(-200*t2+400*t1-199+2,3),1); t3 <= min(100*t1+99,intDiv(-200*t2+400*t1+398,3),1000); t3++) {
+      for(t4 = max(t3,200*t1-t3,intDiv(200*t2+t3+1,2)); t4 <= min(2*t3+1,intDiv(200*t2+t3+199,2),200*t1-t3+199); t4++) {
+        s1(t1,t2,t3,t4);
+      }
+    }
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/lefur01 b/omega/examples/old_test/lefur01
new file mode 100644
index 0000000..495c4f3
--- /dev/null
+++ b/omega/examples/old_test/lefur01
@@ -0,0 +1,14 @@
+R := { [i, j, k, l] :
+  0 <= i <= 19 &&
+  0 <= j <= 19 &&
+  1 <= k <= 1000 &&
+  -k + l >= 0 &&
+  2 k - l + 1 >= 0 &&
+  -200 i + k + l >= 0 &&
+  200 i - k - l + 199 >= 0 &&
+  -200 j - k + 2 l >= 0 &&
+  200 j + k -2 l + 199 >= 0
+} ;
+
+codegen R;
+codegen 2 R;
diff --git a/omega/examples/old_test/lefur01.oc-rt b/omega/examples/old_test/lefur01.oc-rt
new file mode 100644
index 0000000..4437f93
--- /dev/null
+++ b/omega/examples/old_test/lefur01.oc-rt
@@ -0,0 +1,103 @@
+>>> R := { [i, j, k, l] :
+>>>   0 <= i <= 19 &&
+>>>   0 <= j <= 19 &&
+>>>   1 <= k <= 1000 &&
+>>>   -k + l >= 0 &&
+>>>   2 k - l + 1 >= 0 &&
+>>>   -200 i + k + l >= 0 &&
+>>>   200 i - k - l + 199 >= 0 &&
+>>>   -200 j - k + 2 l >= 0 &&
+>>>   200 j + k -2 l + 199 >= 0
+>>> } ;
+>>> 
+>>> codegen R;
+for(t1 = 0; t1 <= 15; t1++) {
+  for(t2 = max(2*t1-15,intDiv(t1-1+1,2)); t2 <= min(t1+1,15); t2++) {
+    for(t3 = max(intDiv(200*t1-1+2,3),intDiv(200*t2-2+2,3),intDiv(400*t1-200*t2-199+2,3),1); t3 <= min(100*t1+99,intDiv(400*t1-200*t2+398,3),1000); t3++) {
+      for(t4 = max(t3,-t3+200*t1,intDiv(t3+200*t2+1,2)); t4 <= min(2*t3+1,-t3+200*t1+199,intDiv(t3+200*t2+199,2)); t4++) {
+        s1(t1,t2,t3,t4);
+      }
+    }
+  }
+}
+
+>>> codegen 2 R;
+for(t1 = 0; t1 <= 15; t1++) {
+  for(t2 = max(2*t1-15,intDiv(t1-1+1,2)); t2 <= min(t1+1,15); t2++) {
+    if (t2 <= t1-1) {
+      for(t3 = intDiv(-200*t2+400*t1-199+2,3); t3 <= min(100*t1-1,intDiv(-200*t2+400*t1-2,3)); t3++) {
+        for(t4 = 200*t1-t3; t4 <= intDiv(t3+200*t2+199,2); t4++) {
+          s1(t1,t2,t3,t4);
+        }
+      }
+    }
+    for(t3 = max(intDiv(200*t1-1+2,3),intDiv(200*t2-2+2,3)); t3 <= min(100*t1-1,intDiv(200*t2+195,3),intDiv(400*t1-200*t2+398,3),1000); t3++) {
+      for(t4 = intDiv(t3+200*t2+1,2); t4 <= 2*t3+1; t4++) {
+        s1(t1,t2,t3,t4);
+      }
+    }
+    for(t3 = max(intDiv(200*t2+196+2,3),intDiv(-200*t2+400*t1-1+2,3)); t3 <= min(100*t1-1,intDiv(-200*t2+400*t1+198,3),1000); t3++) {
+      for(t4 = intDiv(200*t2+t3+1,2); t4 <= intDiv(200*t2+t3+199,2); t4++) {
+        s1(t1,t2,t3,t4);
+      }
+    }
+    if (t2 <= t1) {
+      for(t3 = intDiv(-200*t2+400*t1+199+2,3); t3 <= min(intDiv(-200*t2+400*t1+398,3),100*t1-1,1000); t3++) {
+        for(t4 = intDiv(200*t2+t3+1,2); t4 <= -t3+200*t1+199; t4++) {
+          s1(t1,t2,t3,t4);
+        }
+      }
+    }
+    if (t2 == 1 && t1 == 1) {
+      for(t3 = 100; t3 <= 132; t3++) {
+        for(t4 = intDiv(t3+200+1,2); t4 <= 2*t3+1; t4++) {
+          s1(1,1,t3,t4);
+        }
+      }
+    }
+    if (2*t2 == t1+1 && t2 >= 2) {
+      for(t3 = 200*t2-100; t3 <= 200*t2-68; t3++) {
+        for(t4 = intDiv(200*t2+t3+1,2); t4 <= intDiv(200*t2+t3+199,2); t4++) {
+          s1(t1,intDiv(t1+1,2),t3,t4);
+        }
+      }
+    }
+    if (2*t2 >= t1+1) {
+      for(t3 = max(intDiv(200*t2-2+2,3),intDiv(-200*t2+400*t1+199+2,3),100*t1); t3 <= min(intDiv(-200*t2+400*t1+398,3),1000); t3++) {
+        for(t4 = intDiv(t3+200*t2+1,2); t4 <= 200*t1-t3+199; t4++) {
+          s1(t1,t2,t3,t4);
+        }
+      }
+    }
+    if (t2 == 0 && t1 <= 0) {
+      for(t3 = 1; t3 <= 65; t3++) {
+        for(t4 = t3; t4 <= 2*t3+1; t4++) {
+          s1(0,0,t3,t4);
+        }
+      }
+    }
+    if (t2 == 0) {
+      for(t3 = max(100*t1,66); t3 <= intDiv(200*t1+198,3); t3++) {
+        for(t4 = t3; t4 <= intDiv(t3+199,2); t4++) {
+          s1(t1,0,t3,t4);
+        }
+      }
+    }
+    if (2*t2 <= t1) {
+      for(t3 = max(100*t1,intDiv(200*t1+199+2,3)); t3 <= min(200*t2+199,intDiv(400*t1-200*t2+200,3),1000); t3++) {
+        for(t4 = t3; t4 <= intDiv(t3+200*t2+199,2); t4++) {
+          s1(t1,t2,t3,t4);
+        }
+      }
+    }
+    if (2*t2 == t1 && t2 <= 4) {
+      for(t3 = 200*t2+67; t3 <= 200*t2+99; t3++) {
+        for(t4 = t3; t4 <= -t3+400*t2+199; t4++) {
+          s1(t1,intDiv(t1,2),t3,t4);
+        }
+      }
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/lefur03 b/omega/examples/old_test/lefur03
new file mode 100644
index 0000000..c237eca
--- /dev/null
+++ b/omega/examples/old_test/lefur03
@@ -0,0 +1,16 @@
+# From Fabien Coelho
+
+R := { [i,j,k,l,m,n] :
+  0 <= i <= 3  &&
+  0 <= j <= 3  &&
+  0 <= k <= 3  &&
+  0 <= l <= 3  &&
+  1 <= m <= 1000  &&
+  -1 <= 3 m - 1000 k <= 998  &&
+  m <= n <= 2 m + 1  &&
+  0 <= m + n - 1000 i <= 999  &&
+  0 <= 2 n - m - 1000 j <= 999  &&
+  2 <= n + 2 m - 1000 l <= 1001
+} ;
+
+codegen R;
diff --git a/omega/examples/old_test/lefur03-3 b/omega/examples/old_test/lefur03-3
new file mode 100644
index 0000000..1c576a1
--- /dev/null
+++ b/omega/examples/old_test/lefur03-3
@@ -0,0 +1,20 @@
+# From Fabien Coelho
+
+R := { [i,j,k,l,m,n] :
+  0 <= i <= 3  &&
+  0 <= j <= 3  &&
+  0 <= k <= 3  &&
+  0 <= l <= 3  &&
+  1 <= m <= 1000  &&
+  -1 <= 3 m - 1000 k <= 998  &&
+  m <= n <= 2 m + 1  &&
+  0 <= m + n - 1000 i <= 999  &&
+  0 <= 2 n - m - 1000 j <= 999  &&
+  2 <= n + 2 m - 1000 l <= 1001
+} ;
+
+codegen R;
+codegen R;
+codegen R;
+codegen R;
+codegen R;
diff --git a/omega/examples/old_test/lefur03-3.oc-rt b/omega/examples/old_test/lefur03-3.oc-rt
new file mode 100644
index 0000000..a1aa81a
--- /dev/null
+++ b/omega/examples/old_test/lefur03-3.oc-rt
@@ -0,0 +1,107 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # From Fabien Coelho
+# 
+# R := { [i,j,k,l,m,n] :
+#   0 <= i <= 3  &&
+#   0 <= j <= 3  &&
+#   0 <= k <= 3  &&
+#   0 <= l <= 3  &&
+#   1 <= m <= 1000  &&
+#   -1 <= 3 m - 1000 k <= 998  &&
+#   m <= n <= 2 m + 1  &&
+#   0 <= m + n - 1000 i <= 999  &&
+#   0 <= 2 n - m - 1000 j <= 999  &&
+#   2 <= n + 2 m - 1000 l <= 1001
+# } ;
+# 
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/lefur03.c b/omega/examples/old_test/lefur03.c
new file mode 100644
index 0000000..7df0865
--- /dev/null
+++ b/omega/examples/old_test/lefur03.c
@@ -0,0 +1,36 @@
+
+#include <stdio.h>
+#include "basic/util.h"
+
+template int max(int, int);
+template int min(int, int);
+
+void Exit(int foo) {
+  exit(foo);
+  }
+
+int main() {
+
+int t1,t2,t3,t4,t5,t6;
+
+
+
+
+
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(-t2+2*t1+1,3*t2+2,3); t3++) {
+      for(t4 = max(max(int_div(5*t3+3*t2-6+5,6),int_div(5*t1-t2-4+2,3)),max(t2,0)); t4 <= min(int_div(5*t3+3*t2+7,6),int_div(5*t1-t2+4,3),3); t4++) {
+        for(t5 = max(max(max(int_div(1000*t2-2+2,3),250*t4+1),max(int_div(2000*t1-1000*t2-999+2,3),400*t4-200*t2-199)),int_div(1000*t3-1+2,3)); 
+		t5 <= min(min(min(400*t4-200*t2+400,500*t1+499),min(int_div(1000*t3+998,3),int_div(1000*t4+1001,3))),1000); t5++) {
+          for(t6 = max(max(int_div(t5+1000*t2+1,2),t5),max(1000*t1-t5,-2*t5+1000*t4+2)); t6 <= min(min(int_div(t5+1000*t2+999,2),2*t5+1),min(1000*t1-t5+999,-2*t5+1000*t4+1001)); t6++) {
+	    printf("%d,%d,%d,%d,%d,%d\n",
+		    t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
diff --git a/omega/examples/old_test/lefur03.oc-rt b/omega/examples/old_test/lefur03.oc-rt
new file mode 100644
index 0000000..3fbb8cb
--- /dev/null
+++ b/omega/examples/old_test/lefur03.oc-rt
@@ -0,0 +1,35 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # From Fabien Coelho
+# 
+# R := { [i,j,k,l,m,n] :
+#   0 <= i <= 3  &&
+#   0 <= j <= 3  &&
+#   0 <= k <= 3  &&
+#   0 <= l <= 3  &&
+#   1 <= m <= 1000  &&
+#   -1 <= 3 m - 1000 k <= 998  &&
+#   m <= n <= 2 m + 1  &&
+#   0 <= m + n - 1000 i <= 999  &&
+#   0 <= 2 n - m - 1000 j <= 999  &&
+#   2 <= n + 2 m - 1000 l <= 1001
+# } ;
+# 
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(t1+1,3); t2++) {
+    for(t3 = t1; t3 <= min(2*t1-t2+1,3*t2+2,3); t3++) {
+      for(t4 = max(intDiv(t3+3*t1-3+2,3),intDiv(5*t3+3*t2-6+5,6),intDiv(4*t2-3+2,3),0); t4 <= min(intDiv(-t2+5*t1+4,3),intDiv(5*t3+3*t2+7,6),3); t4++) {
+        if (t1 <= t4+1) {
+          for(t5 = max(intDiv(1000*t3-1+2,3),250*t4+1,intDiv(-1000*t2+2000*t1-999+2,3),intDiv(1000*t2-2+2,3),-200*t2+400*t4-199); t5 <= min(intDiv(1000*t4+1001,3),-200*t2+400*t4+400,intDiv(1000*t3+998,3),500*t1+499,1000); t5++) {
+            for(t6 = max(t5,intDiv(t5+1000*t2+1,2),-2*t5+1000*t4+2,-t5+1000*t1); t6 <= min(-2*t5+1000*t4+1001,2*t5+1,intDiv(t5+1000*t2+999,2),-t5+1000*t1+999); t6++) {
+              s1(t1,t2,t3,t4,t5,t6);
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/lefur04 b/omega/examples/old_test/lefur04
new file mode 100644
index 0000000..4a9e0c4
--- /dev/null
+++ b/omega/examples/old_test/lefur04
@@ -0,0 +1,19 @@
+# From Fabien Coelho
+
+R := { [i, j, k, l, m, n, o, p] :
+ 0 <= i <= 3 && 
+ 0 <= j <= 3 &&
+ 0 <= k <= 3 &&
+ 0 <= l <= 3 &&
+ 0 <= m <= 3 &&
+ 0 <= n <= 3 &&
+ 1 <= o <= 1000 && o <= p <= 2 o +1 && 
+ 0 <= -1000 i + o + p <= 999 &&
+ 0 <= -1000 j - o + 2p <= 999 &&
+ -1 <= -1000 k + 3 o <= 998 &&
+ 2 <= -1000 l + 2 o + p <= 1001 &&
+ 0 <= -1000 m + o <= 999 &&
+ 3 <= -1000 n + 2 p<= 1002
+} ;
+
+codegen R;
diff --git a/omega/examples/old_test/lefur04.oc-rt b/omega/examples/old_test/lefur04.oc-rt
new file mode 100644
index 0000000..b449d8c
--- /dev/null
+++ b/omega/examples/old_test/lefur04.oc-rt
@@ -0,0 +1,42 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # From Fabien Coelho
+# 
+# R := { [i, j, k, l, m, n, o, p] :
+#  0 <= i <= 3 && 
+#  0 <= j <= 3 &&
+#  0 <= k <= 3 &&
+#  0 <= l <= 3 &&
+#  0 <= m <= 3 &&
+#  0 <= n <= 3 &&
+#  1 <= o <= 1000 && o <= p <= 2 o +1 && 
+#  0 <= -1000 i + o + p <= 999 &&
+#  0 <= -1000 j - o + 2p <= 999 &&
+#  -1 <= -1000 k + 3 o <= 998 &&
+#  2 <= -1000 l + 2 o + p <= 1001 &&
+#  0 <= -1000 m + o <= 999 &&
+#  3 <= -1000 n + 2 p<= 1002
+# } ;
+# 
+# 
+# codegen R;
+for(t1 = 0; t1 <= 3; t1++) {
+  for(t2 = max(2*t1-3,0); t2 <= min(intDiv(3*t1+2,2),3); t2++) {
+    for(t3 = t1; t3 <= min(-t2+2*t1+1,intDiv(3*t1+2,2),3); t3++) {
+      for(t4 = max(intDiv(2*t3-2+2,3),intDiv(-t2+5*t1-4+2,3),intDiv(3*t2+5*t3-6+5,6),intDiv(4*t2-3+2,3)); t4 <= min(intDiv(t2+5,2),intDiv(4*t3+3,3),intDiv(-t2+5*t1+4,3),3); t4++) {
+        for(t5 = max(intDiv(t2-2+2,3),intDiv(t3-2+2,3)); t5 <= intDiv(t3,3); t5++) {
+          for(t6 = max(intDiv(6*t4-4*t3-6+2,3),intDiv(2*t3-3+2,3),2*t4-4,intDiv(4*t2-3+2,3),intDiv(t3+3*t2-3+2,3),0); t6 <= min(intDiv(6*t4-4*t3+5,3),t2+1,t4); t6++) {
+            if (t4 >= t1-1) {
+              for(t7 = max(intDiv(2000*t1-1000*t2-999+2,3),1000*t1-500*t6-501,250*t4+1,400*t4-200*t2-199,intDiv(1000*t3-1+2,3),intDiv(1000*t2-2+2,3)); t7 <= min(1000*t1-500*t6+997,intDiv(1000*t4+1001,3),400*t4-200*t2+400,500*t1+499,500*t6+501,intDiv(1000*t3+998,3),1000); t7++) {
+                for(t8 = max(1000*t1-t7,500*t6+2,1000*t4-2*t7+2,t7,intDiv(t7+1000*t2+1,2)); t8 <= min(1000*t1-t7+999,500*t6+501,1000*t4-2*t7+1001,2*t7+1,intDiv(t7+1000*t2+999,2)); t8++) {
+                  s1(t1,t2,t3,t4,t5,t6,t7,t8);
+                }
+              }
+            }
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/lefur05 b/omega/examples/old_test/lefur05
new file mode 100644
index 0000000..436ac54
--- /dev/null
+++ b/omega/examples/old_test/lefur05
@@ -0,0 +1,49 @@
+# From Fabien Coelho
+
+R := { [i, j, k, l, m, n, o, p] :
+ 0 <= i <= 3 && 
+ 0 <= j <= 3 &&
+ 0 <= k <= 3 &&
+ 0 <= l <= 3 &&
+ 0 <= m <= 3 &&
+ 0 <= n <= 3 &&
+ 1 <= o <= 1000 && o <= p <= 2 o +1 && 
+ 0 <= -1000 i + o + p <= 999 &&
+ 0 <= -1000 j - o + 2p <= 999 &&
+ -1 <= -1000 k + 3 o <= 998 &&
+ 2 <= -1000 l + 2 o + p <= 1001 &&
+ 0 <= -1000 m + o <= 999 &&
+ 3 <= -1000 n + 2 p<= 1002
+} ;
+
+R;
+
+R7 :=  { [i, j, k, l, m, n, o, p] 
+		 -> [i, j, k, l, m, n, o ]}(R);
+R7;
+approximate R7;
+R6 :=  { [i, j, k, l, m, n, o] 
+		 -> [i, j, k, l, m, n ]}(R7);
+R6;
+approximate R6;
+R5 :=  { [i, j, k, l, m, n] 
+		 -> [i, j, k, l, m ]}(R6);
+R5;
+approximate R5;
+R4 :=  { [i, j, k, l, m] 
+		 -> [i, j, k, l ]}(R5);
+R4;
+approximate R4;
+R3 :=  { [i, j, k, l] 
+		 -> [i, j, k ]}(R4);
+R3;
+approximate R3;
+R2 :=  { [i, j, k] 
+		 -> [i, j ]}(R3);
+R2;
+approximate R2;
+R1 :=  { [i, j] 
+		 -> [i]}(R2);
+R1;
+approximate R1;
+
diff --git a/omega/examples/old_test/lefur05.oc-rt b/omega/examples/old_test/lefur05.oc-rt
new file mode 100644
index 0000000..6d5e45e
--- /dev/null
+++ b/omega/examples/old_test/lefur05.oc-rt
@@ -0,0 +1,118 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # From Fabien Coelho
+# 
+# R := { [i, j, k, l, m, n, o, p] :
+#  0 <= i <= 3 && 
+#  0 <= j <= 3 &&
+#  0 <= k <= 3 &&
+#  0 <= l <= 3 &&
+#  0 <= m <= 3 &&
+#  0 <= n <= 3 &&
+#  1 <= o <= 1000 && o <= p <= 2 o +1 && 
+#  0 <= -1000 i + o + p <= 999 &&
+#  0 <= -1000 j - o + 2p <= 999 &&
+#  -1 <= -1000 k + 3 o <= 998 &&
+#  2 <= -1000 l + 2 o + p <= 1001 &&
+#  0 <= -1000 m + o <= 999 &&
+#  3 <= -1000 n + 2 p<= 1002
+# } ;
+# 
+# 
+# R;
+
+{[i,j,k,l,m,n,o,p]: 1000m <= o <= p <= 500n+501, 2o+1 && o <= 1000m+999, 1000 && 1000i <= o+p && o+p <= 999+1000i && 1000j+o <= 2p && 2p <= 999+1000j+o && 1000k <= 1+3o && 3o <= 998+1000k && 2+500n <= p && 0 <= n && 2+1000l <= 2o+p && 2o+p <= 1001+1000l}
+
+# 
+# 
+# R7 :=  { [i, j, k, l, m, n, o, p] 
+# 		 -> [i, j, k, l, m, n, o ]}(R);
+# 
+# R7;
+
+{[i,j,k,l,m,n,o]: 1000m, 250n+1 <= o <= 1000m+999, 1000, 500n+501, 1000j+999, 500i+499 && 200j+o <= 400+400l && 1000j+o <= 1002+1000n && 1000i <= 1+3o && 1000j+3o <= 1998+2000i && 1000k <= 1+3o && 3o <= 998+1000k && 1000j <= 2+3o && 2000i <= 999+1000j+3o && 0 <= n && 1000i <= 501+500n+o && 250n+o <= 499+500l && 1000n <= 995+1000j+o && 500n+o <= 997+1000i && 3o <= 1001+1000l && 500l <= 249+250n+o && 400l <= 199+200j+o && 1000l <= 997+1000i+o}
+
+# 
+# approximate R7;
+
+{[i,j,k,l,m,n,o]: 1000m, 250n+1 <= o <= 1000m+999, 1000, 500n+501, 1000j+999, 500i+499 && 200j+o <= 400+400l && 1000j+o <= 1002+1000n && 1000i <= 1+3o && 1000j+3o <= 1998+2000i && 1000k <= 1+3o && 3o <= 998+1000k && 1000j <= 2+3o && 2000i <= 999+1000j+3o && 0 <= n && 1000i <= 501+500n+o && 250n+o <= 499+500l && 1000n <= 995+1000j+o && 500n+o <= 997+1000i && 3o <= 1001+1000l && 500l <= 249+250n+o && 400l <= 199+200j+o && 1000l <= 997+1000i+o}
+
+# 
+# R6 :=  { [i, j, k, l, m, n, o] 
+# 		 -> [i, j, k, l, m, n ]}(R7);
+# 
+# R6;
+
+{[i,j,k,l,m,n]: Exists ( alpha : 0, 2l-4 <= n <= 3, j+1, l, 2j+1 && 3m <= k <= 3, 3m+2 && 2i-3 <= j <= 3m+2 && 2k <= 2+3i && 1000i <= 1+3alpha && 1000j+3alpha <= 1998+2000i && 4j <= 3+3n && 1000k <= 1+3alpha && 3alpha <= 998+1000k && 1000j <= 2+3alpha && 2000i <= 999+1000j+3alpha && 4k+3n <= 5+6l && 6i <= 5+2l+3n && 3alpha <= 1001+1000l && 3j+5k <= 6+6l && 4l <= 7+2j+5n && 2l <= 2+3i && 2k <= 3+3n)}
+
+# 
+# approximate R6;
+
+{[i,j,k,l,m,n]: 2l-4, 0 <= n <= 3, j+1, l, 2j+1 && 3m, i <= k <= 3m+2, 3 && 2i-3 <= j <= 3m+2 && 2k <= 2+3i && j+k <= 1+2i && 4j <= 3+3n && 2l <= 2+3i && 2k <= 3+3n && 4l <= 7+2j+5n && 4k+3n <= 5+6l && 6i <= 5+2l+3n && 3j+5k <= 6+6l}
+
+# 
+# R5 :=  { [i, j, k, l, m, n] 
+# 		 -> [i, j, k, l, m ]}(R6);
+# 
+# R5;
+
+{[i,j,k,l,m]: Exists ( alpha,beta : 2i-3, 0 <= j <= 3m+2 && 3m <= k <= 3, 3m+2 && l <= 3 && 2k <= 2+3i && 2k <= 3+3alpha && 1000i <= 1+3beta && 1000j+3beta <= 1998+2000i && 4j <= 3+3alpha && 1000k <= 1+3beta && 3beta <= 998+1000k && 1000j <= 2+3beta && 2000i <= 999+1000j+3beta && 4k+3alpha <= 5+6l && 6i <= 5+2l+3alpha && 6i <= 5+5l && 3beta <= 1001+1000l && 4j <= 3+3l && 2k <= 2+3l && 3j+5k <= 6+6l && 4l <= 7+2j+5alpha && 2l <= 2+3i)}
+
+# 
+# approximate R5;
+
+{[i,j,k,l,m]: i, 3m <= k <= 3m+2, 3 && 0, 2i-3 <= j <= 3m+2 && l <= 3 && 2k <= 2+3i && 2l <= 2+3i && 2k <= 2+3l && j+k <= 1+2i && 3j+5k <= 6+6l && 6i <= 5+5l && 4j <= 3+3l}
+
+# 
+# R4 :=  { [i, j, k, l, m] 
+# 		 -> [i, j, k, l ]}(R5);
+# 
+# R4;
+
+{[i,j,k,l]: Exists ( alpha,beta,gamma : 2i-3, 0 <= j <= 3alpha+2 && 3alpha <= k <= 3, 3alpha+2 && l <= 3 && 2k <= 2+3i && 2k <= 3+3beta && 1000i <= 1+3gamma && 1000j+3gamma <= 1998+2000i && 4j <= 3+3beta && 1000k <= 1+3gamma && 3gamma <= 998+1000k && 1000j <= 2+3gamma && 2000i <= 999+1000j+3gamma && 4k+3beta <= 5+6l && 6i <= 5+2l+3beta && 6i <= 5+5l && 3gamma <= 1001+1000l && 4j <= 3+3l && 2k <= 2+3l && 3j+5k <= 6+6l && 4l <= 7+2j+5beta && 2l <= 2+3i)}
+
+# 
+# approximate R4;
+
+{[i,j,k,l]: i <= k <= 3 && l <= 3 && 2k <= 2+3i && 2l <= 2+3i && 6i <= 5+5l && j+k <= 1+2i && 3j+5k <= 6+6l && 4j <= 3+3l && 2i <= 3+j && 2k <= 2+3l && 0 <= j}
+
+# 
+# R3 :=  { [i, j, k, l] 
+# 		 -> [i, j, k ]}(R4);
+# 
+# R3;
+
+{[i,j,k]: Exists ( alpha,beta,gamma,delta : 2i-3, 0 <= j <= 3beta+2 && 3beta <= k <= 3, 3beta+2 && alpha <= 3 && 2k <= 2+3i && 2k <= 3+3gamma && 1000i <= 1+3delta && 1000j+3delta <= 1998+2000i && 4j <= 3+3gamma && 1000k <= 1+3delta && 3delta <= 998+1000k && 1000j <= 2+3delta && 2000i <= 999+1000j+3delta && 4k+3gamma <= 5+6alpha && 6i <= 5+2alpha+3gamma && 6i <= 5+5alpha && 3delta <= 1001+1000alpha && 4j <= 3+3alpha && 2k <= 2+3alpha && 3j+5k <= 6+6alpha && 4alpha <= 7+2j+5gamma && 2alpha <= 2+3i)}
+
+# 
+# approximate R3;
+
+{[i,j,k]: 0, 2i-3 <= j <= 3 && i <= k <= 3 && 2k <= 2+3i && j+k <= 1+2i}
+
+# 
+# R2 :=  { [i, j, k] 
+# 		 -> [i, j ]}(R3);
+# 
+# R2;
+
+{[i,j]: Exists ( alpha,beta,gamma,delta,tau : 2i-3, 0 <= j <= 3tau+2 && 3tau <= alpha <= 3, 3tau+2 && delta <= 3 && 2alpha <= 2+3i && 2alpha <= 3+3beta && 1000i <= 1+3gamma && 1000j+3gamma <= 1998+2000i && 4j <= 3+3beta && 1000alpha <= 1+3gamma && 3gamma <= 998+1000alpha && 1000j <= 2+3gamma && 2000i <= 999+1000j+3gamma && 4alpha+3beta <= 5+6delta && 6i <= 5+3beta+2delta && 6i <= 5+5delta && 3gamma <= 1001+1000delta && 4j <= 3+3delta && 2alpha <= 2+3delta && 3j+5alpha <= 6+6delta && 4delta <= 7+2j+5beta && 2delta <= 2+3i)}
+
+# 
+# approximate R2;
+
+{[i,j]: 0, 2i-3 <= j <= i+1, 3}
+
+# 
+# R1 :=  { [i, j] 
+# 		 -> [i]}(R2);
+# 
+# R1;
+
+{[i]: Exists ( alpha,beta,gamma,delta,tau,sigma : 2i-3, 0 <= alpha <= 3beta+2 && 3beta <= gamma <= 3, 3beta+2 && sigma <= 3 && 2gamma <= 2+3i && 2gamma <= 3+3delta && 1000i <= 1+3tau && 1000alpha+3tau <= 1998+2000i && 4alpha <= 3+3delta && 1000gamma <= 1+3tau && 3tau <= 998+1000gamma && 1000alpha <= 2+3tau && 2000i <= 999+1000alpha+3tau && 4gamma+3delta <= 5+6sigma && 6i <= 5+3delta+2sigma && 6i <= 5+5sigma && 3tau <= 1001+1000sigma && 4alpha <= 3+3sigma && 2gamma <= 2+3sigma && 3alpha+5gamma <= 6+6sigma && 4sigma <= 7+2alpha+5delta && 2sigma <= 2+3i)}
+
+# 
+# approximate R1;
+
+{[i]: -1 <= i <= 3}
+
+# 
+# 
diff --git a/omega/examples/old_test/lift1 b/omega/examples/old_test/lift1
new file mode 100644
index 0000000..fb3ada1
--- /dev/null
+++ b/omega/examples/old_test/lift1
@@ -0,0 +1,16 @@
+I1 := { [i,j,k,l,m] : 1 <= i <= 60 && 1 <= j,k,l,m <= 100 };
+I2 := { [i,j,k,l,m] : 1 <= i,j,k,l,m <= 100 };
+
+codegen 0 I1,I2;
+
+#default
+codegen 1 I1,I2;
+
+codegen 2 I1,I2;
+
+codegen 3 I1,I2;
+
+codegen 4 I1,I2;
+
+codegen 5 I1,I2;
+
diff --git a/omega/examples/old_test/lift1.oc-rt b/omega/examples/old_test/lift1.oc-rt
new file mode 100644
index 0000000..683ac07
--- /dev/null
+++ b/omega/examples/old_test/lift1.oc-rt
@@ -0,0 +1,147 @@
+>>> I1 := { [i,j,k,l,m] : 1 <= i <= 60 && 1 <= j,k,l,m <= 100 };
+>>> I2 := { [i,j,k,l,m] : 1 <= i,j,k,l,m <= 100 };
+>>> 
+>>> codegen 0 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s2(t1,t2,t3,t4,t5);
+          if (t1 <= 60) {
+            s1(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> #default
+>>> codegen 1 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        if (t1 <= 60) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+        if (t1 >= 61) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 2 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      if (t1 <= 60) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+      if (t1 >= 61) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 3 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    if (t1 <= 60) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+    if (t1 >= 61) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 4 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  if (t1 <= 60) {
+    for(t2 = 1; t2 <= 100; t2++) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+  if (t1 >= 61) {
+    for(t2 = 1; t2 <= 100; t2++) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 5 I1,I2;
+for(t1 = 1; t1 <= 60; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s1(t1,t2,t3,t4,t5);
+          s2(t1,t2,t3,t4,t5);
+        }
+      }
+    }
+  }
+}
+for(t1 = 61; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s2(t1,t2,t3,t4,t5);
+        }
+      }
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/lift2 b/omega/examples/old_test/lift2
new file mode 100644
index 0000000..fada83e
--- /dev/null
+++ b/omega/examples/old_test/lift2
@@ -0,0 +1,16 @@
+I1 := { [i,j,k,l,m] : 5 <= i <= 60 && 1 <= j,k,l,m <= 100 };
+I2 := { [i,j,k,l,m] : 1 <= i,j,k,l,m <= 100 };
+
+codegen 0 I1,I2;
+
+#default
+codegen 1 I1,I2;
+
+codegen 2 I1,I2;
+
+codegen 3 I1,I2;
+
+codegen 4 I1,I2;
+
+codegen 5 I1,I2;
+
diff --git a/omega/examples/old_test/lift2.oc-rt b/omega/examples/old_test/lift2.oc-rt
new file mode 100644
index 0000000..41e1fa8
--- /dev/null
+++ b/omega/examples/old_test/lift2.oc-rt
@@ -0,0 +1,190 @@
+>>> I1 := { [i,j,k,l,m] : 5 <= i <= 60 && 1 <= j,k,l,m <= 100 };
+>>> I2 := { [i,j,k,l,m] : 1 <= i,j,k,l,m <= 100 };
+>>> 
+>>> codegen 0 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s2(t1,t2,t3,t4,t5);
+          if (t1 >= 5 && t1 <= 60) {
+            s1(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> #default
+>>> codegen 1 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        if (t1 <= 4) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+        if (t1 >= 5 && t1 <= 60) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+        if (t1 >= 61) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 2 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      if (t1 <= 4) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+      if (t1 >= 5 && t1 <= 60) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+      if (t1 >= 61) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 3 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    if (t1 <= 4) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+    if (t1 >= 5 && t1 <= 60) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+    if (t1 >= 61) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 4 I1,I2;
+for(t1 = 1; t1 <= 100; t1++) {
+  if (t1 <= 4) {
+    for(t2 = 1; t2 <= 100; t2++) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+  if (t1 >= 5 && t1 <= 60) {
+    for(t2 = 1; t2 <= 100; t2++) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s1(t1,t2,t3,t4,t5);
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+  if (t1 >= 61) {
+    for(t2 = 1; t2 <= 100; t2++) {
+      for(t3 = 1; t3 <= 100; t3++) {
+        for(t4 = 1; t4 <= 100; t4++) {
+          for(t5 = 1; t5 <= 100; t5++) {
+            s2(t1,t2,t3,t4,t5);
+          }
+        }
+      }
+    }
+  }
+}
+
+>>> 
+>>> codegen 5 I1,I2;
+for(t1 = 1; t1 <= 4; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s2(t1,t2,t3,t4,t5);
+        }
+      }
+    }
+  }
+}
+for(t1 = 5; t1 <= 60; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s1(t1,t2,t3,t4,t5);
+          s2(t1,t2,t3,t4,t5);
+        }
+      }
+    }
+  }
+}
+for(t1 = 61; t1 <= 100; t1++) {
+  for(t2 = 1; t2 <= 100; t2++) {
+    for(t3 = 1; t3 <= 100; t3++) {
+      for(t4 = 1; t4 <= 100; t4++) {
+        for(t5 = 1; t5 <= 100; t5++) {
+          s2(t1,t2,t3,t4,t5);
+        }
+      }
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/long_input b/omega/examples/old_test/long_input
new file mode 100644
index 0000000..6112756
--- /dev/null
+++ b/omega/examples/old_test/long_input
@@ -0,0 +1,2 @@
+{ [i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c] -> [j] : 1 <= i < j <= 20 };
+{ [j] -> [i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v] : 1 <= i < j <= 20 };
diff --git a/omega/examples/old_test/long_input.oc-rt b/omega/examples/old_test/long_input.oc-rt
new file mode 100644
index 0000000..281d321
--- /dev/null
+++ b/omega/examples/old_test/long_input.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# { [i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c] -> [j] : 1 <= i < j <= 20 };
+
+{[i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c] -> [j] : 1 <= i < j <= 20}
+
+# 
+# { [j] -> [i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v] : 1 <= i < j <= 20 };
+
+{[j] -> [i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z,a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v] : 1 <= i < j <= 20}
+
+# 
diff --git a/omega/examples/old_test/lu_ijk b/omega/examples/old_test/lu_ijk
new file mode 100644
index 0000000..5f60bfa
--- /dev/null
+++ b/omega/examples/old_test/lu_ijk
@@ -0,0 +1,17 @@
+symbolic n,lb,ub;
+I5 := {[k,j] : 1 <= k < j <= n};
+I7 := {[k,j,i] : 1 <= k < j,i <= n};
+T5 := {[k,j] -> [k,j,1,0]};
+T7 := {[k,j,i] -> [i,j,0,k]};
+D57 := {[k,j] -> [k,j,i] : 1 <= k < j,i <= n};
+D75 := {[k,j,k+1] -> [k+1,j] : 1 <= k <= j-2 && j <= n} union
+	{[k,k+1,k+1] -> [k+1,j'] : 1 <= k <= j'-2 && j' <= n};
+D77 := {[k,j,i] -> [k+1,j,i] : 1 <= k <= i-2, j-2 && j <= n && i <= n}
+	union
+	{[k,k+1,i] -> [k+1,j',i] : 1 <= k <= i-2, j'-2 && j' <= n && i <= n};
+difference ( (inverse T5) join D57 join T7 );
+difference ( (inverse T7) join D75 join T5 );
+difference ( (inverse T7) join D77 join T7 );
+codegen T5:I5,T7:I7;
+codegen 2 T5:I5,T7:I7;
+codegen 3 T5:I5,T7:I7;
diff --git a/omega/examples/old_test/lu_ijk.oc-rt b/omega/examples/old_test/lu_ijk.oc-rt
new file mode 100644
index 0000000..d067dff
--- /dev/null
+++ b/omega/examples/old_test/lu_ijk.oc-rt
@@ -0,0 +1,81 @@
+>>> symbolic n,lb,ub;
+>>> I5 := {[k,j] : 1 <= k < j <= n};
+>>> I7 := {[k,j,i] : 1 <= k < j,i <= n};
+>>> T5 := {[k,j] -> [k,j,1,0]};
+>>> T7 := {[k,j,i] -> [i,j,0,k]};
+>>> D57 := {[k,j] -> [k,j,i] : 1 <= k < j,i <= n};
+>>> D75 := {[k,j,k+1] -> [k+1,j] : 1 <= k <= j-2 && j <= n} union
+>>> 	{[k,k+1,k+1] -> [k+1,j'] : 1 <= k <= j'-2 && j' <= n};
+>>> D77 := {[k,j,i] -> [k+1,j,i] : 1 <= k <= i-2, j-2 && j <= n && i <= n}
+>>> 	union
+>>> 	{[k,k+1,i] -> [k+1,j',i] : 1 <= k <= i-2, j'-2 && j' <= n && i <= n};
+>>> difference ( (inverse T5) join D57 join T7 );
+{[In_1,0,-1,In_4]: 1 <= In_4 && In_1+In_4 <= n && 1 <= In_1}
+>>> difference ( (inverse T7) join D75 join T5 );
+{[0,0,1,In_4]: -n+2 <= In_4 <= -1} union
+ {[0,In_2,1,In_4]: In_4 <= -1 && 1 <= In_2 && In_2 < n+In_4}
+>>> difference ( (inverse T7) join D77 join T7 );
+{[0,0,0,1]: 3 <= n} union
+ {[0,In_2,0,1]: 1 <= In_2 <= n-2}
+>>> codegen T5:I5,T7:I7;
+if (n >= 2) {
+  for(t1 = 1; t1 <= n; t1++) {
+    for(t2 = 2; t2 <= n; t2++) {
+      for(t4 = 1; t4 <= min(t2-1,t1-1); t4++) {
+        s2(t4,t2,t1);
+      }
+      if (t1 <= t2-1) {
+        s1(t1,t2);
+      }
+    }
+  }
+}
+
+>>> codegen 2 T5:I5,T7:I7;
+if (n >= 2) {
+  for(t1 = 1; t1 <= n; t1++) {
+    if (t1 <= 1) {
+      for(t2 = 2; t2 <= n; t2++) {
+        s1(1,t2);
+      }
+    }
+    for(t2 = 2; t2 <= t1; t2++) {
+      for(t4 = 1; t4 <= t2-1; t4++) {
+        s2(t4,t2,t1);
+      }
+    }
+    if (t1 >= 2) {
+      for(t2 = t1+1; t2 <= n; t2++) {
+        for(t4 = 1; t4 <= t1-1; t4++) {
+          s2(t4,t2,t1);
+        }
+        s1(t1,t2);
+      }
+    }
+  }
+}
+
+>>> codegen 3 T5:I5,T7:I7;
+for(t2 = 2; t2 <= n; t2++) {
+  s1(1,t2);
+}
+for(t1 = 2; t1 <= n-1; t1++) {
+  for(t2 = 2; t2 <= t1; t2++) {
+    for(t4 = 1; t4 <= t2-1; t4++) {
+      s2(t4,t2,t1);
+    }
+  }
+  for(t2 = t1+1; t2 <= n; t2++) {
+    for(t4 = 1; t4 <= t1-1; t4++) {
+      s2(t4,t2,t1);
+    }
+    s1(t1,t2);
+  }
+}
+for(t2 = 2; t2 <= n; t2++) {
+  for(t4 = 1; t4 <= t2-1; t4++) {
+    s2(t4,t2,n);
+  }
+}
+
+
diff --git a/omega/examples/old_test/lu_spmd b/omega/examples/old_test/lu_spmd
new file mode 100644
index 0000000..6587ef0
--- /dev/null
+++ b/omega/examples/old_test/lu_spmd
@@ -0,0 +1,19 @@
+symbolic n,lb,ub;
+I1 := {[k,i] : 1 <= k < i <= n && lb <= k <= ub};
+I2 := {[k,i,j] : 1 <= k <= i,j <= n && lb <= j <= ub};
+p := {[k,i] : 1, lb <= k <= ub < n && k < i <= n};
+w := {[k,i,j,k,i] : 1 <= k <= i,j <= n && k < lb = j <= ub};
+
+T1 := {[k,i] -> [k,i,0,0,0,0,0,0]};
+T2 := {[k,i,j] -> [k,i,1,j,0,0,0,0]};
+Tp := {[k,i] -> [k,i,0,0,1,0,0,0]};
+Tw := {[k,i,j,t1,t2] -> [k,i,1,j,-1,t1,t2,0]};
+
+known := {[*,*,*,*,*,*,*,*] : 1 <= lb && ub <= n};
+known2 := {[*,*,*,*,*,*,*,*] : 1 <= lb <= ub <= n};
+
+codegen 0 T1:I1,T2:I2,Tp:p,Tw:w given known;
+codegen 1 T1:I1,T2:I2,Tp:p,Tw:w given known;
+# codegen 2 T1:I1,T2:I2,Tp:p,Tw:w given known;
+# codegen 1 T1:I1,T2:I2,Tp:p,Tw:w given known2;
+# codegen 2 T1:I1,T2:I2,Tp:p,Tw:w given known2;
diff --git a/omega/examples/old_test/lu_spmd.oc-rt b/omega/examples/old_test/lu_spmd.oc-rt
new file mode 100644
index 0000000..f221d8e
--- /dev/null
+++ b/omega/examples/old_test/lu_spmd.oc-rt
@@ -0,0 +1,58 @@
+>>> symbolic n,lb,ub;
+>>> I1 := {[k,i] : 1 <= k < i <= n && lb <= k <= ub};
+>>> I2 := {[k,i,j] : 1 <= k <= i,j <= n && lb <= j <= ub};
+>>> p := {[k,i] : 1, lb <= k <= ub < n && k < i <= n};
+>>> w := {[k,i,j,k,i] : 1 <= k <= i,j <= n && k < lb = j <= ub};
+>>> 
+>>> T1 := {[k,i] -> [k,i,0,0,0,0,0,0]};
+>>> T2 := {[k,i,j] -> [k,i,1,j,0,0,0,0]};
+>>> Tp := {[k,i] -> [k,i,0,0,1,0,0,0]};
+>>> Tw := {[k,i,j,t1,t2] -> [k,i,1,j,-1,t1,t2,0]};
+>>> 
+>>> known := {[*,*,*,*,*,*,*,*] : 1 <= lb && ub <= n};
+>>> known2 := {[*,*,*,*,*,*,*,*] : 1 <= lb <= ub <= n};
+>>> 
+>>> codegen 0 T1:I1,T2:I2,Tp:p,Tw:w given known;
+if (lb <= ub) {
+  for(t1 = 1; t1 <= ub; t1++) {
+    for(t2 = t1; t2 <= n; t2++) {
+      if (t1 >= lb && t2 >= t1+1) {
+        s1(t1,t2);
+      }
+      if (ub <= n-1 && t2 >= t1+1 && t1 >= lb) {
+        s3(t1,t2);
+      }
+      for(t4 = max(lb,t1); t4 <= ub; t4++) {
+        if (t4 >= t1+1 && t4 <= lb) {
+          s4(t1,t2,t4,t1,t2);
+        }
+        s2(t1,t2,t4);
+      }
+    }
+  }
+}
+
+>>> codegen 1 T1:I1,T2:I2,Tp:p,Tw:w given known;
+if (lb <= ub) {
+  for(t1 = 1; t1 <= ub; t1++) {
+    for(t2 = t1; t2 <= n; t2++) {
+      if (t1 >= lb && t2 >= t1+1) {
+        s1(t1,t2);
+      }
+      if (ub <= n-1 && t2 >= t1+1 && t1 >= lb) {
+        s3(t1,t2);
+      }
+      for(t4 = max(lb,t1); t4 <= ub; t4++) {
+        if (t4 >= t1+1 && t4 <= lb) {
+          s4(t1,t2,t4,t1,t2);
+        }
+        s2(t1,t2,t4);
+      }
+    }
+  }
+}
+
+>>> # codegen 2 T1:I1,T2:I2,Tp:p,Tw:w given known;
+>>> # codegen 1 T1:I1,T2:I2,Tp:p,Tw:w given known2;
+>>> # codegen 2 T1:I1,T2:I2,Tp:p,Tw:w given known2;
+
diff --git a/omega/examples/old_test/m1 b/omega/examples/old_test/m1
new file mode 100644
index 0000000..1ff50d1
--- /dev/null
+++ b/omega/examples/old_test/m1
@@ -0,0 +1,6 @@
+T1:={[i,j]->[i,j,0]};
+T2:={[i,j]->[i,j,1]};
+R1:={[1:9,1:9]};
+R2:={[5,1:9]};
+codegen T1:R1,T2:R2;
+codegen 2 T1:R1,T2:R2;
diff --git a/omega/examples/old_test/m1.oc-rt b/omega/examples/old_test/m1.oc-rt
new file mode 100644
index 0000000..ad2c49c
--- /dev/null
+++ b/omega/examples/old_test/m1.oc-rt
@@ -0,0 +1,41 @@
+>>> T1:={[i,j]->[i,j,0]};
+>>> T2:={[i,j]->[i,j,1]};
+>>> R1:={[1:9,1:9]};
+>>> R2:={[5,1:9]};
+>>> codegen T1:R1,T2:R2;
+for(t1 = 1; t1 <= 9; t1++) {
+  if (t1 <= 4) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 == 5) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(5,t2);
+      s2(5,t2);
+    }
+  }
+  if (t1 >= 6) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+
+>>> codegen 2 T1:R1,T2:R2;
+for(t1 = 1; t1 <= 4; t1++) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t1,t2);
+  }
+}
+for(t2 = 1; t2 <= 9; t2++) {
+  s1(5,t2);
+  s2(5,t2);
+}
+for(t1 = 6; t1 <= 9; t1++) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t1,t2);
+  }
+}
+
+
diff --git a/omega/examples/old_test/m10 b/omega/examples/old_test/m10
new file mode 100644
index 0000000..01fa540
--- /dev/null
+++ b/omega/examples/old_test/m10
@@ -0,0 +1,5 @@
+IS:={[i,j]: 1 <= i,j <= 9};
+T1:={[i,j]->[4j,i,0]};
+T2:={[i,j]->[2j,i,1]};
+codegen T1:IS,T2:IS;
+codegen 2 T1:IS,T2:IS;
diff --git a/omega/examples/old_test/m10.oc-rt b/omega/examples/old_test/m10.oc-rt
new file mode 100644
index 0000000..c782e1d
--- /dev/null
+++ b/omega/examples/old_test/m10.oc-rt
@@ -0,0 +1,47 @@
+>>> IS:={[i,j]: 1 <= i,j <= 9};
+>>> T1:={[i,j]->[4j,i,0]};
+>>> T2:={[i,j]->[2j,i,1]};
+>>> codegen T1:IS,T2:IS;
+for(t1 = 2; t1 <= 36; t1 += 2) {
+  if (intMod(t1,4) == 0 && t1 <= 16) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+      s2(t2,intDiv(t1,2));
+    }
+  }
+  if (intMod(t1,4) == 0 && t1 >= 20) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+    }
+  }
+  if (intMod(t1-2,4) == 0 && t1 <= 18) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,intDiv(t1,2));
+    }
+  }
+}
+
+>>> codegen 2 T1:IS,T2:IS;
+for(t1 = 2; t1 <= 16; t1 += 2) {
+  if (intMod(t1,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+      s2(t2,intDiv(t1,2));
+    }
+  }
+  if (intMod(t1-2,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,intDiv(t1,2));
+    }
+  }
+}
+for(t2 = 1; t2 <= 9; t2++) {
+  s2(t2,9);
+}
+for(t1 = 20; t1 <= 36; t1 += 4) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,intDiv(t1,4));
+  }
+}
+
+
diff --git a/omega/examples/old_test/m11 b/omega/examples/old_test/m11
new file mode 100644
index 0000000..1367ff8
--- /dev/null
+++ b/omega/examples/old_test/m11
@@ -0,0 +1,10 @@
+symbolic m;
+I := {[p1,p2,c2,a1,a2,b1,b2] :
+	1 <= p1  <= 4 && 1 <= p2 <= 2 && 17p1<=16+2m
+	&& 1<=2c2+p2 <= 6
+	&& 0 <= 10c2+5p2-a2 <= 4
+	&& 0 <= 17p1-2a1 <= 16 && a1 <= 30 && a2-m+a1 <= 1
+	&& 17 <= 2b1-2a1+17p1 <= 18
+	&& b2 = 5 + a2-5p2-5c2};
+I;
+codegen I;
diff --git a/omega/examples/old_test/m11.oc-rt b/omega/examples/old_test/m11.oc-rt
new file mode 100644
index 0000000..4218a2e
--- /dev/null
+++ b/omega/examples/old_test/m11.oc-rt
@@ -0,0 +1,32 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic m;
+# 
+# I := {[p1,p2,c2,a1,a2,b1,b2] :
+# 	1 <= p1  <= 4 && 1 <= p2 <= 2 && 17p1<=16+2m
+# 	&& 1<=2c2+p2 <= 6
+# 	&& 0 <= 10c2+5p2-a2 <= 4
+# 	&& 0 <= 17p1-2a1 <= 16 && a1 <= 30 && a2-m+a1 <= 1
+# 	&& 17 <= 2b1-2a1+17p1 <= 18
+# 	&& b2 = 5 + a2-5p2-5c2};
+# 
+# I;
+
+{[p1,p2,c2,a1,a2,b1,a2-5p2-5c2+5]: 1, -2c2+1 <= p2 <= 2, -2c2+6 && a1 <= 30 && 1 <= p1 && 17p1+2b1 <= 18+2a1 && 17+2a1 <= 17p1+2b1 && a2 <= 5p2+10c2 && 5p2+10c2 <= 4+a2 && 2a1 <= 17p1 && 17p1 <= 16+2a1 && a1+a2 <= 1+m}
+
+# 
+# codegen I;
+for(t1 = 1; t1 <= min(intDiv(2*m+16,17),4); t1++) {
+  for(t2 = 1; t2 <= min(intDiv(2*m-17*t1+26,10),2); t2++) {
+    for(t3 = 0; t3 <= min(intDiv(2*m-10*t2-17*t1+26,20),2); t3++) {
+      for(t4 = intDiv(17*t1-16+1,2); t4 <= min(intDiv(17*t1,2),m-5*t2-10*t3+5,30); t4++) {
+        for(t5 = 5*t2+10*t3-4; t5 <= min(m-t4+1,5*t2+10*t3); t5++) {
+          for(t6 = intDiv(-17*t1+2*t4+17+1,2); t6 <= intDiv(-17*t1+2*t4+18,2); t6++) {
+            s1(t1,t2,t3,t4,t5,t6,t5+-5*t2+-5*t3+5);
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/m12 b/omega/examples/old_test/m12
new file mode 100644
index 0000000..2f1101f
--- /dev/null
+++ b/omega/examples/old_test/m12
@@ -0,0 +1,8 @@
+symbolic n,m;
+I1 := {[1,1:n,1:m,0]};
+I2 := {[2,1:n,0,0]};
+I3 := {[3,1:m,1,1:n]};
+I4 := {[3,1:m,2,1:n]};
+I5 := {[4,1:m,0,0]};
+codegen I1;
+codegen I1,I1,I2,I2,I3,I3,I4,I4,I5,I5;
diff --git a/omega/examples/old_test/m12.oc-rt b/omega/examples/old_test/m12.oc-rt
new file mode 100644
index 0000000..ab5953b
--- /dev/null
+++ b/omega/examples/old_test/m12.oc-rt
@@ -0,0 +1,54 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# I1 := {[1,1:n,1:m,0]};
+# 
+# I2 := {[2,1:n,0,0]};
+# 
+# I3 := {[3,1:m,1,1:n]};
+# 
+# I4 := {[3,1:m,2,1:n]};
+# 
+# I5 := {[4,1:m,0,0]};
+# 
+# codegen I1;
+if (m >= 1) {
+  for(t2 = 1; t2 <= n; t2++) {
+    for(t3 = 1; t3 <= m; t3++) {
+      s1(1,t2,t3,0);
+    }
+  }
+}
+
+# 
+# codegen I1,I1,I2,I2,I3,I3,I4,I4,I5,I5;
+if (m >= 1) {
+  for(t2 = 1; t2 <= n; t2++) {
+    for(t3 = 1; t3 <= m; t3++) {
+      s1(1,t2,t3,0);
+      s2(1,t2,t3,0);
+    }
+  }
+}
+for(t2 = 1; t2 <= n; t2++) {
+  s3(2,t2,0,0);
+  s4(2,t2,0,0);
+}
+if (n >= 1) {
+  for(t2 = 1; t2 <= m; t2++) {
+    for(t4 = 1; t4 <= n; t4++) {
+      s5(3,t2,1,t4);
+      s6(3,t2,1,t4);
+    }
+    for(t4 = 1; t4 <= n; t4++) {
+      s7(3,t2,2,t4);
+      s8(3,t2,2,t4);
+    }
+  }
+}
+for(t2 = 1; t2 <= m; t2++) {
+  s9(4,t2,0,0);
+  s10(4,t2,0,0);
+}
+
+# 
diff --git a/omega/examples/old_test/m2 b/omega/examples/old_test/m2
new file mode 100644
index 0000000..be93f8e
--- /dev/null
+++ b/omega/examples/old_test/m2
@@ -0,0 +1,4 @@
+R1:={[i,j]: 2 <= i,j <= 9};
+R2:={[i,j]: 5 <= i <= 9 & 1 <= j <= 9};
+codegen R1,R2;
+codegen 2 R1,R2;
diff --git a/omega/examples/old_test/m2.oc-rt b/omega/examples/old_test/m2.oc-rt
new file mode 100644
index 0000000..cdd76dd
--- /dev/null
+++ b/omega/examples/old_test/m2.oc-rt
@@ -0,0 +1,35 @@
+>>> R1:={[i,j]: 2 <= i,j <= 9};
+>>> R2:={[i,j]: 5 <= i <= 9 & 1 <= j <= 9};
+>>> codegen R1,R2;
+for(t1 = 2; t1 <= 9; t1++) {
+  if (t1 >= 5) {
+    s2(t1,1);
+  }
+  if (t1 <= 4) {
+    for(t2 = 2; t2 <= 9; t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 >= 5) {
+    for(t2 = 2; t2 <= 9; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+  }
+}
+
+>>> codegen 2 R1,R2;
+for(t1 = 2; t1 <= 4; t1++) {
+  for(t2 = 2; t2 <= 9; t2++) {
+    s1(t1,t2);
+  }
+}
+for(t1 = 5; t1 <= 9; t1++) {
+  s2(t1,1);
+  for(t2 = 2; t2 <= 9; t2++) {
+    s1(t1,t2);
+    s2(t1,t2);
+  }
+}
+
+
diff --git a/omega/examples/old_test/m3 b/omega/examples/old_test/m3
new file mode 100644
index 0000000..e160e8c
--- /dev/null
+++ b/omega/examples/old_test/m3
@@ -0,0 +1,2 @@
+I := {[i,j] : 1 <= i+j,j <= 10};
+codegen I;
diff --git a/omega/examples/old_test/m3.oc-rt b/omega/examples/old_test/m3.oc-rt
new file mode 100644
index 0000000..b466eb9
--- /dev/null
+++ b/omega/examples/old_test/m3.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# I := {[i,j] : 1 <= i+j,j <= 10};
+# 
+# codegen I;
+for(t1 = -9; t1 <= 9; t1++) {
+  for(t2 = max(-t1+1,1); t2 <= min(-t1+10,10); t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/m4 b/omega/examples/old_test/m4
new file mode 100644
index 0000000..d25f961
--- /dev/null
+++ b/omega/examples/old_test/m4
@@ -0,0 +1,11 @@
+T1:={[i,j]->[j,i,0]};
+T2:={[i,j]->[j,i,1]};
+IS:={[i,j]: 1 <= i,j <= 9};
+
+newIS1 := T1 \ IS;
+newIS1;
+newIS2 := T2 \ IS;
+newIS2;
+
+codegen T1:IS,T2:IS;
+codegen 2 T1:IS,T2:IS;
diff --git a/omega/examples/old_test/m4.oc-rt b/omega/examples/old_test/m4.oc-rt
new file mode 100644
index 0000000..d710dce
--- /dev/null
+++ b/omega/examples/old_test/m4.oc-rt
@@ -0,0 +1,28 @@
+>>> T1:={[i,j]->[j,i,0]};
+>>> T2:={[i,j]->[j,i,1]};
+>>> IS:={[i,j]: 1 <= i,j <= 9};
+>>> 
+>>> newIS1 := T1 \ IS;
+>>> newIS1;
+{[i,j] -> [j,i,0] : 1 <= i <= 9 && 1 <= j <= 9}
+>>> newIS2 := T2 \ IS;
+>>> newIS2;
+{[i,j] -> [j,i,1] : 1 <= i <= 9 && 1 <= j <= 9}
+>>> 
+>>> codegen T1:IS,T2:IS;
+for(t1 = 1; t1 <= 9; t1++) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,t1);
+    s2(t2,t1);
+  }
+}
+
+>>> codegen 2 T1:IS,T2:IS;
+for(t1 = 1; t1 <= 9; t1++) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,t1);
+    s2(t2,t1);
+  }
+}
+
+
diff --git a/omega/examples/old_test/m7 b/omega/examples/old_test/m7
new file mode 100644
index 0000000..62c0c64
--- /dev/null
+++ b/omega/examples/old_test/m7
@@ -0,0 +1,6 @@
+T1:={[i,j]->[j,i,0]};
+T2:={[i,j]->[j,i,1]};
+R2:={[i,j]: 1 <= i,j <= 9};
+R3:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 2alpha)};
+codegen T1:R2,T2:R3;
+codegen 2 T1:R2,T2:R3;
diff --git a/omega/examples/old_test/m7.oc-rt b/omega/examples/old_test/m7.oc-rt
new file mode 100644
index 0000000..a98c8a7
--- /dev/null
+++ b/omega/examples/old_test/m7.oc-rt
@@ -0,0 +1,35 @@
+>>> T1:={[i,j]->[j,i,0]};
+>>> T2:={[i,j]->[j,i,1]};
+>>> R2:={[i,j]: 1 <= i,j <= 9};
+>>> R3:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 2alpha)};
+>>> codegen T1:R2,T2:R3;
+for(t1 = 1; t1 <= 9; t1++) {
+  if (intMod(-t1,2) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+      s2(t2,t1);
+    }
+  }
+  if (intMod(-t1-1,2) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+    }
+  }
+}
+
+>>> codegen 2 T1:R2,T2:R3;
+for(t1 = 1; t1 <= 9; t1++) {
+  if (intMod(-t1,2) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+      s2(t2,t1);
+    }
+  }
+  if (intMod(-t1-1,2) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/m8 b/omega/examples/old_test/m8
new file mode 100644
index 0000000..eb6938b
--- /dev/null
+++ b/omega/examples/old_test/m8
@@ -0,0 +1,6 @@
+T1:={[i,j]->[j,i,0]};
+T2:={[i,j]->[j,i,1]};
+R2:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 4alpha)};
+R3:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 2alpha)};
+codegen T1:R2,T2:R3;
+codegen 2 T1:R2,T2:R3;
diff --git a/omega/examples/old_test/m8.oc-rt b/omega/examples/old_test/m8.oc-rt
new file mode 100644
index 0000000..670052b
--- /dev/null
+++ b/omega/examples/old_test/m8.oc-rt
@@ -0,0 +1,35 @@
+>>> T1:={[i,j]->[j,i,0]};
+>>> T2:={[i,j]->[j,i,1]};
+>>> R2:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 4alpha)};
+>>> R3:={[i,j]: 1 <= i,j <= 9 && exists (alpha: j = 2alpha)};
+>>> codegen T1:R2,T2:R3;
+for(t1 = 2; t1 <= 8; t1 += 2) {
+  if (intMod(t1,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+      s2(t2,t1);
+    }
+  }
+  if (intMod(t1-2,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,t1);
+    }
+  }
+}
+
+>>> codegen 2 T1:R2,T2:R3;
+for(t1 = 2; t1 <= 8; t1 += 2) {
+  if (intMod(t1,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,t1);
+      s2(t2,t1);
+    }
+  }
+  if (intMod(t1-2,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,t1);
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/m9 b/omega/examples/old_test/m9
new file mode 100644
index 0000000..fb59381
--- /dev/null
+++ b/omega/examples/old_test/m9
@@ -0,0 +1,5 @@
+IS:={[i,j]: 1 <= i,j <= 9};
+T1:={[i,j]->[2j,i,0]};
+T2:={[i,j]->[2j,i,1]};
+codegen T1:IS,T2:IS;
+codegen 2 T1:IS,T2:IS;
diff --git a/omega/examples/old_test/m9.oc-rt b/omega/examples/old_test/m9.oc-rt
new file mode 100644
index 0000000..c331a0c
--- /dev/null
+++ b/omega/examples/old_test/m9.oc-rt
@@ -0,0 +1,20 @@
+>>> IS:={[i,j]: 1 <= i,j <= 9};
+>>> T1:={[i,j]->[2j,i,0]};
+>>> T2:={[i,j]->[2j,i,1]};
+>>> codegen T1:IS,T2:IS;
+for(t1 = 2; t1 <= 18; t1 += 2) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,intDiv(t1,2));
+    s2(t2,intDiv(t1,2));
+  }
+}
+
+>>> codegen 2 T1:IS,T2:IS;
+for(t1 = 2; t1 <= 18; t1 += 2) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,intDiv(t1,2));
+    s2(t2,intDiv(t1,2));
+  }
+}
+
+
diff --git a/omega/examples/old_test/maximize b/omega/examples/old_test/maximize
new file mode 100644
index 0000000..be13c89
--- /dev/null
+++ b/omega/examples/old_test/maximize
@@ -0,0 +1,7 @@
+symbolic n, f(1);
+
+R0 := {[x] : 1 <= x <= n};
+R1 := {[x] : 1 <= x <= n && f(x) >= 0};
+maximize R0;
+maximize R1;
+R1 intersection maximize R0;
diff --git a/omega/examples/old_test/maximize.oc-rt b/omega/examples/old_test/maximize.oc-rt
new file mode 100644
index 0000000..4f1826e
--- /dev/null
+++ b/omega/examples/old_test/maximize.oc-rt
@@ -0,0 +1,24 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n, f(1);
+# 
+# 
+# R0 := {[x] : 1 <= x <= n};
+# 
+# R1 := {[x] : 1 <= x <= n && f(x) >= 0};
+# 
+# maximize R0;
+
+{[n]: 1 <= n}
+
+# 
+# maximize R1;
+
+{[x]: 1 <= x < n && 0 <= f(x) && UNKNOWN} union
+ {[x]: n = x && 0 <= f(x) && 1 <= x}
+
+# 
+# R1 intersection maximize R0;
+
+{[x]: n = x && 1 <= x && 0 <= f(x)}
+
+# 
diff --git a/omega/examples/old_test/olda b/omega/examples/old_test/olda
new file mode 100644
index 0000000..095388b
--- /dev/null
+++ b/omega/examples/old_test/olda
@@ -0,0 +1,9 @@
+T10:={[mp,mq,mi] -> [mi,mq,mp,0]};
+T20:={[mp,mq,mi] -> [mi,mp,mq,1]};
+
+symbolic np,morb;
+IS10 := {[mp,mq,mi]: 1 <= mp <= np && 1 <= mq <= mp && 1 <= mi <= morb};
+IS20 := IS10;
+
+codegen T10:IS10,T20:IS20;
+codegen 2 T10:IS10,T20:IS20;
diff --git a/omega/examples/old_test/olda.oc-rt b/omega/examples/old_test/olda.oc-rt
new file mode 100644
index 0000000..52e3406
--- /dev/null
+++ b/omega/examples/old_test/olda.oc-rt
@@ -0,0 +1,52 @@
+>>> T10:={[mp,mq,mi] -> [mi,mq,mp,0]};
+>>> T20:={[mp,mq,mi] -> [mi,mp,mq,1]};
+>>> 
+>>> Symbolic np,morb;
+>>> IS10 := {[mp,mq,mi]: 1 <= mp <= np && 1 <= mq <= mp && 1 <= mi <= morb};
+>>> IS20 := IS10;
+>>> 
+>>> codegen T10:IS10,T20:IS20;
+if (np >= 1) {
+  for(t1 = 1; t1 <= morb; t1++) {
+    for(t2 = 1; t2 <= np; t2++) {
+      for(t3 = 1; t3 <= t2-1; t3++) {
+        s2(t2,t3,t1);
+      }
+      s1(t2,t2,t1);
+      s2(t2,t2,t1);
+      for(t3 = t2+1; t3 <= np; t3++) {
+        s1(t3,t2,t1);
+      }
+    }
+  }
+}
+
+>>> codegen 2 T10:IS10,T20:IS20;
+if (np >= 1) {
+  for(t1 = 1; t1 <= morb; t1++) {
+    s1(1,1,t1);
+    s2(1,1,t1);
+    for(t3 = 2; t3 <= np; t3++) {
+      s1(t3,1,t1);
+    }
+    for(t2 = 2; t2 <= np-1; t2++) {
+      for(t3 = 1; t3 <= t2-1; t3++) {
+        s2(t2,t3,t1);
+      }
+      s1(t2,t2,t1);
+      s2(t2,t2,t1);
+      for(t3 = t2+1; t3 <= np; t3++) {
+        s1(t3,t2,t1);
+      }
+    }
+    for(t3 = 1; t3 <= np-1; t3++) {
+      s2(np,t3,t1);
+    }
+    if (np >= 2) {
+      s1(np,np,t1);
+      s2(np,np,t1);
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/p.delft b/omega/examples/old_test/p.delft
new file mode 100644
index 0000000..27840a2
--- /dev/null
+++ b/omega/examples/old_test/p.delft
@@ -0,0 +1,22 @@
+# Generate local code for this HPF code fragment
+# !HPF$ template T(0:150,0:150)
+# !HPF$ align X(I,J) with T(3*I,3*J)
+A := { [i,j] -> [3i,3j] };
+# !HPF$ processors P(0:3, 0:3)
+# !HPF$ distribute
+# !HPF$  T(cyclic(4), cyclic(4)) onto P
+D := { [t1,t2] -> [p1,p2,c1,c2,l1,l2] :
+		t1 = 16c1+4p1+l1 
+		&& t2 = 16c2+4p2+l2 
+		&& 0 <= p1,p2 <= 3
+		&& 0 <= l1,l2 <= 3 };
+#      do I = 0, 14
+#         Y(I,I) = 1.0
+#      enddo
+I := { [i] : 0 <= i <= 14 };
+X := { [i] -> [i,i] };
+R := D(A(X(I)));
+R;
+symbolic P1,P2;
+selectLocal := {[P1,P2,c1,c2,l1,l2] -> [c1,c2,l1,l2]};
+codegen selectLocal(R);
diff --git a/omega/examples/old_test/p.delft.oc-rt b/omega/examples/old_test/p.delft.oc-rt
new file mode 100644
index 0000000..d59a886
--- /dev/null
+++ b/omega/examples/old_test/p.delft.oc-rt
@@ -0,0 +1,43 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # Generate local code for this HPF code fragment
+# # !HPF$ template T(0:150,0:150)
+# # !HPF$ align X(I,J) with T(3*I,3*J)
+# A := { [i,j] -> [3i,3j] };
+# 
+# # !HPF$ processors P(0:3, 0:3)
+# # !HPF$ distribute
+# # !HPF$  T(cyclic(4), cyclic(4)) onto P
+# D := { [t1,t2] -> [p1,p2,c1,c2,l1,l2] :
+# 		t1 = 16c1+4p1+l1 
+# 		&& t2 = 16c2+4p2+l2 
+# 		&& 0 <= p1,p2 <= 3
+# 		&& 0 <= l1,l2 <= 3 };
+# 
+# #      do I = 0, 14
+# #         Y(I,I) = 1.0
+# #      enddo
+# I := { [i] : 0 <= i <= 14 };
+# 
+# X := { [i] -> [i,i] };
+# 
+# R := D(A(X(I)));
+# 
+# R;
+
+{[p1,p1,c1,c1,l1,l1]: Exists ( alpha : p1+l1+c1 = 3alpha && 0 <= p1 <= -4c1+10, 3 && 0 <= l1 <= 3 && 0 <= c1)}
+
+# 
+# symbolic P1,P2;
+# 
+# selectLocal := {[P1,P2,c1,c2,l1,l2] -> [c1,c2,l1,l2]};
+# 
+# codegen selectLocal(R);
+if (P1 == P2 && P1 >= 0 && P1 <= 3) {
+  for(t1 = 0; t1 <= min(-P1+4,2); t1++) {
+    for(t3 = intMod((-P1-t1),3); t3 <= 3; t3 += 3) {
+      s1(t1,t1,t3,t3);
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/p.delft2 b/omega/examples/old_test/p.delft2
new file mode 100644
index 0000000..32e5da0
--- /dev/null
+++ b/omega/examples/old_test/p.delft2
@@ -0,0 +1,24 @@
+# Compute Sends and receives for the following HPF fragment
+
+I := { [i,j] : 1 <= i <= 14 && 0 <= j <= 14 };
+X := { [i,j] -> [3i,3j] };
+Y := { [i,j] -> [i',3j] : 3i-1 <= i'<= 3i};
+A := { [i,j] -> [3i,3j] };
+D := { [t1,t2] -> [p1,p2,c1,c2,l1,l2] :
+		t1 = 16c1+4p1+l1 
+		&& t2 = 16c2+4p2+l2 
+		&& 0 <= p1,p2 <= 3
+		&& 0 <= l1,l2 <= 3 };
+P := { [p1,p2,c1,c2,l1,l2] -> [p1,p2]};
+C := { [p1,p2,c1,c2,l1,l2] -> [p1,p2,c1,c2]};
+own := P(D(A(X))) \I;
+own;
+need := D(A(Y)) \I;
+need;
+different := {[p1,p2] -> [q1,q2,c1,c2,l1,l2] : p1 != q1 || p2 != q2};
+ship := (need compose (inverse own) ) intersection different;
+symbolic P1,P2;
+P := {[P1,P2]};
+S := range (ship \ P);
+S;
+codegen S;
diff --git a/omega/examples/old_test/p.delft2.oc-rt b/omega/examples/old_test/p.delft2.oc-rt
new file mode 100644
index 0000000..3ee662e
--- /dev/null
+++ b/omega/examples/old_test/p.delft2.oc-rt
@@ -0,0 +1,80 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # Compute Sends and receives for the following HPF fragment
+# 
+# I := { [i,j] : 1 <= i <= 14 && 0 <= j <= 14 };
+# 
+# X := { [i,j] -> [3i,3j] };
+# 
+# Y := { [i,j] -> [i',3j] : 3i-1 <= i'<= 3i};
+# 
+# A := { [i,j] -> [3i,3j] };
+# 
+# D := { [t1,t2] -> [p1,p2,c1,c2,l1,l2] :
+# 		t1 = 16c1+4p1+l1 
+# 		&& t2 = 16c2+4p2+l2 
+# 		&& 0 <= p1,p2 <= 3
+# 		&& 0 <= l1,l2 <= 3 };
+# 
+# P := { [p1,p2,c1,c2,l1,l2] -> [p1,p2]};
+# 
+# C := { [p1,p2,c1,c2,l1,l2] -> [p1,p2,c1,c2]};
+# 
+# own := P(D(A(X))) \I;
+# 
+# own;
+
+{[i,j] -> [p1,p2] : Exists ( alpha,beta : 1 <= i <= 14 && 0 <= j <= 14 && 0 <= p1 <= 3 && 0 <= p2 <= 3 && 4p1+16alpha <= 9i && 4p2+16beta <= 9j && 9i <= 3+4p1+16alpha && 9j <= 3+4p2+16beta)}
+
+# 
+# need := D(A(Y)) \I;
+# 
+# need;
+
+{[i,j] -> [p1,p2,c1,c2,l1,9j-4p2-16c2] : Exists ( alpha : p1+c1+l1 = 3alpha && 1 <= i <= 14 && 0 <= j <= 14 && 0 <= p1 <= 3 && 0 <= p2 <= 3 && 0 <= l1 <= 3 && 4p2+16c2 <= 9j && 9j <= 3+4p2+16c2 && 9i <= 3+4p1+16c1+l1 && 4p1+16c1+l1 <= 9i)}
+
+# 
+# different := {[p1,p2] -> [q1,q2,c1,c2,l1,l2] : p1 != q1 || p2 != q2};
+# 
+# ship := (need compose (inverse own) ) intersection different;
+# 
+# symbolic P1,P2;
+# 
+# P := {[P1,P2]};
+# 
+# S := range (ship \ P);
+# 
+# S;
+
+{[3,P2,c1,c2,l1,l2]: Exists ( alpha,beta,gamma : 4P2+l2 = 2c2+9beta && l1+c1 = 3alpha && 0 <= P1 <= -4c1+27 && 0 <= P2 <= 3 && -16c1-6 <= l1 <= 3 && 0 <= l2 <= 3 && 0 <= c2 && 4P2+l2+16c2 <= 126 && 9gamma <= 15+l1+16c1 && 16+4P1+16c1 <= 9gamma)} union
+ {[In_1,P2,c1,c2,l1,l2]: Exists ( alpha,beta,gamma : 4P2+l2 = 2c2+9beta && In_1+c1+l1 = 3alpha && 0 <= In_1 < P1 <= -4c1+31, 3 && 0 <= P2 <= 3 && 0 <= l2 <= 3 && l1 <= 3 && 6 <= 4In_1+16c1+l1 && 4P1+16c1 <= 9gamma && 0 <= 4P2+l2+16c2 && 4P2+l2+16c2 <= 126 && 9gamma <= 3+4In_1+16c1+l1)}
+
+# 
+# codegen S;
+if (P1 >= 1 && P2 >= 0 && P1 <= 3 && P2 <= 3) {
+  for(t3 = intDiv(-P1+2+3,4); t3 <= 7; t3++) {
+    for(t4 = 0; t4 <= 7; t4++) {
+      for(t5 = 1+intMod(((-P1-t3+1)-1),3); t5 <= 3; t5 += 3) {
+        if (intMod(4*P1-2*t3+t5-1,9) == 0) {
+          for(t6 = intMod((-4*P2+2*t4),9); t6 <= 3; t6 += 9) {
+            s1(P1-1,P2,t3,t4,t5,t6);
+          }
+        }
+      }
+    }
+  }
+}
+if (P1 == 0 && P2 >= 0 && P2 <= 3) {
+  for(t3 = 0; t3 <= 6; t3++) {
+    for(t4 = 0; t4 <= 7; t4++) {
+      for(t5 = 1+intMod((-t3-1),3); t5 <= 3; t5 += 3) {
+        if (4*t5 == -t3+12) {
+          for(t6 = intMod((-4*P2+2*t4),9); t6 <= 3; t6 += 9) {
+            s1(3,P2,-4*t5+12,t4,t5,t6);
+          }
+        }
+      }
+    }
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/p.delft3 b/omega/examples/old_test/p.delft3
new file mode 100644
index 0000000..b2321f1
--- /dev/null
+++ b/omega/examples/old_test/p.delft3
@@ -0,0 +1,20 @@
+Hull {[p1,p2] -> [p1-1,p2,Out_3,Out_4] : 
+exists ( alpha,gamma : 
+1 <= p1 <= 3 
+&& 0 <= p2 <= 3 
+&& -2Out_4+1 <= alpha <= -2Out_4+14 
+&& -2Out_3+1 <= gamma <= -2Out_3+14 
+&& 4p1 <= 2Out_3+9gamma 
+&& 4p2 <= 2Out_4+9alpha 
+&& 2Out_3+9gamma <= 2+4p1 
+&& 2Out_4+9alpha <= 3+4p2)};
+
+Hull {[0,p2] -> [3,p2,Out_3,Out_4] : 
+exists (alpha,gamma : 
+Out_3+4alpha = 0 
+&& 0 <= p2 <= 3 
+&& 0 <= Out_3 <= 4 
+&& -2Out_4+1 <= gamma <= -2Out_4+14 
+&& 4p2 <= 2Out_4+9gamma 
+&& 2Out_4+9gamma <= 3+4p2)};
+
diff --git a/omega/examples/old_test/p.delft3.oc-rt b/omega/examples/old_test/p.delft3.oc-rt
new file mode 100644
index 0000000..6f85d83
--- /dev/null
+++ b/omega/examples/old_test/p.delft3.oc-rt
@@ -0,0 +1,29 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# hull {[p1,p2] -> [p1-1,p2,Out_3,Out_4] : 
+# Exists ( alpha,gamma : 
+# 1 <= p1 <= 3 
+# && 0 <= p2 <= 3 
+# && -2Out_4+1 <= alpha <= -2Out_4+14 
+# && -2Out_3+1 <= gamma <= -2Out_3+14 
+# && 4p1 <= 2Out_3+9gamma 
+# && 4p2 <= 2Out_4+9alpha 
+# && 2Out_3+9gamma <= 2+4p1 
+# && 2Out_4+9alpha <= 3+4p2)};
+
+{[p1,p2] -> [p1-1,p2,Out_3,Out_4] : 1, -4Out_3+2 <= p1 <= 3 && 0, -4Out_4+2 <= p2 <= 3 && Out_3 <= 7 && Out_4 <= 7}
+
+# 
+# 
+# hull {[0,p2] -> [3,p2,Out_3,Out_4] : 
+# Exists (alpha,gamma : 
+# Out_3+4alpha = 0 
+# && 0 <= p2 <= 3 
+# && 0 <= Out_3 <= 4 
+# && -2Out_4+1 <= gamma <= -2Out_4+14 
+# && 4p2 <= 2Out_4+9gamma 
+# && 2Out_4+9gamma <= 3+4p2)};
+
+{[0,p2] -> [3,p2,Out_3,Out_4] : 0, -4Out_4+2 <= p2 <= 3 && 0 <= Out_3 <= 4 && Out_4 <= 7}
+
+# 
+# 
diff --git a/omega/examples/old_test/p.subset b/omega/examples/old_test/p.subset
new file mode 100644
index 0000000..3c8894c
--- /dev/null
+++ b/omega/examples/old_test/p.subset
@@ -0,0 +1,3 @@
+{ [i] -> [j] : 1 <= i <= 9 } subset { [i] -> [j] : 1 <= i <= 11 };
+
+{ [i] -> [j] : 1 <= i <= 9 } subset { [i] -> [j] : 1 <= i <= 7 };
diff --git a/omega/examples/old_test/p.subset.oc-rt b/omega/examples/old_test/p.subset.oc-rt
new file mode 100644
index 0000000..b35b90f
--- /dev/null
+++ b/omega/examples/old_test/p.subset.oc-rt
@@ -0,0 +1,10 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# { [i] -> [j] : 1 <= i <= 9 } subset { [i] -> [j] : 1 <= i <= 11 };
+
+True
+# 
+# 
+# { [i] -> [j] : 1 <= i <= 9 } subset { [i] -> [j] : 1 <= i <= 7 };
+
+False
+# 
diff --git a/omega/examples/old_test/p1 b/omega/examples/old_test/p1
new file mode 100644
index 0000000..0f29643
--- /dev/null
+++ b/omega/examples/old_test/p1
@@ -0,0 +1 @@
+{ [i] -> [j] : 1 <= i < j <= 20 };
diff --git a/omega/examples/old_test/p1.oc-rt b/omega/examples/old_test/p1.oc-rt
new file mode 100644
index 0000000..3151bd6
--- /dev/null
+++ b/omega/examples/old_test/p1.oc-rt
@@ -0,0 +1,6 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# { [i] -> [j] : 1 <= i < j <= 20 };
+
+{[i] -> [j] : 1 <= i < j <= 20}
+
+# 
diff --git a/omega/examples/old_test/p10 b/omega/examples/old_test/p10
new file mode 100644
index 0000000..c802845
--- /dev/null
+++ b/omega/examples/old_test/p10
@@ -0,0 +1 @@
+{[i,j,k,l,m] -> [i,i,i,i,i] : 1 <= i <= 100 };
diff --git a/omega/examples/old_test/p10.oc-rt b/omega/examples/old_test/p10.oc-rt
new file mode 100644
index 0000000..e10a453
--- /dev/null
+++ b/omega/examples/old_test/p10.oc-rt
@@ -0,0 +1,6 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# {[i,j,k,l,m] -> [i,i,i,i,i] : 1 <= i <= 100 };
+
+{[i,j,k,l,m] -> [i,i,i,i,i] : 1 <= i <= 100}
+
+# 
diff --git a/omega/examples/old_test/p11 b/omega/examples/old_test/p11
new file mode 100644
index 0000000..1871c82
--- /dev/null
+++ b/omega/examples/old_test/p11
@@ -0,0 +1,10 @@
+{[i] : 1 <= i <=  10
+	&& ! i = 3
+	&& ! i = 2
+	&& ! i = 4
+	&& ! i = 7
+	&& ! i = 6
+	&& ! i = 8
+};
+
+
diff --git a/omega/examples/old_test/p11.oc-rt b/omega/examples/old_test/p11.oc-rt
new file mode 100644
index 0000000..04641f2
--- /dev/null
+++ b/omega/examples/old_test/p11.oc-rt
@@ -0,0 +1,17 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# {[i] : 1 <= i <=  10
+# 	&& ! i = 3
+# 	&& ! i = 2
+# 	&& ! i = 4
+# 	&& ! i = 7
+# 	&& ! i = 6
+# 	&& ! i = 8
+# };
+
+{[1]} union
+ {[5]} union
+ {[i]: 9 <= i <= 10}
+
+# 
+# 
+# 
diff --git a/omega/examples/old_test/p12 b/omega/examples/old_test/p12
new file mode 100644
index 0000000..ffe4b1d
--- /dev/null
+++ b/omega/examples/old_test/p12
@@ -0,0 +1,7 @@
+symbolic n,m;
+T := { [i,j] -> [i-1,j] : 1 <= i <= n && 0 <= j <= m } union
+     { [i,j] -> [i,j-1] : 0 <= i <= n && 1 <= j <= m };
+T;
+T+;
+Inverse ( (Inverse T)+);
+T@;
diff --git a/omega/examples/old_test/p12.oc-rt b/omega/examples/old_test/p12.oc-rt
new file mode 100644
index 0000000..51df294
--- /dev/null
+++ b/omega/examples/old_test/p12.oc-rt
@@ -0,0 +1,33 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n,m;
+# 
+# T := { [i,j] -> [i-1,j] : 1 <= i <= n && 0 <= j <= m } union
+#      { [i,j] -> [i,j-1] : 0 <= i <= n && 1 <= j <= m };
+# 
+# T;
+
+{[i,j] -> [i-1,j] : 1 <= i <= n && 0 <= j <= m} union
+ {[i,j] -> [i,j-1] : 0 <= i <= n && 1 <= j <= m}
+
+# 
+# T+;
+
+{[i,0] -> [i',0] : m = 0 && 0 <= i' < i <= n} union
+ {[0,j] -> [0,j'] : n = 0 && 0 <= j' < j <= m} union
+ {[i,j] -> [i',j'] : 0 <= i' < i <= n && 0 <= j' <= j <= m && 1 <= m} union
+ {[i,j] -> [i,j'] : 0 <= j' < j <= m && 0 <= i <= n && 1 <= n}
+
+# 
+# Inverse ( (Inverse T)+);
+
+{[i,0] -> [i',0] : m = 0 && 0 <= i' < i <= n} union
+ {[0,j] -> [0,j'] : n = 0 && 0 <= j' < j <= m} union
+ {[i,j] -> [i',j'] : 0 <= i' < i <= n && 0 <= j' <= j <= m && 1 <= m} union
+ {[i,j] -> [i,j'] : 0 <= j' < j <= m && 0 <= i <= n && 1 <= n}
+
+# 
+# T@;
+
+{[In_1,In_2] -> [Out_1,Out_2] : Out_1 <= In_1 && Out_2 <= In_2 && In_2 <= m+Out_2 && In_1 <= n+Out_1}
+
+# 
diff --git a/omega/examples/old_test/p13 b/omega/examples/old_test/p13
new file mode 100644
index 0000000..28ca23c
--- /dev/null
+++ b/omega/examples/old_test/p13
@@ -0,0 +1,3 @@
+T := { [d1, -1] : d1 > 0 };
+T;
+farkas T;
diff --git a/omega/examples/old_test/p13.oc-rt b/omega/examples/old_test/p13.oc-rt
new file mode 100644
index 0000000..b52c4d6
--- /dev/null
+++ b/omega/examples/old_test/p13.oc-rt
@@ -0,0 +1,13 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# T := { [d1, -1] : d1 > 0 };
+# 
+# T;
+
+{[d1,-1]: 1 <= d1}
+
+# 
+# farkas T;
+
+{[d1,In_2]: 0 <= d1 && In_2 <= constantTerm+d1}
+
+# 
diff --git a/omega/examples/old_test/p2 b/omega/examples/old_test/p2
new file mode 100644
index 0000000..b880627
--- /dev/null
+++ b/omega/examples/old_test/p2
@@ -0,0 +1 @@
+{ [i,j] -> [i+1,j+1] : 1 <= i <= 9 && 5 <= j <= 25 };
diff --git a/omega/examples/old_test/p2.oc-rt b/omega/examples/old_test/p2.oc-rt
new file mode 100644
index 0000000..0d4f77c
--- /dev/null
+++ b/omega/examples/old_test/p2.oc-rt
@@ -0,0 +1,6 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# { [i,j] -> [i+1,j+1] : 1 <= i <= 9 && 5 <= j <= 25 };
+
+{[i,j] -> [i+1,j+1] : 1 <= i <= 9 && 5 <= j <= 25}
+
+# 
diff --git a/omega/examples/old_test/p3 b/omega/examples/old_test/p3
new file mode 100644
index 0000000..226a619
--- /dev/null
+++ b/omega/examples/old_test/p3
@@ -0,0 +1,2 @@
+symbolic n;
+{ [i] -> [i+1] : 1 <= i <= n }+;
diff --git a/omega/examples/old_test/p3.oc-rt b/omega/examples/old_test/p3.oc-rt
new file mode 100644
index 0000000..03c8ebb
--- /dev/null
+++ b/omega/examples/old_test/p3.oc-rt
@@ -0,0 +1,8 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# { [i] -> [i+1] : 1 <= i <= n }+;
+
+{[i] -> [Out_1] : 1 <= i < Out_1 <= n+1}
+
+# 
diff --git a/omega/examples/old_test/p4 b/omega/examples/old_test/p4
new file mode 100644
index 0000000..2fcd2aa
--- /dev/null
+++ b/omega/examples/old_test/p4
@@ -0,0 +1,5 @@
+inverse { [i] -> [i+1] : 1 <= i <= 9 };
+domain { [i] -> [i+1] : 1 <= i <= 9 };
+range { [i] -> [i+1] : 1 <= i <= 9 };
+{ [i] -> [i+1] : 1 <= i <= 9 } compose { [i] -> [i+1] : 1 <= i <= 9 };
+
diff --git a/omega/examples/old_test/p4.oc-rt b/omega/examples/old_test/p4.oc-rt
new file mode 100644
index 0000000..020d1d2
--- /dev/null
+++ b/omega/examples/old_test/p4.oc-rt
@@ -0,0 +1,22 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# inverse { [i] -> [i+1] : 1 <= i <= 9 };
+
+{[In_1] -> [In_1-1] : 2 <= In_1 <= 10}
+
+# 
+# domain { [i] -> [i+1] : 1 <= i <= 9 };
+
+{[i]: 1 <= i <= 9}
+
+# 
+# range { [i] -> [i+1] : 1 <= i <= 9 };
+
+{[In_1]: 2 <= In_1 <= 10}
+
+# 
+# { [i] -> [i+1] : 1 <= i <= 9 } compose { [i] -> [i+1] : 1 <= i <= 9 };
+
+{[i] -> [i+2] : 1 <= i <= 8}
+
+# 
+# 
diff --git a/omega/examples/old_test/p5 b/omega/examples/old_test/p5
new file mode 100644
index 0000000..ae7b242
--- /dev/null
+++ b/omega/examples/old_test/p5
@@ -0,0 +1,8 @@
+symbolic n;
+{[iw] -> [ir]  : 
+	1 <= iw, ir <= 2n and iw=ir 
+	and ! exists ( ik,jk : 1 <= ik <= 2n && 1 <= jk < n and
+			iw <= ik = ir and 2jk = ir )
+	and ! exists ( ik,jk : 1 <= ik <= 2n && 1 <= jk < n and
+			iw <= ik = ir and 2jk+1 = ir )
+	};
diff --git a/omega/examples/old_test/p5.oc-rt b/omega/examples/old_test/p5.oc-rt
new file mode 100644
index 0000000..ef73886
--- /dev/null
+++ b/omega/examples/old_test/p5.oc-rt
@@ -0,0 +1,16 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# {[iw] -> [ir]  : 
+# 	1 <= iw, ir <= 2n and iw=ir 
+# 	and ! exists ( ik,jk : 1 <= ik <= 2n && 1 <= jk < n and
+# 			iw <= ik = ir and 2jk = ir )
+# 	and ! exists ( ik,jk : 1 <= ik <= 2n && 1 <= jk < n and
+# 			iw <= ik = ir and 2jk+1 = ir )
+# 	};
+
+{[iw] -> [iw] : n = 1 && 1 <= iw <= 2} union
+ {[2n] -> [2n] : 2 <= n} union
+ {[1] -> [1] : 2 <= n}
+
+# 
diff --git a/omega/examples/old_test/p6 b/omega/examples/old_test/p6
new file mode 100644
index 0000000..f09634a
--- /dev/null
+++ b/omega/examples/old_test/p6
@@ -0,0 +1,25 @@
+R := { [i] -> [i'] : 1 <= i,i' <= 10 && i' = i+1 };
+R;
+inverse R;
+domain R;
+range R;
+R compose R;
+R+;             # closure of R = R union (R compose R) union (R compose R ...
+complement R;
+S := {[i] : 5 <= i <= 25};
+S;
+R(S);           # apply R to S
+R \ S;          # restrict domain of R to S
+R / S;          # restrict range of R to S
+(R\S) union (R/S);
+(R\S) intersection (R/S);
+(R/S) - (R\S);
+S*S;            # cross product 
+D := S - {[9:16:2]} - {[17:19]};
+D;
+T :=  { [i] : 1 <= i <= 11 & exists (a : i = 2a) };
+T;
+Hull T;
+Hull D;
+codegen D;
+codegen {[i,j] : 1 <= i+j,j <= 10};
diff --git a/omega/examples/old_test/p6.oc-rt b/omega/examples/old_test/p6.oc-rt
new file mode 100644
index 0000000..109e029
--- /dev/null
+++ b/omega/examples/old_test/p6.oc-rt
@@ -0,0 +1,129 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i] -> [i'] : 1 <= i,i' <= 10 && i' = i+1 };
+# 
+# R;
+
+{[i] -> [i+1] : 1 <= i <= 9}
+
+# 
+# inverse R;
+
+{[i] -> [i-1] : 2 <= i <= 10}
+
+# 
+# domain R;
+
+{[i]: 1 <= i <= 9}
+
+# 
+# range R;
+
+{[i]: 2 <= i <= 10}
+
+# 
+# R compose R;
+
+{[i] -> [i+2] : 1 <= i <= 8}
+
+# 
+# R+;
+
+{[i] -> [i'] : 1 <= i < i' <= 10}
+
+#              # closure of R = R union (R compose R) union (R compose R ...
+# complement R;
+
+{[i] -> [i'] : i <= 0} union
+ {[i] -> [i'] : 10 <= i} union
+ {[i] -> [i'] : 1 <= i <= 9, i'-2} union
+ {[i] -> [i'] : 1, i' <= i <= 9}
+
+# 
+# S := {[i] : 5 <= i <= 25};
+# 
+# S;
+
+{[i]: 5 <= i <= 25}
+
+# 
+# R(S);
+
+{[i]: 6 <= i <= 10}
+
+#            # apply R to S
+# R \ S;
+
+{[i] -> [i+1] : 5 <= i <= 9}
+
+#           # restrict domain of R to S
+# R / S;
+
+{[i] -> [i+1] : 4 <= i <= 9}
+
+#           # restrict range of R to S
+# (R\S) union (R/S);
+
+{[i] -> [i+1] : 4 <= i <= 9}
+
+# 
+# (R\S) intersection (R/S);
+
+{[i] -> [i+1] : 5 <= i <= 9}
+
+# 
+# (R/S) - (R\S);
+
+{[4] -> [5] }
+
+# 
+# S*S;
+
+{[i] -> [i'] : 5 <= i <= 25 && 5 <= i' <= 25}
+
+#             # cross product 
+# D := S - {[9:16:2]} - {[17:19]};
+# 
+# D;
+
+{[i]: 5 <= i <= 8} union
+ {[i]: Exists ( alpha : 2alpha = i && 10 <= i <= 16)} union
+ {[i]: 20 <= i <= 25}
+
+# 
+# T :=  { [i] : 1 <= i <= 11 & exists (a : i = 2a) };
+# 
+# T;
+
+{[i]: Exists ( alpha : 2alpha = i && 2 <= i <= 10)}
+
+# 
+# Hull T;
+
+{[i]: 2 <= i <= 10}
+
+# 
+# Hull D;
+
+{[i]: 5 <= i <= 25}
+
+# 
+# codegen D;
+for(t1 = 5; t1 <= 8; t1++) {
+  s1(t1);
+}
+for(t1 = 10; t1 <= 16; t1 += 2) {
+  s1(t1);
+}
+for(t1 = 20; t1 <= 25; t1++) {
+  s1(t1);
+}
+
+# 
+# codegen {[i,j] : 1 <= i+j,j <= 10};
+for(t1 = -9; t1 <= 9; t1++) {
+  for(t2 = max(-t1+1,1); t2 <= min(-t1+10,10); t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/p7 b/omega/examples/old_test/p7
new file mode 100644
index 0000000..d892912
--- /dev/null
+++ b/omega/examples/old_test/p7
@@ -0,0 +1 @@
+{ [i] -> [j] : 1 <= i,j <= 10 and i != j};
diff --git a/omega/examples/old_test/p7.oc-rt b/omega/examples/old_test/p7.oc-rt
new file mode 100644
index 0000000..af7cf5f
--- /dev/null
+++ b/omega/examples/old_test/p7.oc-rt
@@ -0,0 +1,7 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# { [i] -> [j] : 1 <= i,j <= 10 and i != j};
+
+{[i] -> [j] : 1 <= j < i <= 10} union
+ {[i] -> [j] : 1 <= i < j <= 10}
+
+# 
diff --git a/omega/examples/old_test/p8 b/omega/examples/old_test/p8
new file mode 100644
index 0000000..d6031ad
--- /dev/null
+++ b/omega/examples/old_test/p8
@@ -0,0 +1,6 @@
+R1 := {[i] -> [j] : i < j};
+R2 := {[x] -> [y] : x < y};
+inverse R2;
+R1 union R2;
+R2(R1);
+
diff --git a/omega/examples/old_test/p8.oc-rt b/omega/examples/old_test/p8.oc-rt
new file mode 100644
index 0000000..b9d569a
--- /dev/null
+++ b/omega/examples/old_test/p8.oc-rt
@@ -0,0 +1,21 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R1 := {[i] -> [j] : i < j};
+# 
+# R2 := {[x] -> [y] : x < y};
+# 
+# inverse R2;
+
+{[y] -> [x] : x < y}
+
+# 
+# R1 union R2;
+
+{[In_1] -> [Out_1] : In_1 < Out_1}
+
+# 
+# R2(R1);
+
+{[i] -> [y] : i <= y-2}
+
+# 
+# 
diff --git a/omega/examples/old_test/p9 b/omega/examples/old_test/p9
new file mode 100644
index 0000000..8f38d36
--- /dev/null
+++ b/omega/examples/old_test/p9
@@ -0,0 +1,7 @@
+symbolic lot_E;
+{[k_w,l_w] -> [k_r,l_r] : 
+1 <= k_r <= 12 and 
+1 <= l_r <= lot_E and 
+2k_r+96l_r = 12+2k_w+96l_w and 
+1 <= k_w <= 3 and 
+1 <= l_w <= lot_E};
diff --git a/omega/examples/old_test/p9.oc-rt b/omega/examples/old_test/p9.oc-rt
new file mode 100644
index 0000000..b3e1f55
--- /dev/null
+++ b/omega/examples/old_test/p9.oc-rt
@@ -0,0 +1,13 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic lot_E;
+# 
+# {[k_w,l_w] -> [k_r,l_r] : 
+# 1 <= k_r <= 12 and 
+# 1 <= l_r <= lot_E and 
+# 2k_r+96l_r = 12+2k_w+96l_w and 
+# 1 <= k_w <= 3 and 
+# 1 <= l_w <= lot_E};
+
+{[k_w,l_w] -> [k_w+6,l_w] : 1 <= k_w <= 3 && 1 <= l_w <= lot_E}
+
+# 
diff --git a/omega/examples/old_test/pufs1 b/omega/examples/old_test/pufs1
new file mode 100644
index 0000000..908c84f
--- /dev/null
+++ b/omega/examples/old_test/pufs1
@@ -0,0 +1,2 @@
+symbolic n(1);
+{ [i] -> [j] : 1 <= i  <= j <= 100 && n(i) != n(j)};
diff --git a/omega/examples/old_test/pufs1.oc-rt b/omega/examples/old_test/pufs1.oc-rt
new file mode 100644
index 0000000..0a7312f
--- /dev/null
+++ b/omega/examples/old_test/pufs1.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1);
+# 
+# { [i] -> [j] : 1 <= i  <= j <= 100 && n(i) != n(j)};
+
+{[i] -> [j] : 1 <= i < j <= 100 && n(j) < n(i)} union
+ {[i] -> [j] : 1 <= i < j <= 100 && n(i) < n(j)}
+
+# 
diff --git a/omega/examples/old_test/pufs2 b/omega/examples/old_test/pufs2
new file mode 100644
index 0000000..391c9d4
--- /dev/null
+++ b/omega/examples/old_test/pufs2
@@ -0,0 +1,9 @@
+symbolic n(1);
+R := { [i] -> [j] : 1 <= i = j <= 100 && n(i) <= n(j)};
+S := { [i] -> [j] : 1 <= i <= j <= 100 && n(i) = n(j)};
+
+R;
+S;
+R intersection S;
+R union S;
+R intersection complement S;
diff --git a/omega/examples/old_test/pufs2.oc-rt b/omega/examples/old_test/pufs2.oc-rt
new file mode 100644
index 0000000..b71d651
--- /dev/null
+++ b/omega/examples/old_test/pufs2.oc-rt
@@ -0,0 +1,35 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1);
+# 
+# R := { [i] -> [j] : 1 <= i = j <= 100 && n(i) <= n(j)};
+# 
+# S := { [i] -> [j] : 1 <= i <= j <= 100 && n(i) = n(j)};
+# 
+# 
+# R;
+
+{[i] -> [i] : 1 <= i <= 100}
+
+# 
+# S;
+
+{[i] -> [i] : 1 <= i <= 100} union
+ {[i] -> [j] : n(j) = n(i) && 1 <= i < j <= 100}
+
+# 
+# R intersection S;
+
+{[i] -> [i] : 1 <= i <= 100}
+
+# 
+# R union S;
+
+{[i] -> [j] : n(j) = n(i) && 1 <= i < j <= 100} union
+ {[i] -> [i] : 1 <= i <= 100}
+
+# 
+# R intersection complement S;
+
+{[i] -> [j]  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/pufs3 b/omega/examples/old_test/pufs3
new file mode 100644
index 0000000..0a1af56
--- /dev/null
+++ b/omega/examples/old_test/pufs3
@@ -0,0 +1,8 @@
+symbolic n(1);
+R := { [i] -> [j] : 1 <= i = j <= 100 && n(i) <= n(j)};
+S := { [i] -> [j] : 1 <= i <= j <= 100 && n(i) = n(j)};
+
+R intersection complement S;
+inverse R;
+inverse S;
+inverse S intersection complement inverse R;
diff --git a/omega/examples/old_test/pufs3.oc-rt b/omega/examples/old_test/pufs3.oc-rt
new file mode 100644
index 0000000..55f851c
--- /dev/null
+++ b/omega/examples/old_test/pufs3.oc-rt
@@ -0,0 +1,29 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1);
+# 
+# R := { [i] -> [j] : 1 <= i = j <= 100 && n(i) <= n(j)};
+# 
+# S := { [i] -> [j] : 1 <= i <= j <= 100 && n(i) = n(j)};
+# 
+# 
+# R intersection complement S;
+
+{[i] -> [j]  : FALSE }
+
+# 
+# inverse R;
+
+{[j] -> [j] : 1 <= j <= 100}
+
+# 
+# inverse S;
+
+{[j] -> [j] : 1 <= j <= 100} union
+ {[j] -> [i] : n(j) = n(i) && 1 <= i < j <= 100}
+
+# 
+# inverse S intersection complement inverse R;
+
+{[j] -> [i] : n(j) = n(i) && 1 <= i < j <= 100}
+
+# 
diff --git a/omega/examples/old_test/pufs4 b/omega/examples/old_test/pufs4
new file mode 100644
index 0000000..57e868e
--- /dev/null
+++ b/omega/examples/old_test/pufs4
@@ -0,0 +1,16 @@
+# Calculate exposed reads for this code fragment
+# for i := 1 to n do
+#   for j := 1 to m do
+#      if p(i,j) >= 0 then a(i,j) = 1
+#      else a(i,j) = 0
+#      .... a(i,j)
+#
+
+symbolic p(2), n, m;
+R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m };
+W1 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(iw,jw) >= 0 };
+W2 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(iw,jw) <  0 };
+
+Exposed := R-W1-W2;
+
+Exposed;
diff --git a/omega/examples/old_test/pufs4.oc-rt b/omega/examples/old_test/pufs4.oc-rt
new file mode 100644
index 0000000..2c32c83
--- /dev/null
+++ b/omega/examples/old_test/pufs4.oc-rt
@@ -0,0 +1,26 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # Calculate exposed reads for this code fragment
+# # for i := 1 to n do
+# #   for j := 1 to m do
+# #      if p(i,j) >= 0 then a(i,j) = 1
+# #      else a(i,j) = 0
+# #      .... a(i,j)
+# #
+# 
+# symbolic p(2), n, m;
+# 
+# R  := { [ir,jr] : 1 <= ir <= n && 1 <= jr <= m };
+# 
+# W1 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(iw,jw) >= 0 };
+# 
+# W2 := { [iw,jw] : 1 <= iw <= n && 1 <= jw <= m && p(iw,jw) <  0 };
+# 
+# 
+# Exposed := R-W1-W2;
+# 
+# 
+# Exposed;
+
+{[iw,jw]  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/pufs5 b/omega/examples/old_test/pufs5
new file mode 100644
index 0000000..19249af
--- /dev/null
+++ b/omega/examples/old_test/pufs5
@@ -0,0 +1,22 @@
+symbolic n(1);
+S :=  { [i] -> [j] : 1 <= i < j <= 100 && n(j) >= 0};
+R := domain S;
+S;
+R;
+upper_bound R;
+lower_bound R;
+
+R - {[1:50]};
+{[1:50]} - R;
+{[1:50]} - upper_bound R;
+{[1:50]} - lower_bound R;
+
+R union {[10:30]}  union {[25:100]} union {[1:10]};
+upper_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+lower_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[101:200]} - R;
+{[1:200]} - R;
+{[1:200]} - R - {[10:30]}  - {[25:100]};
+{[1:200]} - (R union {[10:30]}  union {[25:100]} union {[1:10]});
+{[1:200]} - R - {[10:30]}  - {[25:100]} - {[1:10]};
diff --git a/omega/examples/old_test/pufs5.oc-rt b/omega/examples/old_test/pufs5.oc-rt
new file mode 100644
index 0000000..614a9fb
--- /dev/null
+++ b/omega/examples/old_test/pufs5.oc-rt
@@ -0,0 +1,98 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1);
+# 
+# S :=  { [i] -> [j] : 1 <= i < j <= 100 && n(j) >= 0};
+# 
+# R := domain S;
+# 
+# S;
+
+{[i] -> [j] : 1 <= i < j <= 100 && 0 <= n(j)}
+
+# 
+# R;
+
+{[i]: 1 <= i <= 99 && UNKNOWN}
+
+# 
+# upper_bound R;
+
+{[i]: 1 <= i <= 99}
+
+# 
+# lower_bound R;
+
+{[i]  : FALSE }
+
+# 
+# 
+# R - {[1:50]};
+
+{[i]: 51 <= i <= 99 && UNKNOWN}
+
+# 
+# {[1:50]} - R;
+
+{[i]: 1 <= i <= 50 && UNKNOWN}
+
+# 
+# {[1:50]} - upper_bound R;
+
+{[i]  : FALSE }
+
+# 
+# {[1:50]} - lower_bound R;
+
+{[i]: 1 <= i <= 50}
+
+# 
+# 
+# R union {[10:30]}  union {[25:100]} union {[1:10]};
+
+{[i]: 1 <= i <= 99 && UNKNOWN} union
+ {[i]: 10 <= i <= 30} union
+ {[i]: 25 <= i <= 100} union
+ {[i]: 1 <= i <= 10}
+
+# 
+# upper_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 1 <= i <= 99} union
+ {[i]: 25 <= i <= 100}
+
+# 
+# lower_bound (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 10 <= i <= 30} union
+ {[i]: 25 <= i <= 100} union
+ {[i]: 1 <= i <= 10}
+
+# 
+# 
+# {[101:200]} - R;
+
+{[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - R;
+
+{[i]: 1 <= i <= 99 && UNKNOWN} union
+ {[i]: 100 <= i <= 200}
+
+# 
+# {[1:200]} - R - {[10:30]}  - {[25:100]};
+
+{[i]: 1 <= i <= 9 && UNKNOWN} union
+ {[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - (R union {[10:30]}  union {[25:100]} union {[1:10]});
+
+{[i]: 101 <= i <= 200}
+
+# 
+# {[1:200]} - R - {[10:30]}  - {[25:100]} - {[1:10]};
+
+{[i]: 101 <= i <= 200}
+
+# 
diff --git a/omega/examples/old_test/pufs6 b/omega/examples/old_test/pufs6
new file mode 100644
index 0000000..e24aa12
--- /dev/null
+++ b/omega/examples/old_test/pufs6
@@ -0,0 +1,19 @@
+symbolic n, f(1), f_last, f_first;
+
+True := { [] : 1 = 1 };
+
+old_R1 := { [x] -> [] : (1 <= x <= n and f(x) > 0)};
+old_R2 := { [x] -> [] : (1 <= x <= n and f(x) <=0)};
+True - range old_R1 - range old_R2;
+
+R1 := { [x] -> [] : (3 <= x <= n-1 and f(x) > 0)
+		 or (1 <= n and f_last > 0)
+		 or (1 <= n and f_first > 0) };
+R2 := { [x] -> [] : (3 <= x <= n-1 and f(x) <=0)
+		 or (1 <= n and f_last <=0)
+		 or (1 <= n and f_first <=0) };
+True - range R1 - range R2;
+
+R1a := { [x] -> [] : (1 <= x <= n and (f(x) > 0 or f_first > 0 or f_last > 0)) };
+R2a := { [x] -> [] : (1 <= x <= n and (f(x) <=0 or f_first <=0 or f_last <=0)) };
+True - range R1a - range R2a;
diff --git a/omega/examples/old_test/pufs6.oc-rt b/omega/examples/old_test/pufs6.oc-rt
new file mode 100644
index 0000000..d782cfc
--- /dev/null
+++ b/omega/examples/old_test/pufs6.oc-rt
@@ -0,0 +1,42 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Symbolic n, f(1), f_last, f_first;
+# 
+# 
+# True := { [] : 1 = 1 };
+# 
+# 
+# old_R1 := { [x] -> [] : (1 <= x <= n and f(x) > 0)};
+# 
+# old_R2 := { [x] -> [] : (1 <= x <= n and f(x) <=0)};
+# 
+# True - range old_R1 - range old_R2;
+
+{ 1 <= n && UNKNOWN} union
+ { n <= 0}
+
+# 
+# 
+# R1 := { [x] -> [] : (3 <= x <= n-1 and f(x) > 0)
+# 		 or (1 <= n and f_last > 0)
+# 		 or (1 <= n and f_first > 0) };
+# 
+# R2 := { [x] -> [] : (3 <= x <= n-1 and f(x) <=0)
+# 		 or (1 <= n and f_last <=0)
+# 		 or (1 <= n and f_first <=0) };
+# 
+# True - range R1 - range R2;
+
+{ n <= 0}
+
+# 
+# 
+# R1a := { [x] -> [] : (1 <= x <= n and (f(x) > 0 or f_first > 0 or f_last > 0)) };
+# 
+# R2a := { [x] -> [] : (1 <= x <= n and (f(x) <=0 or f_first <=0 or f_last <=0)) };
+# 
+# True - range R1a - range R2a;
+
+{ f_last <= 0 && n <= 0} union
+ { n <= 0 && 1 <= f_last}
+
+# 
diff --git a/omega/examples/old_test/pufs7 b/omega/examples/old_test/pufs7
new file mode 100644
index 0000000..33905bf
--- /dev/null
+++ b/omega/examples/old_test/pufs7
@@ -0,0 +1,6 @@
+symbolic n(1),m;
+{[i] : n(i) >= 0}  union {[i] : n(i) <=0};
+
+{[i] : n(i) >= 1 && 1 <= i <= m} 
+	union {[i] : n(i) <1 && 1 <= i <= m};
+
diff --git a/omega/examples/old_test/pufs7.oc-rt b/omega/examples/old_test/pufs7.oc-rt
new file mode 100644
index 0000000..84a8b93
--- /dev/null
+++ b/omega/examples/old_test/pufs7.oc-rt
@@ -0,0 +1,18 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n(1),m;
+# 
+# {[i] : n(i) >= 0}  union {[i] : n(i) <=0};
+
+{[i]: 0 <= n(i)} union
+ {[i]: n(i) <= 0}
+
+# 
+# 
+# {[i] : n(i) >= 1 && 1 <= i <= m} 
+# 	union {[i] : n(i) <1 && 1 <= i <= m};
+
+{[i]: 1 <= i <= m && 1 <= n(i)} union
+ {[i]: 1 <= i <= m && n(i) <= 0}
+
+# 
+# 
diff --git a/omega/examples/old_test/reach1 b/omega/examples/old_test/reach1
new file mode 100644
index 0000000..268868f
--- /dev/null
+++ b/omega/examples/old_test/reach1
@@ -0,0 +1,5 @@
+
+reachable (a,b,c)
+	  { a->b:{[1]->[2]},
+	     b->c:{[2]->[3]},
+	     a:{[1]}};
diff --git a/omega/examples/old_test/reach1.oc-rt b/omega/examples/old_test/reach1.oc-rt
new file mode 100644
index 0000000..8333ede
--- /dev/null
+++ b/omega/examples/old_test/reach1.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# reachable (a,b,c)
+# 	  { a->b:{[1]->[2]},
+# 	     b->c:{[2]->[3]},
+# 	     a:{[1]}};
+Node b: {[2]}
+Node c: {[3]}
+# 
diff --git a/omega/examples/old_test/reach2 b/omega/examples/old_test/reach2
new file mode 100644
index 0000000..1a692a0
--- /dev/null
+++ b/omega/examples/old_test/reach2
@@ -0,0 +1,29 @@
+
+a2b:={[1]->[2]};
+
+b2c1:={[i]->[i]};
+b2c2:={[i]->[j]};
+
+a2a:={[i]->[i]};
+b2b:={[i]->[i]};
+c2c:={[i]->[i]};
+
+
+
+reachable (a,b,c){ a->b:a2b, b->c:b2c1, a->a:a2a, b->b:b2b, c->c:c2c,
+          a:{[1]}};
+
+reachable (a,b,c) { a->b:a2b, b->c:b2c2, a->a:a2a, b->b:b2b, c->c:c2c,
+          a:{[1]}};
+
+b2c3:={[i]->[i+1]};
+b2b2:={[i]->[i+1]};
+
+reachable (a,b,c){ a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+                   a:{[1]}};
+
+b2c3:={[i]->[i]};
+
+reachable (a,b,c){ a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+          a:{[1]}};
+
diff --git a/omega/examples/old_test/reach2.oc-rt b/omega/examples/old_test/reach2.oc-rt
new file mode 100644
index 0000000..8a8a904
--- /dev/null
+++ b/omega/examples/old_test/reach2.oc-rt
@@ -0,0 +1,61 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# a2b:={[1]->[2]};
+# 
+# 
+# b2c1:={[i]->[i]};
+# 
+# b2c2:={[i]->[j]};
+# 
+# 
+# a2a:={[i]->[i]};
+# 
+# b2b:={[i]->[i]};
+# 
+# c2c:={[i]->[i]};
+# 
+# 
+# 
+# 
+# reachable (a,b,c){ a->b:a2b, b->c:b2c1, a->a:a2a, b->b:b2b, c->c:c2c,
+#           a:{[1]}};
+Node a: {[1]}
+Node b: {[2]}
+Node c: {[2]}
+# 
+# 
+# reachable (a,b,c) { a->b:a2b, b->c:b2c2, a->a:a2a, b->b:b2b, c->c:c2c,
+#           a:{[1]}};
+Node a: {[1]}
+Node b: {[2]}
+Node c: {[In_1]}
+# 
+# 
+# b2c3:={[i]->[i+1]};
+# 
+# b2b2:={[i]->[i+1]};
+# 
+# 
+# reachable (a,b,c){ a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+#                    a:{[1]}};
+Node a: {[1]}
+Node b: {[2]} union
+ {[In_1]: 4 <= In_1} union
+ {[3]}
+Node c: {[i]: 4 <= i} union
+ {[3]}
+# 
+# 
+# b2c3:={[i]->[i]};
+# 
+# 
+# reachable (a,b,c){ a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+#           a:{[1]}};
+Node a: {[1]}
+Node b: {[2]} union
+ {[In_1]: 4 <= In_1} union
+ {[3]}
+Node c: {[i]: 3 <= i} union
+ {[2]}
+# 
+# 
diff --git a/omega/examples/old_test/reach3 b/omega/examples/old_test/reach3
new file mode 100644
index 0000000..39c954d
--- /dev/null
+++ b/omega/examples/old_test/reach3
@@ -0,0 +1,18 @@
+
+a2b:={[1]->[2]};
+a2a:={[i]->[i]};
+b2b2:={[i]->[i+1]};
+b2c3:={[i]->[i]};
+c2c:={[i]->[i]};
+
+reachable of a in (a,b,c) {
+                  a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+                  a:{[1]}
+	          };
+reachable of b in (a,b,c) {
+                  a->b:a2b, b->c:b2c3, a->a:a2a, a:{[1]}, b->b:b2b2, c->c:c2c
+	          };
+cr := reachable of c in (a,b,c) { 
+                  a:{[1]},a->b:a2b, b->c:b2c3, a->a:a2a,
+		  b->b:b2b2, c->c:c2c };
+cr;
diff --git a/omega/examples/old_test/reach3.oc-rt b/omega/examples/old_test/reach3.oc-rt
new file mode 100644
index 0000000..3418061
--- /dev/null
+++ b/omega/examples/old_test/reach3.oc-rt
@@ -0,0 +1,40 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# a2b:={[1]->[2]};
+# 
+# a2a:={[i]->[i]};
+# 
+# b2b2:={[i]->[i+1]};
+# 
+# b2c3:={[i]->[i]};
+# 
+# c2c:={[i]->[i]};
+# 
+# 
+# reachable of a in (a,b,c) {
+#                   a->b:a2b, b->c:b2c3, a->a:a2a, b->b:b2b2, c->c:c2c,
+#                   a:{[1]}
+# 	          };
+
+{[1]}
+
+# 
+# reachable of b in (a,b,c) {
+#                   a->b:a2b, b->c:b2c3, a->a:a2a, a:{[1]}, b->b:b2b2, c->c:c2c
+# 	          };
+
+{[2]} union
+ {[In_1]: 4 <= In_1} union
+ {[3]}
+
+# 
+# cr := reachable of c in (a,b,c) { 
+#                   a:{[1]},a->b:a2b, b->c:b2c3, a->a:a2a,
+# 		  b->b:b2b2, c->c:c2c };
+# 
+# cr;
+
+{[i]: 3 <= i} union
+ {[2]}
+
+# 
diff --git a/omega/examples/old_test/red1 b/omega/examples/old_test/red1
new file mode 100644
index 0000000..1a479b3
--- /dev/null
+++ b/omega/examples/old_test/red1
@@ -0,0 +1,3 @@
+R1 := {[i,j,k] : 17i=12j+170};
+R2 :=  {[i,j,k] : k >= 0};
+gist R1 given R2;
diff --git a/omega/examples/old_test/red1.oc-rt b/omega/examples/old_test/red1.oc-rt
new file mode 100644
index 0000000..32cbb97
--- /dev/null
+++ b/omega/examples/old_test/red1.oc-rt
@@ -0,0 +1,10 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R1 := {[i,j,k] : 17i=12j+170};
+# 
+# R2 :=  {[i,j,k] : k >= 0};
+# 
+# gist R1 given R2;
+
+{[i,j,k]: 17i = 170+12j}
+
+# 
diff --git a/omega/examples/old_test/saman b/omega/examples/old_test/saman
new file mode 100644
index 0000000..bf44452
--- /dev/null
+++ b/omega/examples/old_test/saman
@@ -0,0 +1,20 @@
+# Passing array sections through array reshaping
+# procedure foo()
+# real a(1:5,1:64,1:64,1:5)
+# for i = 1 to 64 do
+#   for j = 1 to 64 do
+#     bar(a(1,i,j,1))
+# ...
+# procedure bar(x(*))
+# x(1:5) = ...
+#
+# Question which element of a are effected by the call to bar?
+#
+symbolic i,j;
+R := {[i1,i2,i3,i4] -> [o1] :
+		(i1-1) + (i2-i)*5 + (i3-j)*5*64 + (i4-1)*5*64*64
+		= o1-1
+	&& 1 <= i1,i4 <= 5
+	&& 1 <= i,j,i2,i3 <= 64};
+R;
+(inverse R)({[1:5]});
diff --git a/omega/examples/old_test/saman.oc-rt b/omega/examples/old_test/saman.oc-rt
new file mode 100644
index 0000000..d75d4df
--- /dev/null
+++ b/omega/examples/old_test/saman.oc-rt
@@ -0,0 +1,31 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # Passing array sections through array reshaping
+# # procedure foo()
+# # real a(1:5,1:64,1:64,1:5)
+# # for i = 1 to 64 do
+# #   for j = 1 to 64 do
+# #     bar(a(1,i,j,1))
+# # ...
+# # procedure bar(x(*))
+# # x(1:5) = ...
+# #
+# # Question which element of a are effected by the call to bar?
+# #
+# symbolic i,j;
+# 
+# R := {[i1,i2,i3,i4] -> [o1] :
+# 		(i1-1) + (i2-i)*5 + (i3-j)*5*64 + (i4-1)*5*64*64
+# 		= o1-1
+# 	&& 1 <= i1,i4 <= 5
+# 	&& 1 <= i,j,i2,i3 <= 64};
+# 
+# R;
+
+{[i1,i2,i3,i4] -> [i1-320j-5i+5i2+320i3+20480i4-20480] : 1 <= j <= 64 && 1 <= i <= 64 && 1 <= i1 <= 5 && 1 <= i2 <= 64 && 1 <= i3 <= 64 && 1 <= i4 <= 5}
+
+# 
+# (inverse R)({[1:5]});
+
+{[i1,i,j,1]: 1 <= i <= 64 && 1 <= j <= 64 && 1 <= i1 <= 5}
+
+# 
diff --git a/omega/examples/old_test/sample1 b/omega/examples/old_test/sample1
new file mode 100644
index 0000000..fb292b3
--- /dev/null
+++ b/omega/examples/old_test/sample1
@@ -0,0 +1,14 @@
+example { [i] -> [j] : 1 <= i < j <= 20 };
+
+example { [i,j] -> [i+1,j+1] : 1 <= i <= 9 && 5 <= j <= 25 };
+
+example (inverse { [i] -> [i+1] : 1 <= i <= 9 });
+
+example (domain { [i] -> [i+1] : 1 <= i <= 9 });
+
+example (range { [i] -> [i+1] : 1 <= i <= 9 });
+
+example ({[i] -> [i+1] : 1 <= i <= 9 } compose { [i] -> [i+1] : 1 <= i <= 9 });
+
+
+
diff --git a/omega/examples/old_test/sample1.oc-rt b/omega/examples/old_test/sample1.oc-rt
new file mode 100644
index 0000000..bb19b15
--- /dev/null
+++ b/omega/examples/old_test/sample1.oc-rt
@@ -0,0 +1,39 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# example { [i] -> [j] : 1 <= i < j <= 20 };
+
+{[19] -> [20] }
+
+# 
+# 
+# example { [i,j] -> [i+1,j+1] : 1 <= i <= 9 && 5 <= j <= 25 };
+
+{[1,5] -> [2,6] }
+
+# 
+# 
+# example (inverse { [i] -> [i+1] : 1 <= i <= 9 });
+
+{[2] -> [1] }
+
+# 
+# 
+# example (domain { [i] -> [i+1] : 1 <= i <= 9 });
+
+{[1]}
+
+# 
+# 
+# example (range { [i] -> [i+1] : 1 <= i <= 9 });
+
+{[2]}
+
+# 
+# 
+# example ({[i] -> [i+1] : 1 <= i <= 9 } compose { [i] -> [i+1] : 1 <= i <= 9 });
+
+{[1] -> [3] }
+
+# 
+# 
+# 
+# 
diff --git a/omega/examples/old_test/sample2 b/omega/examples/old_test/sample2
new file mode 100644
index 0000000..1ca6b19
--- /dev/null
+++ b/omega/examples/old_test/sample2
@@ -0,0 +1,11 @@
+symbolic n,m;
+
+example { [i] -> [j] : 1 <= i <= 20 };
+
+example {[i] : 1 <= i <= n};
+
+example {[i] : m <= i <= n};
+
+example {[i] : exists ( alpha : i <= 2alpha)};
+
+example {[i] : exists ( alpha : i = 2alpha)};
diff --git a/omega/examples/old_test/sample2.oc-rt b/omega/examples/old_test/sample2.oc-rt
new file mode 100644
index 0000000..e18d650
--- /dev/null
+++ b/omega/examples/old_test/sample2.oc-rt
@@ -0,0 +1,33 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Symbolic n,m;
+# 
+# 
+# example { [i] -> [j] : 1 <= i <= 20 };
+
+{[1] -> [42] }
+
+# 
+# 
+# example {[i] : 1 <= i <= n};
+
+{[1]: n = 1}
+
+# 
+# 
+# example {[i] : m <= i <= n};
+
+{[42]: m = 42 && n = 42}
+
+# 
+# 
+# example {[i] : exists ( alpha : i <= 2alpha)};
+
+{[42]}
+
+# 
+# 
+# example {[i] : exists ( alpha : i = 2alpha)};
+
+{[0]}
+
+# 
diff --git a/omega/examples/old_test/sample3 b/omega/examples/old_test/sample3
new file mode 100644
index 0000000..44a481d
--- /dev/null
+++ b/omega/examples/old_test/sample3
@@ -0,0 +1,11 @@
+symbolic n,m;
+
+sym_example {[i] : 1 <= i <= n};
+
+sym_example {[i] : m <= i <= n};
+
+sym_example {[i] : m <= i <= n && exists (alpha : i = 2alpha)};
+example {[i] : m <= i <= n && exists (alpha : i = 2alpha)};
+example {[i] : m < i <= n && exists (alpha : i = 2alpha)};
+example {[i] : m < i < n};
+
diff --git a/omega/examples/old_test/sample3.oc-rt b/omega/examples/old_test/sample3.oc-rt
new file mode 100644
index 0000000..a486bdd
--- /dev/null
+++ b/omega/examples/old_test/sample3.oc-rt
@@ -0,0 +1,37 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Symbolic n,m;
+# 
+# 
+# sym_example {[i] : 1 <= i <= n};
+
+{[1]: 1 <= n}
+
+# 
+# 
+# sym_example {[i] : m <= i <= n};
+
+{[m]: m <= n}
+
+# 
+# 
+# sym_example {[i] : m <= i <= n && exists (alpha : i = 2alpha)};
+
+{[0]: m <= 0 && 0 <= n}
+
+# 
+# example {[i] : m <= i <= n && exists (alpha : i = 2alpha)};
+
+{[42]: m = 42 && n = 42}
+
+# 
+# example {[i] : m < i <= n && exists (alpha : i = 2alpha)};
+
+{[44]: m = 42 && n = 44}
+
+# 
+# example {[i] : m < i < n};
+
+{[43]: m = 42 && n = 44}
+
+# 
+# 
diff --git a/omega/examples/old_test/stodghil b/omega/examples/old_test/stodghil
new file mode 100644
index 0000000..99e9430
--- /dev/null
+++ b/omega/examples/old_test/stodghil
@@ -0,0 +1,21 @@
+symbolic n;
+
+S := {[k_w,j_w,l_w]->[k_r,j_r,l_r] : ((1 <= k_w) and (k_w <= n) and ((k_w + 1) <= j_w) 
+and (j_w <= n) 
+and ((k_w + 1) <= l_w) and (l_w <= j_w) and (1 <= k_r) 
+and (k_r <= n) and ((k_r + 1) <= j_r) and (j_r <= n) 
+and ((k_r + 1) <= l_r) and (l_r <= j_r) and ((k_w < k_r) or ((k_w = k_r) 
+and (j_w < j_r)) or ((k_w = k_r) and (j_w = j_r) and (l_w < l_r))) 
+and (j_w = j_r) and (l_w = l_r) 
+and !exists(k_1 : ((1 <= k_1) and (k_1 <= n) and (k_w < k_1) and ((k_1 < k_r) or (k_1 = k_r)) 
+and (k_1 = j_r) and (k_1 = l_r))) 
+and !exists(k_2,i_2 : ((1 <= k_2) and (k_2 <= n) and ((k_2 + 1) <= i_2) and (i_2 <= n) and (k_w < k_2) and ((k_2 < k_r) or (k_2 = k_r)) and (i_2 = j_r) and (k_2 = l_r))) 
+and !exists(k_3,j_3,l_3 : ((1 <= k_3) and (k_3 <= n) and ((k_3 + 1) <= j_3) 
+	and (j_3 <= n) and ((k_3 + 1) <= l_3) and (l_3 <= j_3) 
+and ((k_w < k_3) or ((k_w = k_3) and (j_w < j_3)) or ((k_w = k_3) 
+and (j_w = j_3) and (l_w < l_3))) 
+and ((k_3 < k_r) or ((k_3 = k_r) and (j_3 < j_r)) or ((k_3 = k_r) 
+and (j_3 = j_r) and (l_3 < l_r))) and (j_3 = j_r) and (l_3 = l_r))
+))};
+
+S;
diff --git a/omega/examples/old_test/stodghil.oc-rt b/omega/examples/old_test/stodghil.oc-rt
new file mode 100644
index 0000000..0d554d2
--- /dev/null
+++ b/omega/examples/old_test/stodghil.oc-rt
@@ -0,0 +1,28 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# 
+# S := {[k_w,j_w,l_w]->[k_r,j_r,l_r] : ((1 <= k_w) and (k_w <= n) and ((k_w + 1) <= j_w) 
+# and (j_w <= n) 
+# and ((k_w + 1) <= l_w) and (l_w <= j_w) and (1 <= k_r) 
+# and (k_r <= n) and ((k_r + 1) <= j_r) and (j_r <= n) 
+# and ((k_r + 1) <= l_r) and (l_r <= j_r) and ((k_w < k_r) or ((k_w = k_r) 
+# and (j_w < j_r)) or ((k_w = k_r) and (j_w = j_r) and (l_w < l_r))) 
+# and (j_w = j_r) and (l_w = l_r) 
+# and !exists(k_1 : ((1 <= k_1) and (k_1 <= n) and (k_w < k_1) and ((k_1 < k_r) or (k_1 = k_r)) 
+# and (k_1 = j_r) and (k_1 = l_r))) 
+# and !exists(k_2,i_2 : ((1 <= k_2) and (k_2 <= n) and ((k_2 + 1) <= i_2) and (i_2 <= n) and (k_w < k_2) and ((k_2 < k_r) or (k_2 = k_r)) and (i_2 = j_r) and (k_2 = l_r))) 
+# and !exists(k_3,j_3,l_3 : ((1 <= k_3) and (k_3 <= n) and ((k_3 + 1) <= j_3) 
+# 	and (j_3 <= n) and ((k_3 + 1) <= l_3) and (l_3 <= j_3) 
+# and ((k_w < k_3) or ((k_w = k_3) and (j_w < j_3)) or ((k_w = k_3) 
+# and (j_w = j_3) and (l_w < l_3))) 
+# and ((k_3 < k_r) or ((k_3 = k_r) and (j_3 < j_r)) or ((k_3 = k_r) 
+# and (j_3 = j_r) and (l_3 < l_r))) and (j_3 = j_r) and (l_3 = l_r))
+# ))};
+# 
+# 
+# S;
+
+{[k_w,j_w,l_w] -> [k_w+1,j_w,l_w] : k_w+2 <= l_w <= j_w <= n && 1 <= k_w}
+
+# 
diff --git a/omega/examples/old_test/stride1 b/omega/examples/old_test/stride1
new file mode 100644
index 0000000..fc2b727
--- /dev/null
+++ b/omega/examples/old_test/stride1
@@ -0,0 +1,2 @@
+R := { [i] : i < 10 && i > 1 && exists ( alpha : i = 3alpha) };
+codegen R;
diff --git a/omega/examples/old_test/stride1.oc-rt b/omega/examples/old_test/stride1.oc-rt
new file mode 100644
index 0000000..a577449
--- /dev/null
+++ b/omega/examples/old_test/stride1.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i] : i < 10 && i > 1 && exists ( alpha : i = 3alpha) };
+# 
+# codegen R;
+for(t1 = 3; t1 <= 9; t1 += 3) {
+  s1(t1);
+}
+
+# 
diff --git a/omega/examples/old_test/stride2 b/omega/examples/old_test/stride2
new file mode 100644
index 0000000..37a355f
--- /dev/null
+++ b/omega/examples/old_test/stride2
@@ -0,0 +1,4 @@
+symbolic n;
+new_IS := {[t1,t2] : exists (alpha : t1 = 32alpha && 
+	                     t2 - 31,0 <= t1 <= t2 <= n)};
+codegen new_IS;
diff --git a/omega/examples/old_test/stride2.oc-rt b/omega/examples/old_test/stride2.oc-rt
new file mode 100644
index 0000000..ee8fb75
--- /dev/null
+++ b/omega/examples/old_test/stride2.oc-rt
@@ -0,0 +1,14 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Sym n;
+# 
+# new_IS := {[t1,t2] : exists (alpha : t1 = 32alpha && 
+# 	                     t2 - 31,0 <= t1 <= t2 <= n)};
+# 
+# codegen new_IS;
+for(t1 = 0; t1 <= n; t1 += 32) {
+  for(t2 = t1; t2 <= min(n,t1+31); t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/stride3 b/omega/examples/old_test/stride3
new file mode 100644
index 0000000..859e9b8
--- /dev/null
+++ b/omega/examples/old_test/stride3
@@ -0,0 +1,4 @@
+symbolic n;
+new_IS := {[t1,t2] : exists (alpha : t1 = 32alpha+3 && 
+	                     t2 - 31,0 <= t1 <= t2 <= n)};
+codegen new_IS;
diff --git a/omega/examples/old_test/stride3.oc-rt b/omega/examples/old_test/stride3.oc-rt
new file mode 100644
index 0000000..7ba925f
--- /dev/null
+++ b/omega/examples/old_test/stride3.oc-rt
@@ -0,0 +1,14 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Sym n;
+# 
+# new_IS := {[t1,t2] : exists (alpha : t1 = 32alpha+3 && 
+# 	                     t2 - 31,0 <= t1 <= t2 <= n)};
+# 
+# codegen new_IS;
+for(t1 = 3; t1 <= n; t1 += 32) {
+  for(t2 = t1; t2 <= min(n,t1+31); t2++) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/stride4 b/omega/examples/old_test/stride4
new file mode 100644
index 0000000..21781a2
--- /dev/null
+++ b/omega/examples/old_test/stride4
@@ -0,0 +1,4 @@
+symbolic n;
+new_IS := {[i] : exists (alpha : i = 5alpha-2 && 
+	                         i >= 17 && i <= 100)};
+codegen new_IS;
diff --git a/omega/examples/old_test/stride4.oc-rt b/omega/examples/old_test/stride4.oc-rt
new file mode 100644
index 0000000..3905486
--- /dev/null
+++ b/omega/examples/old_test/stride4.oc-rt
@@ -0,0 +1,12 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Sym n;
+# 
+# new_IS := {[i] : exists (alpha : i = 5alpha-2 && 
+# 	                         i >= 17 && i <= 100)};
+# 
+# codegen new_IS;
+for(t1 = 18; t1 <= 98; t1 += 5) {
+  s1(t1);
+}
+
+# 
diff --git a/omega/examples/old_test/stride5 b/omega/examples/old_test/stride5
new file mode 100644
index 0000000..9c4f1b0
--- /dev/null
+++ b/omega/examples/old_test/stride5
@@ -0,0 +1,4 @@
+symbolic n;
+R := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+             j >= i+2n && j <=401 && exists (alpha : j = 2 alpha)};
+codegen R;
diff --git a/omega/examples/old_test/stride5.oc-rt b/omega/examples/old_test/stride5.oc-rt
new file mode 100644
index 0000000..85e9551
--- /dev/null
+++ b/omega/examples/old_test/stride5.oc-rt
@@ -0,0 +1,14 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Sym n;
+# 
+# R := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+#              j >= i+2n && j <=401 && exists (alpha : j = 2 alpha)};
+# 
+# codegen R;
+for(t1 = 2; t1 <= min(-2*n+400,100); t1 += 2) {
+  for(t2 = 2*n+t1; t2 <= 400; t2 += 2) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/stride6 b/omega/examples/old_test/stride6
new file mode 100644
index 0000000..364e24c
--- /dev/null
+++ b/omega/examples/old_test/stride6
@@ -0,0 +1,10 @@
+symbolic n;
+R := {[i,j]: i >= 1 && i <= 101 &&
+             j >= i && j <=401 && exists (alpha : j = 2 alpha)};
+codegen R;
+S := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+             j >= i && j <=401 && exists (alpha : j = 2 alpha)};
+codegen S;
+T := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+             j >= i && j <=401 && exists (alpha : 2j = 4 alpha)};
+codegen T;
diff --git a/omega/examples/old_test/stride6.oc-rt b/omega/examples/old_test/stride6.oc-rt
new file mode 100644
index 0000000..eeb242f
--- /dev/null
+++ b/omega/examples/old_test/stride6.oc-rt
@@ -0,0 +1,36 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# Sym n;
+# 
+# R := {[i,j]: i >= 1 && i <= 101 &&
+#              j >= i && j <=401 && exists (alpha : j = 2 alpha)};
+# 
+# codegen R;
+for(t1 = 1; t1 <= 101; t1++) {
+  for(t2 = 2*intDiv(t1+1,2); t2 <= 400; t2 += 2) {
+    s1(t1,t2);
+  }
+}
+
+# 
+# S := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+#              j >= i && j <=401 && exists (alpha : j = 2 alpha)};
+# 
+# codegen S;
+for(t1 = 2; t1 <= 100; t1 += 2) {
+  for(t2 = t1; t2 <= 400; t2 += 2) {
+    s1(t1,t2);
+  }
+}
+
+# 
+# T := {[i,j]: i >= 1 && i <= 101 && exists (alpha : i = 2 alpha) &&
+#              j >= i && j <=401 && exists (alpha : 2j = 4 alpha)};
+# 
+# codegen T;
+for(t1 = 2; t1 <= 100; t1 += 2) {
+  for(t2 = t1; t2 <= 400; t2 += 2) {
+    s1(t1,t2);
+  }
+}
+
+# 
diff --git a/omega/examples/old_test/stride7 b/omega/examples/old_test/stride7
new file mode 100644
index 0000000..4bfe1cd
--- /dev/null
+++ b/omega/examples/old_test/stride7
@@ -0,0 +1,6 @@
+IS:={[i,j]: 1 <= i,j <= 9};
+T1:={[i,j]->[4j,i,0]};
+T2:={[i,j]->[j,i,1]};
+codegen T1:IS,T2:IS;
+codegen 2 T1:IS,T2:IS;
+
diff --git a/omega/examples/old_test/stride7.oc-rt b/omega/examples/old_test/stride7.oc-rt
new file mode 100644
index 0000000..60ac1d4
--- /dev/null
+++ b/omega/examples/old_test/stride7.oc-rt
@@ -0,0 +1,47 @@
+>>> IS:={[i,j]: 1 <= i,j <= 9};
+>>> T1:={[i,j]->[4j,i,0]};
+>>> T2:={[i,j]->[j,i,1]};
+>>> codegen T1:IS,T2:IS;
+for(t1 = 1; t1 <= 36; t1++) {
+  if (intMod(t1,4) == 0 && t1 <= 8) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+      s2(t2,t1);
+    }
+  }
+  if (intMod(t1,4) == 0 && t1 >= 12) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+    }
+  }
+  if (t1-3 <= 4*intDiv(t1-1,4) && t1 <= 9) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,t1);
+    }
+  }
+}
+
+>>> codegen 2 T1:IS,T2:IS;
+for(t1 = 1; t1 <= 8; t1++) {
+  if (intMod(t1,4) == 0) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s1(t2,intDiv(t1,4));
+      s2(t2,t1);
+    }
+  }
+  if (t1-3 <= 4*intDiv(t1-1,4)) {
+    for(t2 = 1; t2 <= 9; t2++) {
+      s2(t2,t1);
+    }
+  }
+}
+for(t2 = 1; t2 <= 9; t2++) {
+  s2(t2,9);
+}
+for(t1 = 12; t1 <= 36; t1 += 4) {
+  for(t2 = 1; t2 <= 9; t2++) {
+    s1(t2,intDiv(t1,4));
+  }
+}
+
+
diff --git a/omega/examples/old_test/subsets1 b/omega/examples/old_test/subsets1
new file mode 100644
index 0000000..1b3721d
--- /dev/null
+++ b/omega/examples/old_test/subsets1
@@ -0,0 +1,20 @@
+R := {[x]:x > 1 };
+R;
+R2 := subsetof R;
+R2;
+
+R - R2;
+R subset R2;
+R2 - R;
+R2 subset R;
+
+S := {[x]: x > 0};
+S - R; 
+R subset S;
+S - R2;
+R2 subset S;
+
+S2 := {[x]: x > -1};
+S3 := subsetof S2;
+S3 - S;
+S subset S3;
diff --git a/omega/examples/old_test/subsets1.oc-rt b/omega/examples/old_test/subsets1.oc-rt
new file mode 100644
index 0000000..345639f
--- /dev/null
+++ b/omega/examples/old_test/subsets1.oc-rt
@@ -0,0 +1,70 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := {[x]:x > 1 };
+# 
+# R;
+
+{[x]: 2 <= x}
+
+# 
+# R2 := subsetof R;
+# 
+# R2;
+
+{[x]: 2 <= x && UNKNOWN}
+
+# 
+# 
+# R - R2;
+
+{[x]: 2 <= x && UNKNOWN}
+
+# 
+# R subset R2;
+
+False
+# 
+# R2 - R;
+
+{[x]  : FALSE }
+
+# 
+# R2 subset R;
+
+True
+# 
+# 
+# S := {[x]: x > 0};
+# 
+# S - R;
+
+{[1]}
+
+#  
+# R subset S;
+
+True
+# 
+# S - R2;
+
+{[x]: 2 <= x && UNKNOWN} union
+ {[1]}
+
+# 
+# R2 subset S;
+
+True
+# 
+# 
+# S2 := {[x]: x > -1};
+# 
+# S3 := subsetof S2;
+# 
+# S3 - S;
+
+{[0]: UNKNOWN}
+
+# 
+# S subset S3;
+
+False
+# 
diff --git a/omega/examples/old_test/subsets2 b/omega/examples/old_test/subsets2
new file mode 100644
index 0000000..4d4a98a
--- /dev/null
+++ b/omega/examples/old_test/subsets2
@@ -0,0 +1,5 @@
+(subsetof {[1:10]}) - subsetof {[1:10]}; 
+
+{[1:10]} - subsetof {[1:10]}; 
+
+(subsetof {[1:10]}) - {[1:10]}; 
diff --git a/omega/examples/old_test/subsets2.oc-rt b/omega/examples/old_test/subsets2.oc-rt
new file mode 100644
index 0000000..0bbb1c7
--- /dev/null
+++ b/omega/examples/old_test/subsets2.oc-rt
@@ -0,0 +1,18 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# (subsetof {[1:10]}) - subsetof {[1:10]};
+
+{[In_1]: 1 <= In_1 <= 10 && UNKNOWN}
+
+#  
+# 
+# {[1:10]} - subsetof {[1:10]};
+
+{[In_1]: 1 <= In_1 <= 10 && UNKNOWN}
+
+#  
+# 
+# (subsetof {[1:10]}) - {[1:10]};
+
+{[In_1]  : FALSE }
+
+#  
diff --git a/omega/examples/old_test/tex1 b/omega/examples/old_test/tex1
new file mode 100644
index 0000000..ca84924
--- /dev/null
+++ b/omega/examples/old_test/tex1
@@ -0,0 +1,49 @@
+#
+# Extract from omega4
+#  removed "eqnarray" commands, associated &'s, and overbrace commands
+#  added declaration of n
+#  added semicolon
+#
+# It would be nice not to have to do the following:
+#  removed \ in front of variable names
+# 
+
+$$
+symbolic n;
+R := \{\ [ii] \rightarrow [ki] \mid
+1 \leq ii \leq 2n
+	\ \land \  1 \leq ki \leq 2n
+\land ii = ki 
+\land ii = ki\\
+\t \land 
+	\ \neg (\ \exists [ji, jj] \st
+(1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
+\land (ii \leq ji \land ji \leq ki) \land (2jj = ki)\ )\\ 
+\t 
+\land \ 
+\neg (\ \exists [ji, jj] \st
+(1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
+\land (ii \leq ji \land ji \leq ki) \land (2jj\!+\!1 = ki)\ )
+\   \}
+;
+
+R;
+$$
+# S := \{\ [\ii] \rightarrow [\ki] \mid
+# 1 \leq \ii \leq 2\n
+# 	\ \land \  1 \leq \ki \leq 2\n
+# \land \ii = \ki 
+# \land \ii = \ki\\
+# \t \land 
+# 	\ \neg (\ \exists [\ji, \jj] \st
+# (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
+# \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj = \ki)\ )\\ 
+# \t 
+# \land \ 
+# \neg (\ \exists [\ji, \jj] \st
+# (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
+# \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj\!+\!1 = \ki)\ )
+# \   \}
+# ;
+# 
+# S;
diff --git a/omega/examples/old_test/tex1.oc-rt b/omega/examples/old_test/tex1.oc-rt
new file mode 100644
index 0000000..fd138d0
--- /dev/null
+++ b/omega/examples/old_test/tex1.oc-rt
@@ -0,0 +1,58 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# #
+# # Extract from omega4
+# #  removed "eqnarray" commands, associated &'s, and overbrace commands
+# #  added declaration of n
+# #  added semicolon
+# #
+# # It would be nice not to have to do the following:
+# #  removed \ in front of variable names
+# # 
+# 
+# $$
+# symbolic n;
+# 
+# R := \{\ [ii] \rightarrow [ki] \mid
+# 1 \leq ii \leq 2n
+# 	\ \land \  1 \leq ki \leq 2n
+# \land ii = ki 
+# \land ii = ki\\
+# \t \land 
+# 	\ \neg (\ \exists [ji, jj] \st
+# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
+# \land (ii \leq ji \land ji \leq ki) \land (2jj = ki)\ )\\ 
+# \t 
+# \land \ 
+# \neg (\ \exists [ji, jj] \st
+# (1 \leq ji \leq 2n \land 1 \leq jj \leq n\!-\!1)
+# \land (ii \leq ji \land ji \leq ki) \land (2jj\!+\!1 = ki)\ )
+# \   \}
+# ;
+# 
+# 
+# R;
+
+{[ii] -> [ii] : n = 1 && 1 <= ii <= 2} union
+ {[2n] -> [2n] : 2 <= n} union
+ {[1] -> [1] : 2 <= n}
+
+# 
+# $$
+# # S := \{\ [\ii] \rightarrow [\ki] \mid
+# # 1 \leq \ii \leq 2\n
+# # 	\ \land \  1 \leq \ki \leq 2\n
+# # \land \ii = \ki 
+# # \land \ii = \ki\\
+# # \t \land 
+# # 	\ \neg (\ \exists [\ji, \jj] \st
+# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
+# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj = \ki)\ )\\ 
+# # \t 
+# # \land \ 
+# # \neg (\ \exists [\ji, \jj] \st
+# # (1 \leq \ji \leq 2\n \land 1 \leq \jj \leq \n\!-\!1)
+# # \land (\ii \leq \ji \land \ji \leq \ki) \land (2\jj\!+\!1 = \ki)\ )
+# # \   \}
+# # ;
+# # 
+# # S;
diff --git a/omega/examples/old_test/tricky b/omega/examples/old_test/tricky
new file mode 100644
index 0000000..d12077c
--- /dev/null
+++ b/omega/examples/old_test/tricky
@@ -0,0 +1,11 @@
+symbolic N,M,k;
+{ [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
+                      and not ( exists [i2,j2] :
+                              0 <= i2 <= M  and  0 <= j2 <= N
+                              and 2i2+j2 = k
+                              and i < i2 )                };
+{ [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
+                      and not (  i < M &&  2i-2 <= k &&
+				N-k <= 2M
+				&& ( N-k < k or N <= 2k && (exists a : k = 2 a)
+				))};
diff --git a/omega/examples/old_test/tricky.oc-rt b/omega/examples/old_test/tricky.oc-rt
new file mode 100644
index 0000000..8282b7f
--- /dev/null
+++ b/omega/examples/old_test/tricky.oc-rt
@@ -0,0 +1,25 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic N,M,k;
+# 
+# { [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
+#                       and NOT( exists [i2,j2] :
+#                               0 <= i2 <= M  and  0 <= j2 <= N
+#                               and 2i2+j2 = k
+#                               and i < i2 )                };
+
+{[i,k-2i] -> : 2i <= k <= 2i+1 && 0 <= i <= M && k <= N+2i} union
+ {[M,k-2M] -> : 2+2M <= k && k <= N+2M && 0 <= M}
+
+# 
+# { [i,j] -> [] : 0 <= i <= M and 0 <= j <= N and 2i+j = k
+#                       and NOT(  i < M &&  2i-2 <= k &&
+# 				N-k <= 2M
+# 				&& ( N-k < k or N <= 2k && (exists a : k = 2 a)
+# 				))};
+
+{[i,k-2i] -> : 0 <= i <= M && 2M+k < N && 2i <= k} union
+ {[M,k-2M] -> : N <= 2M+k && k <= N+2M && 2M <= k} union
+ {[i,k-2i] -> : 2k < N && N <= 2M+k && 0 <= i && 2i <= k} union
+ {[i,k-2i] -> : Exists ( alpha : N = 2k && 2i = 1+k+2alpha && 2i+1 <= k <= 2M-1 && 0 <= i)}
+
+# 
diff --git a/omega/examples/old_test/ts1d-check-sblock b/omega/examples/old_test/ts1d-check-sblock
new file mode 100644
index 0000000..01757ea
--- /dev/null
+++ b/omega/examples/old_test/ts1d-check-sblock
@@ -0,0 +1,155 @@
+# This is the file facts.prew, which is prepended to the .prew files
+# for the particular code generation we want, defines things like the
+# iteration space and dependences.  Known facts are inserted by the
+# Makefile.
+#
+# If you're looking at a .w file instead of facts.prew, then you should
+# remember to edit the original .prew files, not the .w files.
+#
+# This facts.prew file describes the program
+#
+# for(i = 0; i <= N-1; i++) {
+#  cur[i]=...
+# }
+# for(t = 0; t < T; t++) {
+#   for(i = 0; i <= N-1; i++) {
+#     old[i]=cur[i];
+#   }
+#   for(i = 1; i <= N-2; i++) {
+#     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+#   }
+# }
+
+
+
+# first, the spaces and memory maps
+
+symbolic T, N;
+
+IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+
+IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+
+IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+
+RESULTS := { [3,0,0,0,0] };
+
+
+# memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+
+FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+BWD5 := inverse FWD5;
+BWD7 := inverse FWD7;
+EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+
+# output deps
+
+OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+
+# combined flow/anti deps
+
+FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+
+# total memory deps in the "core"
+
+COREMEMDEPS := OAA union OCC union FAC union FCA;
+
+
+
+# data flow for original code:
+
+DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+
+DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+
+
+# data flow for array expanded code,
+# after forward substitution of "old[i] = cur[i]"
+
+DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+
+# total data flow
+
+COREDATAFLOW := DF1C union DF2C union DF3C;
+
+
+# arity expansion relations
+ex_0_5v := {             [] -> [a,b,c,d,e]     };
+ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+
+ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+
+
+# stuff used in skew and tskew
+
+# Here is the description of time skewing from the current draft of the paper.
+IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+
+IS_Tinv := inverse IS_Trans;
+
+# We use it to transform the iteration spaces
+TS_IS_CALC := IS_CALC join IS_Trans;
+# for some reason OC refuses do to this "join" but will do the reverse:
+# TS_IS_INIT := ex_7_5 join IS_INIT;
+TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+
+# Now we can update the data flow relations to correspond to the new I.S.'s
+TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+
+ 
+KNOWN := { [] : T >= 0 and N >= 4 };
+ 
+IS_INIT_EXP := { [1,t,1,i,0] : (0=t && 0<=i<=N-1) ||
+			       (1=t && 0=i) ||
+			       (1=t && N-1=i) };
+
+TSKEW := { [2, t, 1, i, 1] -> [2, tb, t+i, tt, 0] :
+		 1000*tb+tt = t and 0 <= tt < 1000 };
+
+codegen
+ 	IS_INIT_EXP, TSKEW : IS_CALC
+given	(KNOWN join ex_0_5v);
+
diff --git a/omega/examples/old_test/ts1d-check-sblock.oc-rt b/omega/examples/old_test/ts1d-check-sblock.oc-rt
new file mode 100644
index 0000000..492fa30
--- /dev/null
+++ b/omega/examples/old_test/ts1d-check-sblock.oc-rt
@@ -0,0 +1,227 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # This is the file facts.prew, which is prepended to the .prew files
+# # for the particular code generation we want, defines things like the
+# # iteration space and dependences.  Known facts are inserted by the
+# # Makefile.
+# #
+# # If you're looking at a .w file instead of facts.prew, then you should
+# # remember to edit the original .prew files, not the .w files.
+# #
+# # This facts.prew file describes the program
+# #
+# # for(i = 0; i <= N-1; i++) {
+# #  cur[i]=...
+# # }
+# # for(t = 0; t < T; t++) {
+# #   for(i = 0; i <= N-1; i++) {
+# #     old[i]=cur[i];
+# #   }
+# #   for(i = 1; i <= N-2; i++) {
+# #     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+# #   }
+# # }
+# 
+# 
+# 
+# # first, the spaces and memory maps
+# 
+# symbolic T, N;
+# 
+# 
+# IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+# 
+# MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+# 
+# 
+# IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+# 
+# MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+# 
+# 
+# IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+# 
+# MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+# 
+# 
+# RESULTS := { [3,0,0,0,0] };
+# 
+# 
+# 
+# # memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+# 
+# FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+# 
+# FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+# 
+# BWD5 := inverse FWD5;
+# 
+# BWD7 := inverse FWD7;
+# 
+# EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+# 
+# 
+# # output deps
+# 
+# OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+# 
+# OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+# 
+# 
+# # combined flow/anti deps
+# 
+# FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+# 
+# FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+# 
+# 
+# # total memory deps in the "core"
+# 
+# COREMEMDEPS := OAA union OCC union FAC union FCA;
+# 
+# 
+# 
+# 
+# # data flow for original code:
+# 
+# DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+# 
+# DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+# 
+# DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+# 
+# DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+# 
+# 
+# DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+# 
+# DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+# 
+# DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+# 
+# 
+# 
+# # data flow for array expanded code,
+# # after forward substitution of "old[i] = cur[i]"
+# 
+# DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# 
+# # total data flow
+# 
+# COREDATAFLOW := DF1C union DF2C union DF3C;
+# 
+# 
+# 
+# # arity expansion relations
+# ex_0_5v := {             [] -> [a,b,c,d,e]     };
+# 
+# ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+# 
+# ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+# 
+# ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+# 
+# ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+# 
+# 
+# ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+# 
+# ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+# 
+# ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+# 
+# 
+# 
+# # stuff used in skew and tskew
+# 
+# # Here is the description of time skewing from the current draft of the paper.
+# IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+# 	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+# 
+# 
+# IS_Tinv := inverse IS_Trans;
+# 
+# 
+# # We use it to transform the iteration spaces
+# TS_IS_CALC := IS_CALC join IS_Trans;
+# 
+# # for some reason OC refuses do to this "join" but will do the reverse:
+# # TS_IS_INIT := ex_7_5 join IS_INIT;
+# TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+# 
+# 
+# # Now we can update the data flow relations to correspond to the new I.S.'s
+# TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+# 
+# TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+# 
+# TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+# 
+# TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+# 
+# TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+# 
+# TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+# 
+# TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+# 
+# TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+# 
+# 
+#  
+# KNOWN := { [] : T >= 0 and N >= 4 };
+# 
+#  
+# IS_INIT_EXP := { [1,t,1,i,0] : (0=t && 0<=i<=N-1) ||
+# 			       (1=t && 0=i) ||
+# 			       (1=t && N-1=i) };
+# 
+# 
+# TSKEW := { [2, t, 1, i, 1] -> [2, tb, t+i, tt, 0] :
+# 		 1000*tb+tt = t and 0 <= tt < 1000 };
+# 
+# 
+# codegen
+#  	IS_INIT_EXP, TSKEW : IS_CALC
+# given	(KNOWN join ex_0_5v);
+for(t4 = 0; t4 <= N-1; t4++) {
+  s1(1,0,1,t4,0);
+}
+s1(1,1,1,0,0);
+s1(1,1,1,N-1,0);
+for(t2 = 0; t2 <= intDiv(T-1,1000); t2++) {
+  for(t3 = 1000*t2+1; t3 <= min(N+1000*t2+997,N+T-3); t3++) {
+    for(t4 = max(-N+t3-1000*t2+2,0); t4 <= min(T-1000*t2-1,t3-1000*t2-1,999); t4++) {
+      s2(2,t4+1000*t2,1,t3-t4+-1000*t2,1);
+    }
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/ts1d-check0 b/omega/examples/old_test/ts1d-check0
new file mode 100644
index 0000000..9db25df
--- /dev/null
+++ b/omega/examples/old_test/ts1d-check0
@@ -0,0 +1,176 @@
+# This is the file facts.prew, which is prepended to the .prew files
+# for the particular code generation we want, defines things like the
+# iteration space and dependences.  Known facts are inserted by the
+# Makefile.
+#
+# If you're looking at a .w file instead of facts.prew, then you should
+# remember to edit the original .prew files, not the .w files.
+#
+# This facts.prew file describes the program
+#
+# for(i = 0; i <= N-1; i++) {
+#  cur[i]=...
+# }
+# for(t = 0; t < T; t++) {
+#   for(i = 0; i <= N-1; i++) {
+#     old[i]=cur[i];
+#   }
+#   for(i = 1; i <= N-2; i++) {
+#     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+#   }
+# }
+
+
+
+# first, the spaces and memory maps
+
+symbolic T, N;
+
+IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+
+IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+
+IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+
+RESULTS := { [3,0,0,0,0] };
+
+
+# memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+
+FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+BWD5 := inverse FWD5;
+BWD7 := inverse FWD7;
+EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+
+# output deps
+
+OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+
+# combined flow/anti deps
+
+FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+
+# total memory deps in the "core"
+
+COREMEMDEPS := OAA union OCC union FAC union FCA;
+
+
+
+# data flow for original code:
+
+DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+
+DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+
+
+# data flow for array expanded code,
+# after forward substitution of "old[i] = cur[i]"
+
+DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+
+# total data flow
+
+COREDATAFLOW := DF1C union DF2C union DF3C;
+
+
+# arity expansion relations
+ex_0_5v := {             [] -> [a,b,c,d,e]     };
+ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+
+ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+
+
+# stuff used in skew and tskew
+
+# Here is the description of time skewing from the current draft of the paper.
+IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+
+IS_Tinv := inverse IS_Trans;
+
+# We use it to transform the iteration spaces
+TS_IS_CALC := IS_CALC join IS_Trans;
+# for some reason OC refuses do to this "join" but will do the reverse:
+# TS_IS_INIT := ex_7_5 join IS_INIT;
+TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+
+# Now we can update the data flow relations to correspond to the new I.S.'s
+TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+
+ 
+KNOWN := { [] : T >= 0 and N >= 4 };
+ 
+# Lets try to build up the equivalent of the time skewing transformation,
+# IS_Trans := { [2,t,1,i,1] -> [2,tb,1,x,1,y,1] :
+# 	1000*tb<=t-1<=1000*(tb+1)-1 && y=t-1000*tb && x=y+i };
+# for both statements together, right from the diagram in the new TOPLAS stuff.
+
+# original code without mmap
+#
+
+# First, look at it as a wider space
+
+WIDEN := { [2, t, s, i , 1] -> [2, 2t+s, 0, i, 1] : 0<=s<=1 };
+TSKEW := { [2, t, 0, i , 1] -> [2, tb, t+i, tt, 1] :
+		 1000*tb+tt = t and 0 <= tt < 1000 };
+
+TSKEW_2LOOPS := WIDEN join TSKEW;
+# print this for the paper
+
+# I think this should work but it blows up codegen:
+# codegen
+# 	IS_INIT, TSKEW_2LOOPS : IS_COPY, TSKEW_2LOOPS : IS_CALC
+# given	(KNOWN join ex_0_5v);
+
+# So we fake it as follows,
+# relying on the fact that neither "t" nor "s" is used in any statement
+
+WIDEN0 := { [2, t, 0, i , 1] -> [2, 2t, 0, i, 1] };
+WIDEN1 := { [2, t, 1, i , 1] -> [2, 2t+1, 0, i, 1] };
+
+codegen
+ 	IS_INIT, TSKEW : (IS_COPY join WIDEN0) , TSKEW : (IS_CALC join WIDEN1)
+given	(KNOWN join ex_0_5v);
+
diff --git a/omega/examples/old_test/ts1d-check0.oc-rt b/omega/examples/old_test/ts1d-check0.oc-rt
new file mode 100644
index 0000000..a258f26
--- /dev/null
+++ b/omega/examples/old_test/ts1d-check0.oc-rt
@@ -0,0 +1,260 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # This is the file facts.prew, which is prepended to the .prew files
+# # for the particular code generation we want, defines things like the
+# # iteration space and dependences.  Known facts are inserted by the
+# # Makefile.
+# #
+# # If you're looking at a .w file instead of facts.prew, then you should
+# # remember to edit the original .prew files, not the .w files.
+# #
+# # This facts.prew file describes the program
+# #
+# # for(i = 0; i <= N-1; i++) {
+# #  cur[i]=...
+# # }
+# # for(t = 0; t < T; t++) {
+# #   for(i = 0; i <= N-1; i++) {
+# #     old[i]=cur[i];
+# #   }
+# #   for(i = 1; i <= N-2; i++) {
+# #     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+# #   }
+# # }
+# 
+# 
+# 
+# # first, the spaces and memory maps
+# 
+# symbolic T, N;
+# 
+# 
+# IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+# 
+# MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+# 
+# 
+# IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+# 
+# MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+# 
+# 
+# IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+# 
+# MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+# 
+# 
+# RESULTS := { [3,0,0,0,0] };
+# 
+# 
+# 
+# # memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+# 
+# FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+# 
+# FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+# 
+# BWD5 := inverse FWD5;
+# 
+# BWD7 := inverse FWD7;
+# 
+# EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+# 
+# 
+# # output deps
+# 
+# OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+# 
+# OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+# 
+# 
+# # combined flow/anti deps
+# 
+# FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+# 
+# FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+# 
+# 
+# # total memory deps in the "core"
+# 
+# COREMEMDEPS := OAA union OCC union FAC union FCA;
+# 
+# 
+# 
+# 
+# # data flow for original code:
+# 
+# DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+# 
+# DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+# 
+# DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+# 
+# DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+# 
+# 
+# DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+# 
+# DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+# 
+# DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+# 
+# 
+# 
+# # data flow for array expanded code,
+# # after forward substitution of "old[i] = cur[i]"
+# 
+# DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# 
+# # total data flow
+# 
+# COREDATAFLOW := DF1C union DF2C union DF3C;
+# 
+# 
+# 
+# # arity expansion relations
+# ex_0_5v := {             [] -> [a,b,c,d,e]     };
+# 
+# ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+# 
+# ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+# 
+# ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+# 
+# ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+# 
+# 
+# ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+# 
+# ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+# 
+# ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+# 
+# 
+# 
+# # stuff used in skew and tskew
+# 
+# # Here is the description of time skewing from the current draft of the paper.
+# IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+# 	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+# 
+# 
+# IS_Tinv := inverse IS_Trans;
+# 
+# 
+# # We use it to transform the iteration spaces
+# TS_IS_CALC := IS_CALC join IS_Trans;
+# 
+# # for some reason OC refuses do to this "join" but will do the reverse:
+# # TS_IS_INIT := ex_7_5 join IS_INIT;
+# TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+# 
+# 
+# # Now we can update the data flow relations to correspond to the new I.S.'s
+# TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+# 
+# TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+# 
+# TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+# 
+# TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+# 
+# TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+# 
+# TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+# 
+# TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+# 
+# TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+# 
+# 
+#  
+# KNOWN := { [] : T >= 0 and N >= 4 };
+# 
+#  
+# # Lets try to build up the equivalent of the time skewing transformation,
+# # IS_Trans := { [2,t,1,i,1] -> [2,tb,1,x,1,y,1] :
+# # 	1000*tb<=t-1<=1000*(tb+1)-1 && y=t-1000*tb && x=y+i };
+# # for both statements together, right from the diagram in the new TOPLAS stuff.
+# 
+# # original code without mmap
+# #
+# 
+# # First, look at it as a wider space
+# 
+# WIDEN := { [2, t, s, i , 1] -> [2, 2t+s, 0, i, 1] : 0<=s<=1 };
+# 
+# TSKEW := { [2, t, 0, i , 1] -> [2, tb, t+i, tt, 1] :
+# 		 1000*tb+tt = t and 0 <= tt < 1000 };
+# 
+# 
+# TSKEW_2LOOPS := WIDEN join TSKEW;
+# 
+# # print this for the paper
+# 
+# # I think this should work but it blows up codegen:
+# # codegen
+# # 	IS_INIT, TSKEW_2LOOPS : IS_COPY, TSKEW_2LOOPS : IS_CALC
+# # given	(KNOWN join ex_0_5v);
+# 
+# # So we fake it as follows,
+# # relying on the fact that neither "t" nor "s" is used in any statement
+# 
+# WIDEN0 := { [2, t, 0, i , 1] -> [2, 2t, 0, i, 1] };
+# 
+# WIDEN1 := { [2, t, 1, i , 1] -> [2, 2t+1, 0, i, 1] };
+# 
+# 
+# codegen
+#  	IS_INIT, TSKEW : (IS_COPY join WIDEN0) , TSKEW : (IS_CALC join WIDEN1)
+# given	(KNOWN join ex_0_5v);
+for(t2 = 0; t2 <= N-1; t2++) {
+  s1(1,t2,1,0,0);
+}
+for(t2 = 0; t2 <= intDiv(T-1,500); t2++) {
+  for(t3 = 1000*t2; t3 <= min(1000*t2+N+997,N+2*T-3); t3++) {
+    if (intMod(-N+t3+1,2) == 0 && 1000*t2 <= -N+t3+1) {
+      s2(2,t3-N+1,0,N-1,1);
+    }
+    for(t4 = max(-1000*t2-N+t3+2,0); t4 <= min(-1000*t2+2*T-1,-1000*t2+t3-1,999); t4++) {
+      if (intMod(t4,2) == 0) {
+        s2(2,t4+1000*t2,0,t3-t4+-1000*t2,1);
+      }
+      if (intMod(t4+1,2) == 0) {
+        s3(2,t4+1000*t2,0,t3-t4+-1000*t2,1);
+      }
+    }
+    if (intMod(t3,2) == 0 && 2*T >= t3+2 && 1000*t2 >= t3-998) {
+      s2(2,t3,0,0,1);
+    }
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/ts1d-mp-i_ts-m_b b/omega/examples/old_test/ts1d-mp-i_ts-m_b
new file mode 100644
index 0000000..f288263
--- /dev/null
+++ b/omega/examples/old_test/ts1d-mp-i_ts-m_b
@@ -0,0 +1,289 @@
+# This is the file facts.prew, which is prepended to the .prew files
+# for the particular code generation we want, defines things like the
+# iteration space and dependences.  Known facts are inserted by the
+# Makefile.
+#
+# If you're looking at a .w file instead of facts.prew, then you should
+# remember to edit the original .prew files, not the .w files.
+#
+# This facts.prew file describes the program
+#
+# for(i = 0; i <= N-1; i++) {
+#  cur[i]=...
+# }
+# for(t = 0; t < T; t++) {
+#   for(i = 0; i <= N-1; i++) {
+#     old[i]=cur[i];
+#   }
+#   for(i = 1; i <= N-2; i++) {
+#     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+#   }
+# }
+
+
+
+# first, the spaces and memory maps
+
+symbolic T, N;
+
+IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+
+IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+
+IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+
+RESULTS := { [3,0,0,0,0] };
+
+
+# memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+
+FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+BWD5 := inverse FWD5;
+BWD7 := inverse FWD7;
+EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+
+# output deps
+
+OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+
+# combined flow/anti deps
+
+FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+
+# total memory deps in the "core"
+
+COREMEMDEPS := OAA union OCC union FAC union FCA;
+
+
+
+# data flow for original code:
+
+DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+
+DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+
+
+# data flow for array expanded code,
+# after forward substitution of "old[i] = cur[i]"
+
+DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+
+# total data flow
+
+COREDATAFLOW := DF1C union DF2C union DF3C;
+
+
+# arity expansion relations
+ex_0_5v := {             [] -> [a,b,c,d,e]     };
+ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+
+ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+
+
+# stuff used in skew and tskew
+
+# Here is the description of time skewing from the current draft of the paper.
+IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+	0<=tt<500 && s=i+1*t && t=500*tb+tt };
+
+IS_Tinv := inverse IS_Trans;
+
+# We use it to transform the iteration spaces
+TS_IS_CALC := IS_CALC join IS_Trans;
+# for some reason OC refuses do to this "join" but will do the reverse:
+# TS_IS_INIT := ex_7_5 join IS_INIT;
+TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+
+# Now we can update the data flow relations to correspond to the new I.S.'s
+TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+
+ 
+KNOWN := { [] : T >= 0 and N >= 4 };
+ 
+#
+#  multiprocessor version
+#  time skewed iteration space
+#  blocked memory mapping 
+#
+
+#
+# First of all, if 500 is much less than 4000,
+#  there's a problem with the constraints below.
+# To keep send and recv. slices from "crashing", 4000>=2BS+2 (safe approx?)
+#
+
+assertUnsatisfiable( { [] : 4000 < 2 * 500 + 2 } );
+
+# this transformation has no existentially quantified variables;
+#  basically, it factors out the common stuff below,
+#  but the quantified variables are left in the output, so we can get them
+#  everything after the 000 is not needed in final xform
+
+#
+# DANGER WILL ROBINSON!
+#  the .c file depends on the fact that t4 is always the processor number
+#
+
+MP_TSKEW_ALL  := { [2, t, 1, i, 1] ->
+		   [2, tb, slice, proc, t+i, tt, 000, t, i, lproc, t0, i0, ie]:
+##
+##	define time block and tt
+##
+		500*tb+tt = t and 0 <= tt < 500 
+##
+##		define "logical proc", then "wrap" onto physical later:
+##		"logical proc" (lproc) = (t-i) div sigma
+##
+		and	4000*lproc <= t-i < 4000*(lproc+1)
+##
+##  for uniproc. test, just do proc = -lproc (for multi, proc = lproc % 8)
+##
+		and	proc = -lproc
+##
+##  t0,i0 = first iteration in a block;
+##  t0,ie = maximum "i" in t0 of this block)
+##
+		and	t0=500*tb
+		and	t0-ie=4000*lproc
+		and	i0+4000-1=ie
+};
+
+#
+# We need to send things "down" (to same time block of next proc.)
+# and "right" (to next time block of next proc.)
+# The "+2" is for the things to send right (not mentioned in IPDPS paper).
+#
+
+MP_TSKEW_SEND_SL := MP_TSKEW_ALL join
+	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+	  [2, tb, 1, proc, t_p_i, tt, 0] :
+##  define send slice...
+			(t+i) <= (t0+(500-2) + i0+(500-1) + 2)
+};
+
+MP_TSKEW_SEND_ME := MP_TSKEW_ALL join
+	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+	  [2, tb, 2, proc, t_p_i, tt, 0] :
+##  in the send slice
+			(t+i) <= (t0+(500-2) + i0+(500-1) + 2)
+##  and near the (t-i) border:
+		and	(t-i) >= ((t0-i0)-1)
+};
+
+MP_TSKEW_COMP_SL := MP_TSKEW_ALL join
+	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+	  [2, tb, 3, proc, t_p_i, tt, 0] :
+##  define computation slice...
+##  not send
+			(t+i) >  (t0+(500-2) + i0+(500-1) + 2)
+##  and not recv
+		and	(t+i) <= (t0+ie)
+};
+
+
+
+# Receive the iterations that we sent,
+# but after the calculation,
+# and on the neighbor (lower) processor
+
+MP_TSKEW_R_FROM_ME := MP_TSKEW_SEND_ME join 
+	{ [2, tb, 2, proc, t_p_i, tt, 0] ->
+	  [2, tb, 4, proc-1, t_p_i, tt, 0] };
+
+
+MP_TSKEW_RECV_SL := MP_TSKEW_ALL join
+	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+	  [2, tb, 5, proc, t_p_i, tt, 0] :
+##  define recv slice...
+			(t+i) > (t0+ie)
+};
+
+
+
+
+## stuff to gather each processor's final results...
+
+IS_GATHER := IS_CALC intersection { [2,t,1,i,1] : t=T-1 };
+
+GATHER_EXPANDER := MP_TSKEW_ALL join
+	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+	  [3, tb, 7, proc, t_p_i, tt, 0] };
+
+## stuff to initialize things right in the first place
+
+### NOTE THAT t4 (processor #) is used in a loop in initialization
+
+IS_INIT_EXP := { [1,t,i,0,0] : (-1=t && 0<=i<=N-1) ||
+			       (0<=t<T && 0=i) ||
+			       (0<=t<T && N-1=i) };
+
+
+# send_slice + calc_slice + recv slice == total
+
+TheSendIS := domain(MP_TSKEW_SEND_SL restrictDomain IS_CALC);
+TheCompIS := domain(MP_TSKEW_COMP_SL restrictDomain IS_CALC);
+TheRecvIS := domain(MP_TSKEW_RECV_SL restrictDomain IS_CALC);
+
+assertUnsatisfiable(TheSendIS intersection TheCompIS);
+assertUnsatisfiable(TheCompIS intersection TheRecvIS);
+assertUnsatisfiable(TheSendIS intersection TheRecvIS);
+#
+# These cause inexact negation and thus blow up...
+#
+# assertUnsatisfiable(IS_CALC - (TheSendIS union TheCompIS union TheRecvIS));
+# assertUnsatisfiable((TheSendIS union TheCompIS union TheRecvIS) - IS_CALC);
+
+
+
+codegen
+	ex_5_7 : IS_INIT_EXP,
+	MP_TSKEW_SEND_SL : IS_CALC,
+	 MP_TSKEW_SEND_ME : IS_CALC,
+	MP_TSKEW_COMP_SL : IS_CALC,
+	 MP_TSKEW_R_FROM_ME : IS_CALC,
+	MP_TSKEW_RECV_SL : IS_CALC,
+	GATHER_EXPANDER : IS_GATHER
+given	(KNOWN join ex_0_7v);
+
diff --git a/omega/examples/old_test/ts1d-mp-i_ts-m_b.oc-rt b/omega/examples/old_test/ts1d-mp-i_ts-m_b.oc-rt
new file mode 100644
index 0000000..6d3ef2a
--- /dev/null
+++ b/omega/examples/old_test/ts1d-mp-i_ts-m_b.oc-rt
@@ -0,0 +1,430 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # This is the file facts.prew, which is prepended to the .prew files
+# # for the particular code generation we want, defines things like the
+# # iteration space and dependences.  Known facts are inserted by the
+# # Makefile.
+# #
+# # If you're looking at a .w file instead of facts.prew, then you should
+# # remember to edit the original .prew files, not the .w files.
+# #
+# # This facts.prew file describes the program
+# #
+# # for(i = 0; i <= N-1; i++) {
+# #  cur[i]=...
+# # }
+# # for(t = 0; t < T; t++) {
+# #   for(i = 0; i <= N-1; i++) {
+# #     old[i]=cur[i];
+# #   }
+# #   for(i = 1; i <= N-2; i++) {
+# #     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+# #   }
+# # }
+# 
+# 
+# 
+# # first, the spaces and memory maps
+# 
+# symbolic T, N;
+# 
+# 
+# IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+# 
+# MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+# 
+# 
+# IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+# 
+# MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+# 
+# 
+# IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+# 
+# MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+# 
+# 
+# RESULTS := { [3,0,0,0,0] };
+# 
+# 
+# 
+# # memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+# 
+# FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+# 
+# FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+# 
+# BWD5 := inverse FWD5;
+# 
+# BWD7 := inverse FWD7;
+# 
+# EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+# 
+# 
+# # output deps
+# 
+# OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+# 
+# OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+# 
+# 
+# # combined flow/anti deps
+# 
+# FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+# 
+# FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+# 
+# 
+# # total memory deps in the "core"
+# 
+# COREMEMDEPS := OAA union OCC union FAC union FCA;
+# 
+# 
+# 
+# 
+# # data flow for original code:
+# 
+# DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+# 
+# DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+# 
+# DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+# 
+# DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+# 
+# 
+# DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+# 
+# DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+# 
+# DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+# 
+# 
+# 
+# # data flow for array expanded code,
+# # after forward substitution of "old[i] = cur[i]"
+# 
+# DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# 
+# # total data flow
+# 
+# COREDATAFLOW := DF1C union DF2C union DF3C;
+# 
+# 
+# 
+# # arity expansion relations
+# ex_0_5v := {             [] -> [a,b,c,d,e]     };
+# 
+# ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+# 
+# ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+# 
+# ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+# 
+# ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+# 
+# 
+# ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+# 
+# ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+# 
+# ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+# 
+# 
+# 
+# # stuff used in skew and tskew
+# 
+# # Here is the description of time skewing from the current draft of the paper.
+# IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+# 	0<=tt<500 && s=i+1*t && t=500*tb+tt };
+# 
+# 
+# IS_Tinv := inverse IS_Trans;
+# 
+# 
+# # We use it to transform the iteration spaces
+# TS_IS_CALC := IS_CALC join IS_Trans;
+# 
+# # for some reason OC refuses do to this "join" but will do the reverse:
+# # TS_IS_INIT := ex_7_5 join IS_INIT;
+# TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+# 
+# 
+# # Now we can update the data flow relations to correspond to the new I.S.'s
+# TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+# 
+# TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+# 
+# TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+# 
+# TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+# 
+# TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+# 
+# TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+# 
+# TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+# 
+# TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+# 
+# 
+#  
+# KNOWN := { [] : T >= 0 and N >= 4 };
+# 
+#  
+# #
+# #  multiprocessor version
+# #  time skewed iteration space
+# #  blocked memory mapping 
+# #
+# 
+# #
+# # First of all, if 500 is much less than 4000,
+# #  there's a problem with the constraints below.
+# # To keep send and recv. slices from "crashing", 4000>=2BS+2 (safe approx?)
+# #
+# 
+# assertUnsatisfiable( { [] : 4000 < 2 * 500 + 2 } );
+
+{ FALSE }
+
+# 
+# 
+# # this transformation has no existentially quantified variables;
+# #  basically, it factors out the common stuff below,
+# #  but the quantified variables are left in the output, so we can get them
+# #  everything after the 000 is not needed in final xform
+# 
+# #
+# # DANGER WILL ROBINSON!
+# #  the .c file depends on the fact that t4 is always the processor number
+# #
+# 
+# MP_TSKEW_ALL  := { [2, t, 1, i, 1] ->
+# 		   [2, tb, slice, proc, t+i, tt, 000, t, i, lproc, t0, i0, ie]:
+# ##
+# ##	define time block and tt
+# ##
+# 		500*tb+tt = t and 0 <= tt < 500 
+# ##
+# ##		define "logical proc", then "wrap" onto physical later:
+# ##		"logical proc" (lproc) = (t-i) div sigma
+# ##
+# 		and	4000*lproc <= t-i < 4000*(lproc+1)
+# ##
+# ##  for uniproc. test, just do proc = -lproc (for multi, proc = lproc % 8)
+# ##
+# 		and	proc = -lproc
+# ##
+# ##  t0,i0 = first iteration in a block;
+# ##  t0,ie = maximum "i" in t0 of this block)
+# ##
+# 		and	t0=500*tb
+# 		and	t0-ie=4000*lproc
+# 		and	i0+4000-1=ie
+# };
+# 
+# 
+# #
+# # We need to send things "down" (to same time block of next proc.)
+# # and "right" (to next time block of next proc.)
+# # The "+2" is for the things to send right (not mentioned in IPDPS paper).
+# #
+# 
+# MP_TSKEW_SEND_SL := MP_TSKEW_ALL join
+# 	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+# 	  [2, tb, 1, proc, t_p_i, tt, 0] :
+# ##  define send slice...
+# 			(t+i) <= (t0+(500-2) + i0+(500-1) + 2)
+# };
+# 
+# 
+# MP_TSKEW_SEND_ME := MP_TSKEW_ALL join
+# 	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+# 	  [2, tb, 2, proc, t_p_i, tt, 0] :
+# ##  in the send slice
+# 			(t+i) <= (t0+(500-2) + i0+(500-1) + 2)
+# ##  and near the (t-i) border:
+# 		and	(t-i) >= ((t0-i0)-1)
+# };
+# 
+# 
+# MP_TSKEW_COMP_SL := MP_TSKEW_ALL join
+# 	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+# 	  [2, tb, 3, proc, t_p_i, tt, 0] :
+# ##  define computation slice...
+# ##  not send
+# 			(t+i) >  (t0+(500-2) + i0+(500-1) + 2)
+# ##  and not recv
+# 		and	(t+i) <= (t0+ie)
+# };
+# 
+# 
+# 
+# 
+# # Receive the iterations that we sent,
+# # but after the calculation,
+# # and on the neighbor (lower) processor
+# 
+# MP_TSKEW_R_FROM_ME := MP_TSKEW_SEND_ME join 
+# 	{ [2, tb, 2, proc, t_p_i, tt, 0] ->
+# 	  [2, tb, 4, proc-1, t_p_i, tt, 0] };
+# 
+# 
+# 
+# MP_TSKEW_RECV_SL := MP_TSKEW_ALL join
+# 	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+# 	  [2, tb, 5, proc, t_p_i, tt, 0] :
+# ##  define recv slice...
+# 			(t+i) > (t0+ie)
+# };
+# 
+# 
+# 
+# 
+# 
+# ## stuff to gather each processor's final results...
+# 
+# IS_GATHER := IS_CALC intersection { [2,t,1,i,1] : t=T-1 };
+# 
+# 
+# GATHER_EXPANDER := MP_TSKEW_ALL join
+# 	{ [2, tb, slice, proc, t_p_i, tt, 000, t, i, lproc, t0, i0, ie] ->
+# 	  [3, tb, 7, proc, t_p_i, tt, 0] };
+# 
+# 
+# ## stuff to initialize things right in the first place
+# 
+# ### NOTE THAT t4 (processor #) is used in a loop in initialization
+# 
+# IS_INIT_EXP := { [1,t,i,0,0] : (-1=t && 0<=i<=N-1) ||
+# 			       (0<=t<T && 0=i) ||
+# 			       (0<=t<T && N-1=i) };
+# 
+# 
+# 
+# # send_slice + calc_slice + recv slice == total
+# 
+# TheSendIS := domain(MP_TSKEW_SEND_SL restrictDomain IS_CALC);
+# 
+# TheCompIS := domain(MP_TSKEW_COMP_SL restrictDomain IS_CALC);
+# 
+# TheRecvIS := domain(MP_TSKEW_RECV_SL restrictDomain IS_CALC);
+# 
+# 
+# assertUnsatisfiable(TheSendIS intersection TheCompIS);
+
+{[In_1,t,In_3,i,In_5]  : FALSE }
+
+# 
+# assertUnsatisfiable(TheCompIS intersection TheRecvIS);
+
+{[In_1,t,In_3,i,In_5]  : FALSE }
+
+# 
+# assertUnsatisfiable(TheSendIS intersection TheRecvIS);
+
+{[In_1,t,In_3,i,In_5]  : FALSE }
+
+# 
+# #
+# # These cause inexact negation and thus blow up...
+# #
+# # assertUnsatisfiable(IS_CALC - (TheSendIS union TheCompIS union TheRecvIS));
+# # assertUnsatisfiable((TheSendIS union TheCompIS union TheRecvIS) - IS_CALC);
+# 
+# 
+# 
+# codegen
+# 	ex_5_7 : IS_INIT_EXP,
+# 	MP_TSKEW_SEND_SL : IS_CALC,
+# 	 MP_TSKEW_SEND_ME : IS_CALC,
+# 	MP_TSKEW_COMP_SL : IS_CALC,
+# 	 MP_TSKEW_R_FROM_ME : IS_CALC,
+# 	MP_TSKEW_RECV_SL : IS_CALC,
+# 	GATHER_EXPANDER : IS_GATHER
+# given	(KNOWN join ex_0_7v);
+for(t3 = 0; t3 <= N-1; t3++) {
+  s1(1,-1,t3,0,0);
+}
+for(t2 = 0; t2 <= T-1; t2++) {
+  s1(1,t2,0,0,0);
+  s1(1,t2,N-1,0,0);
+}
+for(t2 = 0; t2 <= intDiv(T-1,500); t2++) {
+  for(t4 = intDiv(-t2+7+7,8); t4 <= intDiv(-500*t2+N+3997,4000); t4++) {
+    for(t5 = max(1000*t2+4000*t4-3999,500*t2+1); t5 <= min(1000*t2+4000*t4-3000,N+T-3,2*N-4000*t4+3995); t5++) {
+      for(t6 = max(-N+t5-500*t2+2,0); t6 <= min(t5-500*t2-1,T-500*t2-1,intDiv(t5-4000*t4-1000*t2+3999,2)); t6++) {
+        s2(2,500*t2+t6,1,t5+-500*t2-t6,1);
+      }
+    }
+  }
+  for(t4 = max(intDiv(-T+4000+3999,4000),intDiv(-t2+7+7,8)); t4 <= intDiv(-500*t2+N+3997,4000); t4++) {
+    for(t5 = max(1000*t2+4000*t4-3999,-4000*t4+4000); t5 <= min(1000*t2+4000*t4-3000,2*N-4000*t4+3995,2*T+4000*t4-4000); t5++) {
+      for(t6 = intDiv(t5-4000*t4-1000*t2+3998+1,2); t6 <= intDiv(t5-4000*t4-1000*t2+3999,2); t6++) {
+        s3(2,500*t2+t6,1,t5+-500*t2-t6,1);
+      }
+    }
+  }
+  for(t4 = intDiv(-t2+1+7,8); t4 <= min(intDiv(-500*t2+N+3496,4000),intDiv(-1000*t2+N+T+2996,4000)); t4++) {
+    for(t5 = max(500*t2+1,4000*t4+1000*t2-2999); t5 <= min(N+T-3,4000*t4+1000*t2,N+500*t2+497); t5++) {
+      for(t6 = max(-N+t5-500*t2+2,0); t6 <= min(T-500*t2-1,t5-500*t2-1,499); t6++) {
+        s4(2,500*t2+t6,1,t5+-500*t2-t6,1);
+      }
+    }
+  }
+  for(t4 = max(intDiv(-T+3999,4000),intDiv(-t2-1+7,8)); t4 <= intDiv(-500*t2+N-3,4000); t4++) {
+    for(t5 = max(1000*t2+4000*t4+1,-4000*t4); t5 <= min(1000*t2+4000*t4+1000,2*N-4000*t4-5,2*T+4000*t4); t5++) {
+      for(t6 = intDiv(-1000*t2-4000*t4+t5-2+1,2); t6 <= intDiv(-1000*t2-4000*t4+t5-1,2); t6++) {
+        s5(2,500*t2+t6,1,t5+-500*t2-t6,1);
+      }
+    }
+  }
+  if (500*t2 <= T-2) {
+    for(t4 = intDiv(-t2+7,8); t4 <= min(intDiv(-500*t2+N+496,4000),intDiv(-1000*t2+N+T-4,4000)); t4++) {
+      for(t5 = max(1000*t2+4000*t4+1,-4000*t4+2); t5 <= min(2*T+4000*t4-2,N+T-3,N+500*t2+497,1000*t2+4000*t4+998); t5++) {
+        for(t6 = max(-N+t5-500*t2+2,intDiv(t5-4000*t4-1000*t2+1,2)); t6 <= min(t5-500*t2-1,T-500*t2-1,499); t6++) {
+          s6(2,500*t2+t6,1,t5+-500*t2-t6,1);
+        }
+      }
+    }
+  }
+}
+if (T >= 1) {
+  for(t2 = intDiv(T-500+499,500); t2 <= intDiv(T-1,500); t2++) {
+    for(t4 = intDiv(-T+2+3999,4000); t4 <= intDiv(N-T+3998,4000); t4++) {
+      for(t5 = max(4000*t4+2*T-4001,T); t5 <= min(4000*t4+2*T-2,N+T-3); t5++) {
+        s7(2,T-1,1,t5-T+1,1);
+      }
+    }
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/ts1d-orig0 b/omega/examples/old_test/ts1d-orig0
new file mode 100644
index 0000000..48e5a10
--- /dev/null
+++ b/omega/examples/old_test/ts1d-orig0
@@ -0,0 +1,151 @@
+# This is the file facts.prew, which is prepended to the .prew files
+# for the particular code generation we want, defines things like the
+# iteration space and dependences.  Known facts are inserted by the
+# Makefile.
+#
+# If you're looking at a .w file instead of facts.prew, then you should
+# remember to edit the original .prew files, not the .w files.
+#
+# This facts.prew file describes the program
+#
+# for(i = 0; i <= N-1; i++) {
+#  cur[i]=...
+# }
+# for(t = 0; t < T; t++) {
+#   for(i = 0; i <= N-1; i++) {
+#     old[i]=cur[i];
+#   }
+#   for(i = 1; i <= N-2; i++) {
+#     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+#   }
+# }
+
+
+
+# first, the spaces and memory maps
+
+symbolic T, N;
+
+IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+
+IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+
+IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+
+RESULTS := { [3,0,0,0,0] };
+
+
+# memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+
+FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+	(x'>x) or
+	(x'=x and t'>t) or
+	(x'=x and t'=t and y'>y) or
+	(x'=x and t'=t and y'=y and i'>i) or
+	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+BWD5 := inverse FWD5;
+BWD7 := inverse FWD7;
+EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+
+# output deps
+
+OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+
+# combined flow/anti deps
+
+FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+
+# total memory deps in the "core"
+
+COREMEMDEPS := OAA union OCC union FAC union FCA;
+
+
+
+# data flow for original code:
+
+DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+
+DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+
+
+# data flow for array expanded code,
+# after forward substitution of "old[i] = cur[i]"
+
+DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+
+# total data flow
+
+COREDATAFLOW := DF1C union DF2C union DF3C;
+
+
+# arity expansion relations
+ex_0_5v := {             [] -> [a,b,c,d,e]     };
+ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+
+ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+
+
+# stuff used in skew and tskew
+
+# Here is the description of time skewing from the current draft of the paper.
+IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+
+IS_Tinv := inverse IS_Trans;
+
+# We use it to transform the iteration spaces
+TS_IS_CALC := IS_CALC join IS_Trans;
+# for some reason OC refuses do to this "join" but will do the reverse:
+# TS_IS_INIT := ex_7_5 join IS_INIT;
+TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+
+# Now we can update the data flow relations to correspond to the new I.S.'s
+TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+
+ 
+KNOWN := { [] : T >= 0 and N >= 4 };
+ 
+# original code without mmap
+#
+
+codegen
+	IS_INIT, IS_COPY, IS_CALC
+given	(KNOWN join ex_0_5v);
+
diff --git a/omega/examples/old_test/ts1d-orig0.oc-rt b/omega/examples/old_test/ts1d-orig0.oc-rt
new file mode 100644
index 0000000..775af7e
--- /dev/null
+++ b/omega/examples/old_test/ts1d-orig0.oc-rt
@@ -0,0 +1,220 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# # This is the file facts.prew, which is prepended to the .prew files
+# # for the particular code generation we want, defines things like the
+# # iteration space and dependences.  Known facts are inserted by the
+# # Makefile.
+# #
+# # If you're looking at a .w file instead of facts.prew, then you should
+# # remember to edit the original .prew files, not the .w files.
+# #
+# # This facts.prew file describes the program
+# #
+# # for(i = 0; i <= N-1; i++) {
+# #  cur[i]=...
+# # }
+# # for(t = 0; t < T; t++) {
+# #   for(i = 0; i <= N-1; i++) {
+# #     old[i]=cur[i];
+# #   }
+# #   for(i = 1; i <= N-2; i++) {
+# #     cur[i] = (old[i-1]+old[i]+old[i]+old[i+1])*0.25;
+# #   }
+# # }
+# 
+# 
+# 
+# # first, the spaces and memory maps
+# 
+# symbolic T, N;
+# 
+# 
+# IS_INIT := { [1,i,1,0,0]          :           0<=i<=N-1 };
+# 
+# MM_INIT := { [1,i,1,0,0] -> [0,i] :           0<=i<=N-1 };
+# 
+# 
+# IS_COPY := { [2,t,0,i,1]            : 0<=t<T && 0<=i<=N-1 };
+# 
+# MM_COPY := { [2,t,0,i,1] -> [t+1,i] : 0<=t<T && 0<=i<=N-1 };
+# 
+# 
+# IS_CALC := { [2,t,1,i,1]            : 0<=t<T && 0< i< N-1 };
+# 
+# MM_CALC := { [2,t,1,i,1] -> [t+1,i] : 0<=t<T && 0< i< N-1 };
+# 
+# 
+# RESULTS := { [3,0,0,0,0] };
+# 
+# 
+# 
+# # memory-based Output and Flow/anti-dependences (among Assign (copy), and Calc)
+# 
+# FWD5 := {[x,t,y,i,z] -> [x',t',y',i',z'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) };
+# 
+# FWD7 := {[x,t,y,i,z,a,b] -> [x',t',y',i',z',a',b'] :
+# 	(x'>x) or
+# 	(x'=x and t'>t) or
+# 	(x'=x and t'=t and y'>y) or
+# 	(x'=x and t'=t and y'=y and i'>i) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'>z) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'>a) or
+# 	(x'=x and t'=t and y'=y and i'=i and z'=z and a'=a and b'>b) };
+# 
+# BWD5 := inverse FWD5;
+# 
+# BWD7 := inverse FWD7;
+# 
+# EQi := {[x,t,y,i,z] -> [x',t',y',i',z'] : i'=i };
+# 
+# 
+# # output deps
+# 
+# OAA := (IS_COPY * IS_COPY) intersection FWD5 intersection EQi;
+# 
+# OCC := (IS_CALC * IS_CALC) intersection FWD5 intersection EQi;
+# 
+# 
+# # combined flow/anti deps
+# 
+# FAC := (IS_COPY * IS_CALC) intersection FWD5 intersection {[2,t,0,i,1] -> [2,t',1,i',1]  : (i'-1<=i<=i'+1)};
+# 
+# FCA := (IS_CALC * IS_COPY) intersection FWD5 intersection {[2,t,1,i,1] -> [2,t',0,i',1]  : (i-1<=i'<=i+1)};
+# 
+# 
+# # total memory deps in the "core"
+# 
+# COREMEMDEPS := OAA union OCC union FAC union FCA;
+# 
+# 
+# 
+# 
+# # data flow for original code:
+# 
+# DF_12p1 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,0,0,i,1] : 0<i<N-1 };
+# 
+# DF_12p2 := ( IS_INIT * IS_COPY ) intersection {[1,0,1,0,0] -> [2,t,0,0,1] };
+# 
+# DF_12p3 := ( IS_INIT * IS_COPY ) intersection {[1,i,1,0,0] -> [2,t,0,i,1] : i=N-1 && N>1 };
+# 
+# DF_32   := ( IS_CALC * IS_COPY ) intersection {[2,t,1,i,1] -> [2,t+1,0,i,1]};
+# 
+# 
+# DF_23a := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i+1,1] };
+# 
+# DF_23b := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i,1] };
+# 
+# DF_23c := ( IS_COPY * IS_CALC ) intersection {[2,t,0,i,1] -> [2,t,1,i-1,1] };
+# 
+# 
+# 
+# # data flow for array expanded code,
+# # after forward substitution of "old[i] = cur[i]"
+# 
+# DF1Ia := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1Ib := { [1,i,1,0,0] -> [2,t,1,i+1,1] : t>0 && i=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF1C  := { [2,t,1,i,1] -> [2,t+1,1,i+1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF2I  := { [1,i,1,0,0] -> [2,t,1,i,1] :   t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF2C  := { [2,t,1,i,1] -> [2,t+1,1,i+0,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# DF3Ia := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t=0 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3Ib := { [1,i,1,0,0] -> [2,t,1,i-1,1] : t>0 && i=N-1 } restrictDomain IS_INIT restrictRange IS_CALC;
+# 
+# DF3C  := { [2,t,1,i,1] -> [2,t+1,1,i-1,1] } restrictDomain IS_CALC restrictRange IS_CALC;
+# 
+# 
+# # total data flow
+# 
+# COREDATAFLOW := DF1C union DF2C union DF3C;
+# 
+# 
+# 
+# # arity expansion relations
+# ex_0_5v := {             [] -> [a,b,c,d,e]     };
+# 
+# ex_0_7v := {             [] -> [a,b,c,d,e,f,g] };
+# 
+# ex_3_5 := {         [a,b,c] -> [a,b,c,0,0]     };
+# 
+# ex_3_7 := {         [a,b,c] -> [a,b,c,0,0,0,0] };
+# 
+# ex_5_7 := {     [a,b,c,d,e] -> [a,b,c,d,e,0,0] };
+# 
+# 
+# ex_5_3 := {     [a,b,c,0,0] -> [a,b,c]         };
+# 
+# ex_7_3 := { [a,b,c,0,0,0,0] -> [a,b,c]         };
+# 
+# ex_7_5 := { [a,b,c,d,e,0,0] -> [a,b,c,d,e]     };
+# 
+# 
+# 
+# # stuff used in skew and tskew
+# 
+# # Here is the description of time skewing from the current draft of the paper.
+# IS_Trans := { [2,t,1,i,1] -> [2,tb,1,s,1,tt,1] :
+# 	0<=tt<1000 && s=i+1*t && t=1000*tb+tt };
+# 
+# 
+# IS_Tinv := inverse IS_Trans;
+# 
+# 
+# # We use it to transform the iteration spaces
+# TS_IS_CALC := IS_CALC join IS_Trans;
+# 
+# # for some reason OC refuses do to this "join" but will do the reverse:
+# # TS_IS_INIT := ex_7_5 join IS_INIT;
+# TS_IS_INIT := IS_INIT  join (inverse ex_7_5);
+# 
+# 
+# # Now we can update the data flow relations to correspond to the new I.S.'s
+# TS_DF1Ia := ex_7_5  join DF1Ia join IS_Trans;
+# 
+# TS_DF1Ib := ex_7_5  join DF1Ib join IS_Trans;
+# 
+# TS_DF1C  := IS_Tinv join DF1C  join IS_Trans;
+# 
+# TS_DF2I  := ex_7_5  join DF2I  join IS_Trans;
+# 
+# TS_DF2C  := IS_Tinv join DF2C  join IS_Trans;
+# 
+# TS_DF3Ia := ex_7_5  join DF3Ia join IS_Trans;
+# 
+# TS_DF3Ib := ex_7_5  join DF3Ib join IS_Trans;
+# 
+# TS_DF3C  := IS_Tinv join DF3C  join IS_Trans;
+# 
+# 
+#  
+# KNOWN := { [] : T >= 0 and N >= 4 };
+# 
+#  
+# # original code without mmap
+# #
+# 
+# codegen
+# 	IS_INIT, IS_COPY, IS_CALC
+# given	(KNOWN join ex_0_5v);
+for(t2 = 0; t2 <= N-1; t2++) {
+  s1(1,t2,1,0,0);
+}
+for(t2 = 0; t2 <= T-1; t2++) {
+  for(t4 = 0; t4 <= N-1; t4++) {
+    s2(2,t2,0,t4,1);
+  }
+  for(t4 = 1; t4 <= N-2; t4++) {
+    s3(2,t2,1,t4,1);
+  }
+}
+
+# 
+# 
diff --git a/omega/examples/old_test/tseng b/omega/examples/old_test/tseng
new file mode 100644
index 0000000..2ae39f8
--- /dev/null
+++ b/omega/examples/old_test/tseng
@@ -0,0 +1,16 @@
+symbolic n;
+symbolic LV,UV;
+D := {[ i,i+1] -> [i+1,k] : 1 <= i && i+1 < k <= n};
+local := {[i1,k1] -> [i2,k2] : LV <= k1,k2 <= UV };
+sameP := {[i1,k1] -> [i2,k2] : k1=k2  ||  LV <= k1,k2 <= UV };
+myIter := {[i,k]  : LV <= k <= UV};
+lexPos := {[i1,k1] -> [i2,k2] : i1 = i2 && k1 < k2 || i1 < i2};
+
+post := D restrictDomain myIter;
+wait := D restrictRange myIter;
+enforcedTime := sameP intersection lexPos;
+enforcedTime;
+enforced := enforcedTime compose D union D compose enforcedTime union enforcedTime;
+enforced;
+post - enforced;
+wait - enforced;
diff --git a/omega/examples/old_test/tseng.oc-rt b/omega/examples/old_test/tseng.oc-rt
new file mode 100644
index 0000000..53ff139
--- /dev/null
+++ b/omega/examples/old_test/tseng.oc-rt
@@ -0,0 +1,54 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# symbolic LV,UV;
+# 
+# D := {[ i,i+1] -> [i+1,k] : 1 <= i && i+1 < k <= n};
+# 
+# local := {[i1,k1] -> [i2,k2] : LV <= k1,k2 <= UV };
+# 
+# sameP := {[i1,k1] -> [i2,k2] : k1=k2  ||  LV <= k1,k2 <= UV };
+# 
+# myIter := {[i,k]  : LV <= k <= UV};
+# 
+# lexPos := {[i1,k1] -> [i2,k2] : i1 = i2 && k1 < k2 || i1 < i2};
+# 
+# 
+# post := D restrictDomain myIter;
+# 
+# wait := D restrictRange myIter;
+# 
+# enforcedTime := sameP intersection lexPos;
+# 
+# enforcedTime;
+
+{[i1,k1] -> [i1,k2] : LV <= k1 < k2 <= UV} union
+ {[i1,k1] -> [i2,k1] : i1 < i2} union
+ {[i1,k1] -> [i2,k2] : LV <= k1,k2 <= UV && i1 < i2}
+
+# 
+# enforced := enforcedTime compose D union D compose enforcedTime union enforcedTime;
+# 
+# enforced;
+
+{[i1,i1+1] -> [i2,k2] : 1 <= i1 <= n-2, UV-2, i2-2 && LV <= k2 <= UV && LV <= n} union
+ {[i1,k1] -> [i2,k2] : k1 = 1+i1 && 1 <= i1 <= i2-2, k2-2 && k2 <= n} union
+ {[i1,i1+1] -> [i1+1,k2] : 1 <= i1 <= n-2, k2-3 && LV < k2 <= UV && LV <= n} union
+ {[i1,k1] -> [i2,k2] : 2, LV, i1+2 <= i2 < k2 <= n && LV <= k1 <= UV && i2 <= UV} union
+ {[i1,k1] -> [k1,k2] : 2, i1+2 <= k1 < k2 <= n} union
+ {[i1,k1] -> [i1+1,k2] : LV <= k1 <= i1 <= k2-2, UV-1 && k2 <= n && 1 <= i1} union
+ {[i1,k1] -> [i2,k2] : LV <= k1,k2 <= UV && i1 < i2} union
+ {[i1,k1] -> [i2,k1] : i1 < i2} union
+ {[i1,k1] -> [i1,k2] : LV <= k1 < k2 <= UV}
+
+# 
+# post - enforced;
+
+{[In_1,In_1+1] -> [In_1+1,Out_2] : 1, LV-1 <= In_1 < UV < Out_2 <= n}
+
+# 
+# wait - enforced;
+
+{[In_1,In_1+1] -> [In_1+1,LV] : In_1+2 <= LV <= n, UV && 1 <= In_1}
+
+# 
diff --git a/omega/examples/old_test/verlind1 b/omega/examples/old_test/verlind1
new file mode 100644
index 0000000..181b1c5
--- /dev/null
+++ b/omega/examples/old_test/verlind1
@@ -0,0 +1,44 @@
+   without_simplify;
+   
+   R3 := {[x] -> [y] : (y = x) | (y = 3x)};
+
+   Rf := {[x] -> [y] : x <= y <= 3x};
+
+   R3;
+
+   Rf;
+
+   s12 := {[x] : 1 <= x <= 2};
+   s12;
+
+   sd3 := R3(s12);
+   sd3;
+
+   sc3 := Rf(s12);
+   sc3;
+
+   sc3 intersection sd3;
+
+   # I think this is faulty
+   sc3 - sd3;
+
+   # This is OK
+   sd3 - sc3;
+
+   complement sc3;
+   complement sd3;
+
+   sc3;
+
+   sc3 intersection (complement sd3);
+
+   # alternative description of sd3;
+   sd3' := {[y] : 1 <= y <= 3 | y = 6};
+   sd3';
+   sc3 - sd3';
+
+   # sd3 wrt sd3';
+
+   sd3 - sd3';
+
+   sd3' - sd3;
diff --git a/omega/examples/old_test/verlind1.oc-rt b/omega/examples/old_test/verlind1.oc-rt
new file mode 100644
index 0000000..050b199
--- /dev/null
+++ b/omega/examples/old_test/verlind1.oc-rt
@@ -0,0 +1,120 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+#    R3 := {[x] -> [y] : (y = x) | (y = 3x)};
+# 
+# 
+#    Rf := {[x] -> [y] : x <= y <= 3x};
+# 
+# 
+#    R3;
+
+{[x] -> [x] } union
+ {[x] -> [3x] }
+
+# 
+# 
+#    Rf;
+
+{[x] -> [y] : x <= y <= 3x}
+
+# 
+# 
+#    s12 := {[x] : 1 <= x <= 2};
+# 
+#    s12;
+
+{[x]: 1 <= x <= 2}
+
+# 
+# 
+#    sd3 := R3(s12);
+# 
+#    sd3;
+
+{[y]: 1 <= y <= 2} union
+ {[y]: Exists ( alpha : y = 3alpha && 3 <= y <= 6)}
+
+# 
+# 
+#    sc3 := Rf(s12);
+# 
+#    sc3;
+
+{[y]: 1 <= y <= 6}
+
+# 
+# 
+#    sc3 intersection sd3;
+
+{[y]: 1 <= y <= 2} union
+ {[y]: Exists ( alpha : y = 3alpha && 3 <= y <= 6)}
+
+# 
+# 
+#    # I think this is faulty
+#    sc3 - sd3;
+
+{[y]: 4 <= y <= 5}
+
+# 
+# 
+#    # This is OK
+#    sd3 - sc3;
+
+{[y]  : FALSE }
+
+# 
+# 
+#    complement sc3;
+
+{[y]: y <= 0} union
+ {[y]: 7 <= y}
+
+# 
+#    complement sd3;
+
+{[y]: y <= 0} union
+ {[y]: 7 <= y} union
+ {[y]: 4 <= y <= 5}
+
+# 
+# 
+#    sc3;
+
+{[y]: 1 <= y <= 6}
+
+# 
+# 
+#    sc3 intersection (complement sd3);
+
+{[y]: 4 <= y <= 5}
+
+# 
+# 
+#    # alternative description of sd3;
+#    sd3' := {[y] : 1 <= y <= 3 | y = 6};
+# 
+#    sd3';
+
+{[y]: 1 <= y <= 3} union
+ {[6]}
+
+# 
+#    sc3 - sd3';
+
+{[y]: 4 <= y <= 5}
+
+# 
+# 
+#    # sd3 wrt sd3';
+# 
+#    sd3 - sd3';
+
+{[y]  : FALSE }
+
+# 
+# 
+#    sd3' - sd3;
+
+{[y]  : FALSE }
+
+# 
diff --git a/omega/examples/old_test/verlind1a b/omega/examples/old_test/verlind1a
new file mode 100644
index 0000000..e43ec19
--- /dev/null
+++ b/omega/examples/old_test/verlind1a
@@ -0,0 +1,3 @@
+R := { [i] : 1 <= i <= 6 & exists (alpha : 3 alpha + 1 <= i <= 3 alpha + 2)
+	   & not (1 <= i <= 2) };
+R;
diff --git a/omega/examples/old_test/verlind1a.oc-rt b/omega/examples/old_test/verlind1a.oc-rt
new file mode 100644
index 0000000..11e2d1e
--- /dev/null
+++ b/omega/examples/old_test/verlind1a.oc-rt
@@ -0,0 +1,9 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R := { [i] : 1 <= i <= 6 & Exists (alpha : 3 alpha + 1 <= i <= 3 alpha + 2)
+# 	   & not (1 <= i <= 2) };
+# 
+# R;
+
+{[i]: 4 <= i <= 5}
+
+# 
diff --git a/omega/examples/old_test/wak1 b/omega/examples/old_test/wak1
new file mode 100644
index 0000000..5e9e315
--- /dev/null
+++ b/omega/examples/old_test/wak1
@@ -0,0 +1,13 @@
+symbolic a1,a2,a3,b1,b2,b3;
+
+IS1 := {[i] : a1 <= i <= b1 };
+IS2 := {[i] : a2 <= i <= b2 };
+IS3 := {[i] : a3 <= i <= b3 };
+
+T1 := {[i] -> [i,0]};
+T2 := {[i] -> [i,1]};
+T3 := {[i] -> [i,2]};
+
+codegen 0 T1:IS1,T2:IS2,T3:IS3;
+
+codegen T1:IS1,T2:IS2,T3:IS3;
diff --git a/omega/examples/old_test/wak1.oc-rt b/omega/examples/old_test/wak1.oc-rt
new file mode 100644
index 0000000..e8bdf0e
--- /dev/null
+++ b/omega/examples/old_test/wak1.oc-rt
@@ -0,0 +1,87 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# 
+# Symbolic a1,a2,a3,b1,b2,b3;
+# 
+# 
+# IS1 := {[i] : a1 <= i <= b1 };
+# 
+# IS2 := {[i] : a2 <= i <= b2 };
+# 
+# IS3 := {[i] : a3 <= i <= b3 };
+# 
+# 
+# T1 := {[i] -> [i,0]};
+# 
+# T2 := {[i] -> [i,1]};
+# 
+# T3 := {[i] -> [i,2]};
+# 
+# 
+# codegen T1:IS1,T2:IS2,T3:IS3;
+for(t1 = a3; t1 <= min(b3,a1-1,a2-1); t1++) {
+  s3(t1);
+}
+for(t1 = a2; t1 <= min(b2,a1-1,a3-1,b3); t1++) {
+  s2(t1);
+}
+for(t1 = max(a2,a3); t1 <= min(a1-1,b2,b3); t1++) {
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a2,b3+1); t1 <= min(b2,a1-1); t1++) {
+  s2(t1);
+}
+for(t1 = max(a3,a2,b2+1); t1 <= min(b3,a1-1); t1++) {
+  s3(t1);
+}
+for(t1 = a1; t1 <= min(b1,a3-1,b3,a2-1); t1++) {
+  s1(t1);
+}
+for(t1 = max(a1,a3); t1 <= min(b1,a2-1,b3); t1++) {
+  s1(t1);
+  s3(t1);
+}
+for(t1 = max(a1,b3+1); t1 <= min(b1,a2-1); t1++) {
+  s1(t1);
+}
+for(t1 = max(a1,a2); t1 <= min(b1,b2,a3-1); t1++) {
+  s1(t1);
+  s2(t1);
+}
+for(t1 = max(a1,a2,a3); t1 <= min(b1,b2,b3); t1++) {
+  s1(t1);
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a1,a2,a3,b3+1); t1 <= min(b1,b2); t1++) {
+  s1(t1);
+  s2(t1);
+}
+for(t1 = max(a1,b2+1,a2); t1 <= min(b1,a3-1); t1++) {
+  s1(t1);
+}
+for(t1 = max(a1,a2,b2+1,a3); t1 <= min(b1,b3); t1++) {
+  s1(t1);
+  s3(t1);
+}
+for(t1 = max(a1,b3+1,a3,a2,b2+1); t1 <= b1; t1++) {
+  s1(t1);
+}
+for(t1 = max(a3,a1,b1+1); t1 <= min(b3,b2,a2-1); t1++) {
+  s3(t1);
+}
+for(t1 = max(a2,a1,b1+1); t1 <= min(b2,a3-1); t1++) {
+  s2(t1);
+}
+for(t1 = max(a1,b1+1,a2,a3); t1 <= min(b2,b3); t1++) {
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a2,a1,b1+1,b3+1,a3); t1 <= b2; t1++) {
+  s2(t1);
+}
+for(t1 = max(a3,a1,b1+1,b2+1); t1 <= b3; t1++) {
+  s3(t1);
+}
+
+# 
diff --git a/omega/examples/old_test/wak2 b/omega/examples/old_test/wak2
new file mode 100644
index 0000000..927fc2f
--- /dev/null
+++ b/omega/examples/old_test/wak2
@@ -0,0 +1,10 @@
+symbolic a1,a2,b1,b2,c1,c2,d1,d2;
+
+IS1 := {[i,j] : a1 <= i <= b1 && c1 <= j <= d1};
+IS2 := {[i,j] : a2 <= i <= b2 && c2 <= j <= d2};
+
+T1 := {[i,j] -> [i,j,0]};
+T2 := {[i,j] -> [i,j,1]};
+
+codegen T1:IS1,T2:IS2;
+codegen 2 T1:IS1,T2:IS2;
diff --git a/omega/examples/old_test/wak2.oc-rt b/omega/examples/old_test/wak2.oc-rt
new file mode 100644
index 0000000..6dc6270
--- /dev/null
+++ b/omega/examples/old_test/wak2.oc-rt
@@ -0,0 +1,307 @@
+>>> Symbolic a1,a2,b1,b2,c1,c2,d1,d2;
+>>> 
+>>> IS1 := {[i,j] : a1 <= i <= b1 && c1 <= j <= d1};
+>>> IS2 := {[i,j] : a2 <= i <= b2 && c2 <= j <= d2};
+>>> 
+>>> T1 := {[i,j] -> [i,j,0]};
+>>> T2 := {[i,j] -> [i,j,1]};
+>>> 
+>>> codegen T1:IS1,T2:IS2;
+if (d2 >= c2) {
+  for(t1 = a2; t1 <= min(a1-1,b2); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+for(t1 = a1; t1 <= b1; t1++) {
+  if (t1 >= a2 && t1 <= b2) {
+    for(t2 = c2; t2 <= min(c1-1,d2); t2++) {
+      s2(t1,t2);
+    }
+  }
+  if (t1 <= a2-1) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 >= a2 && t1 <= b2) {
+    for(t2 = c1; t2 <= min(d1,c2-1,d2); t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 <= b2 && t1 >= a2) {
+    for(t2 = max(c2,c1); t2 <= min(d2,d1); t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+  }
+  if (t1 >= a2 && t1 <= b2) {
+    for(t2 = max(d2+1,c1); t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 >= a2 && t1 >= b2+1) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+  if (t1 >= a2 && t1 <= b2) {
+    for(t2 = max(c2,d1+1,c1); t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d2 >= c2) {
+  for(t1 = max(a1,a2,b1+1); t1 <= b2; t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+
+>>> codegen 2 T1:IS1,T2:IS2;
+if (d2 >= c2) {
+  for(t1 = a2; t1 <= min(a1-1,b2); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d1 >= c1) {
+  for(t1 = a1; t1 <= min(a2-1,b1); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d1 >= c1 && c1 >= d2+2 && c2 <= d2) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d2 >= c2 && d2 <= c1-2 && d1 <= c1-1) {
+  for(t1 = max(a1,a2); t1 <= min(b2,b1); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (c1 >= c2+1 && d1 <= d2-1 && d1 >= c1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c2; t2 <= c1-1; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d1+1; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (c1 >= c2+1 && c1 <= d2 && d1 >= d2+1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c2; t2 <= c1-1; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d2+1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d1 == d2 && d1 >= c1 && c1 >= c2+1) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c2; t2 <= c1-1; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+  }
+}
+if (d2 == c1-1 && d2 <= d1-1 && d2 >= c2) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c2; t2 <= c1-1; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (c2 <= c1-1 && d2 >= c1 && d1 <= c1-1) {
+  for(t1 = max(a1,a2); t1 <= min(b2,b1); t1++) {
+    for(t2 = c2; t2 <= c1-1; t2++) {
+      s2(t1,t2);
+    }
+    for(t2 = c1; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d2 == c1-1 && d2 >= d1 && d2 >= c2) {
+  for(t1 = max(a1,a2); t1 <= min(b1,b2); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d1 >= c1 && c1 >= c2+1 && d2 <= c2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (c1 <= c2-1 && d1 >= c2 && d1 <= d2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= c2-1; t2++) {
+      s1(t1,t2);
+    }
+    for(t2 = c2; t2 <= d1; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d1+1; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (c1 <= c2-1 && d1 >= d2+1 && c2 <= d2) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= c2-1; t2++) {
+      s1(t1,t2);
+    }
+    for(t2 = c2; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d2+1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d1 == d2 && d1 >= c2 && c1 <= c2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c1; t2 <= c2-1; t2++) {
+      s1(t1,t2);
+    }
+    for(t2 = c2; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+  }
+}
+if (c2 <= d2 && d1 >= c1 && d1 <= c2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d1 >= c1 && d2 <= c2-1 && d1 <= d2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d2 >= c1 && d2 <= c2-1 && d1 >= d2+1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= d2; t2++) {
+      s1(t1,t2);
+    }
+    for(t2 = d2+1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d1 == d2 && d1 <= c2-1 && d1 >= c1) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d2 >= c2 && c2 >= c1+1 && d1 <= c1-1) {
+  for(t1 = max(a1,a2); t1 <= min(b2,b1); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (c2 == c1 && c2 <= d1 && d1 <= d2-1) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d1+1; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (c2 == c1 && d1 >= d2+1 && c2 <= d2) {
+  for(t1 = max(a2,a1); t1 <= min(b2,b1); t1++) {
+    for(t2 = c1; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+    for(t2 = d2+1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (c1 == c2 && d1 == d2 && d1 >= c1) {
+  for(t1 = max(a1,a2); t1 <= min(b2,b1); t1++) {
+    for(t2 = c1; t2 <= d2; t2++) {
+      s1(t1,t2);
+      s2(t1,t2);
+    }
+  }
+}
+if (c1 == c2 && c1 >= d1+1 && d2 >= c1) {
+  for(t1 = max(a1,a2); t1 <= min(b1,b2); t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+if (d1 >= c1 && c1 <= c2 && d2 <= c1-1) {
+  for(t1 = max(a2,a1); t1 <= min(b1,b2); t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d1 >= c1) {
+  for(t1 = max(b2+1,a1,a2); t1 <= b1; t1++) {
+    for(t2 = c1; t2 <= d1; t2++) {
+      s1(t1,t2);
+    }
+  }
+}
+if (d2 >= c2) {
+  for(t1 = max(a1,a2,b1+1); t1 <= b2; t1++) {
+    for(t2 = c2; t2 <= d2; t2++) {
+      s2(t1,t2);
+    }
+  }
+}
+
+
diff --git a/omega/examples/old_test/wak3 b/omega/examples/old_test/wak3
new file mode 100644
index 0000000..51ca234
--- /dev/null
+++ b/omega/examples/old_test/wak3
@@ -0,0 +1,12 @@
+symbolic a,b;
+
+IS1 := {[i] : a <= i <= b };
+IS2 := {[i] : a+10 <= i <= b+10 };
+IS3 := {[i] : a+20 <= i <= b+20 };
+
+T1 := {[i] -> [i,0]};
+T2 := {[i] -> [i,1]};
+T3 := {[i] -> [i,2]};
+
+codegen T1:IS1,T2:IS2,T3:IS3;
+codegen 2 T1:IS1,T2:IS2,T3:IS3;
diff --git a/omega/examples/old_test/wak3.oc-rt b/omega/examples/old_test/wak3.oc-rt
new file mode 100644
index 0000000..825c72f
--- /dev/null
+++ b/omega/examples/old_test/wak3.oc-rt
@@ -0,0 +1,59 @@
+>>> Symbolic a,b;
+>>> 
+>>> IS1 := {[i] : a <= i <= b };
+>>> IS2 := {[i] : a+10 <= i <= b+10 };
+>>> IS3 := {[i] : a+20 <= i <= b+20 };
+>>> 
+>>> T1 := {[i] -> [i,0]};
+>>> T2 := {[i] -> [i,1]};
+>>> T3 := {[i] -> [i,2]};
+>>> 
+>>> codegen T1:IS1,T2:IS2,T3:IS3;
+for(t1 = a; t1 <= min(b,a+9); t1++) {
+  s1(t1);
+}
+for(t1 = a+10; t1 <= min(b,a+19); t1++) {
+  s1(t1);
+  s2(t1);
+}
+for(t1 = a+20; t1 <= b; t1++) {
+  s1(t1);
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a+10,b+1); t1 <= min(b+10,a+19); t1++) {
+  s2(t1);
+}
+for(t1 = max(a+20,b+1); t1 <= b+10; t1++) {
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a+20,b+11); t1 <= b+20; t1++) {
+  s3(t1);
+}
+
+>>> codegen 2 T1:IS1,T2:IS2,T3:IS3;
+for(t1 = a; t1 <= min(b,a+9); t1++) {
+  s1(t1);
+}
+for(t1 = a+10; t1 <= min(b,a+19); t1++) {
+  s1(t1);
+  s2(t1);
+}
+for(t1 = a+20; t1 <= b; t1++) {
+  s1(t1);
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a+10,b+1); t1 <= min(b+10,a+19); t1++) {
+  s2(t1);
+}
+for(t1 = max(a+20,b+1); t1 <= b+10; t1++) {
+  s2(t1);
+  s3(t1);
+}
+for(t1 = max(a+20,b+11); t1 <= b+20; t1++) {
+  s3(t1);
+}
+
+
diff --git a/omega/examples/old_test/wak4 b/omega/examples/old_test/wak4
new file mode 100644
index 0000000..48224b9
--- /dev/null
+++ b/omega/examples/old_test/wak4
@@ -0,0 +1,9 @@
+symbolic a1,a2,a3,a4,a5,b1,b2,b3,b4,b5;
+IS1 := {[i] : a1,a2,a3,a4,a5 <= i <= b1,b2,b3,b4,b5 };
+IS2 := {[i] : a1,a2,a3,a4,a5 <= i <= b1,b2,b3,b4,b5 };
+
+T1 := {[i] -> [i,0]};
+T2 := {[i] -> [i,1]};
+
+codegen T1:IS1,T2:IS2;
+codegen 2 T1:IS1,T2:IS2;
diff --git a/omega/examples/old_test/wak4.oc-rt b/omega/examples/old_test/wak4.oc-rt
new file mode 100644
index 0000000..5f2cacd
--- /dev/null
+++ b/omega/examples/old_test/wak4.oc-rt
@@ -0,0 +1,20 @@
+>>> Symbolic a1,a2,a3,a4,a5,b1,b2,b3,b4,b5;
+>>> IS1 := {[i] : a1,a2,a3,a4,a5 <= i <= b1,b2,b3,b4,b5 };
+>>> IS2 := {[i] : a1,a2,a3,a4,a5 <= i <= b1,b2,b3,b4,b5 };
+>>> 
+>>> T1 := {[i] -> [i,0]};
+>>> T2 := {[i] -> [i,1]};
+>>> 
+>>> codegen T1:IS1,T2:IS2;
+for(t1 = max(a1,a2,a3,a4,a5); t1 <= min(b1,b2,b3,b4,b5); t1++) {
+  s1(t1);
+  s2(t1);
+}
+
+>>> codegen 2 T1:IS1,T2:IS2;
+for(t1 = max(a1,a2,a3,a4,a5); t1 <= min(b1,b2,b3,b4,b5); t1++) {
+  s1(t1);
+  s2(t1);
+}
+
+
diff --git a/omega/examples/old_test/wak5 b/omega/examples/old_test/wak5
new file mode 100644
index 0000000..1232b34
--- /dev/null
+++ b/omega/examples/old_test/wak5
@@ -0,0 +1,4 @@
+S1 := {[1,In_2,0,In_4,In_5,In_6,In_7]: 2 <= In_4 <= 1024 && 2 <= In_2 <= 1024};
+S2 := {[1,In_2,0,In_4,In_5,In_6,In_7]: 1 <= In_4 < In_2 <= 1024};
+
+Hull (S1 union S2);
diff --git a/omega/examples/old_test/wak5.oc-rt b/omega/examples/old_test/wak5.oc-rt
new file mode 100644
index 0000000..2d5830c
--- /dev/null
+++ b/omega/examples/old_test/wak5.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# S1 := {[1,In_2,0,In_4,In_5,In_6,In_7]: 2 <= In_4 <= 1024 && 2 <= In_2 <= 1024};
+# 
+# S2 := {[1,In_2,0,In_4,In_5,In_6,In_7]: 1 <= In_4 < In_2 <= 1024};
+# 
+# 
+# Hull (S1 union S2);
+
+{[1,In_2,0,In_4,In_5,In_6,In_7]: 1 <= In_4 <= 1024 && 2 <= In_2 <= 1024}
+
+# 
diff --git a/omega/examples/old_test/wak6 b/omega/examples/old_test/wak6
new file mode 100644
index 0000000..c251ca6
--- /dev/null
+++ b/omega/examples/old_test/wak6
@@ -0,0 +1,14 @@
+T1 := {[k,i,j] -> [k',i,j] : 1 <= k < k' < i <= 1024 && k'+1 <= j <= 1024};
+T2 := {[k,i,j] -> [j,i,j'] : 1 <= k < j < i <= 1024 && j < j' <= 1024};
+T3 := {[k,k+1,k+1] -> [k+1,i',j'] : 1 <= k <= i'-2, j'-2 && j' <= 1024 && i' <= 1024};
+
+# The following expression evaluates to FALSE, which I believe is incorrect:
+
+T3+;
+
+# And the following cause assertion failures:
+
+(T2 union T3)+;
+(T1 union T2)+;
+
+# This comes from Guassian Elimination.
diff --git a/omega/examples/old_test/wak6.oc-rt b/omega/examples/old_test/wak6.oc-rt
new file mode 100644
index 0000000..458f5e9
--- /dev/null
+++ b/omega/examples/old_test/wak6.oc-rt
@@ -0,0 +1,36 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# T1 := {[k,i,j] -> [k',i,j] : 1 <= k < k' < i <= 1024 && k'+1 <= j <= 1024};
+# 
+# T2 := {[k,i,j] -> [j,i,j'] : 1 <= k < j < i <= 1024 && j < j' <= 1024};
+# 
+# T3 := {[k,k+1,k+1] -> [k+1,i',j'] : 1 <= k <= i'-2, j'-2 && j' <= 1024 && i' <= 1024};
+# 
+# 
+# # The following expression evaluates to FALSE, which I believe is incorrect:
+# 
+# T3+;
+
+{[k,k+1,k+1] -> [Out_1,i,j] : 1 <= k < Out_1 < i <= 1024 && Out_1+1 <= j <= 1024}
+
+# 
+# 
+# # And the following cause assertion failures:
+# 
+# (T2 union T3)+;
+
+{[k,k+1,k+1] -> [j',i',j''] : 1 <= k < j' < i' <= 1024 && j'+1 <= j'' <= 1024} union
+ {[k,i,i-1] -> [j',i',j''] : k+2 <= i <= j' < j'' <= 1024 && j' < i' <= 1024 && 1 <= k} union
+ {[k,i,j] -> [j',i',j''] : j+2 <= i <= j' < i' <= 1024 && 1 <= k < j && j' < j'' <= 1024} union
+ {[k,i,j] -> [j',i,j''] : 1 <= k < j < j' < i <= 1024 && j' < j'' <= 1024} union
+ {[k,i,j] -> [j,i,j''] : 1 <= k < j < i <= 1024 && j < j'' <= 1024}
+
+# 
+# (T1 union T2)+;
+
+{[k,i,j] -> [Out_1,i,j] : 1 <= k < Out_1 < i <= 1024 && Out_1+1 <= j <= 1024} union
+ {[k,i,j] -> [Out_1,i,j'] : 1 <= k < j < Out_1 < i <= 1024 && Out_1 < j' <= 1024} union
+ {[k,i,j] -> [j,i,j'] : 1 <= k < j < i <= 1024 && j < j' <= 1024}
+
+# 
+# 
+# # This comes from Guassian Elimination.
diff --git a/omega/examples/old_test/wak7 b/omega/examples/old_test/wak7
new file mode 100644
index 0000000..b122c5a
--- /dev/null
+++ b/omega/examples/old_test/wak7
@@ -0,0 +1,5 @@
+R :=  {[k,k+1,k+1]: 1 <= k <= 1022}
+	union {[k,i,j]: 2 <= k < i <= 1024 && k < j <= 1024};
+
+Hull R;
+
diff --git a/omega/examples/old_test/wak7.oc-rt b/omega/examples/old_test/wak7.oc-rt
new file mode 100644
index 0000000..3ccdb0a
--- /dev/null
+++ b/omega/examples/old_test/wak7.oc-rt
@@ -0,0 +1,11 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# R :=  {[k,k+1,k+1]: 1 <= k <= 1022}
+# 	union {[k,i,j]: 2 <= k < i <= 1024 && k < j <= 1024};
+# 
+# 
+# Hull R;
+
+{[k,i,j]: k+1, 2 <= j <= 1024 && k < i <= 1024}
+
+# 
+# 
diff --git a/omega/examples/old_test/wak8 b/omega/examples/old_test/wak8
new file mode 100644
index 0000000..f55c2b9
--- /dev/null
+++ b/omega/examples/old_test/wak8
@@ -0,0 +1,15 @@
+ T1 := {[i1,i2,i3] -> [o1,i2,o3] : 2 <= i2 <= 511 && o1 <= 256 
+&& o3 <= 511 && 2 <= i3 && i1+o3 <= i3+o1 
+	&& 255i3+o1 <= i1+255o3 && 1 <= i1};
+
+T1;
+
+ T2 := {[i1,i2,i3] -> [o1,i2,o3] : exists ( x: 2 <= i2 <= 511 
+	&& 2 <= o3 <= 509 && o1 <= 256 
+	&& 3+i1+o3 <= i3+o1 && 2o1+o3 <= 511+2x 
+	&& 2 <= i3 && i1+2o1+o3 <= i3+3x 
+	&& 255i3+511x <= i1+510o1+255o3 && 1 <= i1)};
+
+T2;
+ 
+ T1 compose T2;
diff --git a/omega/examples/old_test/wak8.oc-rt b/omega/examples/old_test/wak8.oc-rt
new file mode 100644
index 0000000..10ba68d
--- /dev/null
+++ b/omega/examples/old_test/wak8.oc-rt
@@ -0,0 +1,30 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+#  T1 := {[i1,i2,i3] -> [o1,i2,o3] : 2 <= i2 <= 511 && o1 <= 256 
+# && o3 <= 511 && 2 <= i3 && i1+o3 <= i3+o1 
+# 	&& 255i3+o1 <= i1+255o3 && 1 <= i1};
+# 
+# 
+# T1;
+
+{[i1,i2,i3] -> [o1,i2,o3] : 2 <= i2 <= 511 && o1 <= 256 && o3 <= 511 && 2 <= i3 && i1+o3 <= i3+o1 && 255i3+o1 <= i1+255o3 && 1 <= i1}
+
+# 
+# 
+#  T2 := {[i1,i2,i3] -> [o1,i2,o3] : Exists ( x: 2 <= i2 <= 511 
+# 	&& 2 <= o3 <= 509 && o1 <= 256 
+# 	&& 3+i1+o3 <= i3+o1 && 2o1+o3 <= 511+2x 
+# 	&& 2 <= i3 && i1+2o1+o3 <= i3+3x 
+# 	&& 255i3+511x <= i1+510o1+255o3 && 1 <= i1)};
+# 
+# 
+# T2;
+
+{[i1,i2,i3] -> [o1,i2,o3] : Exists ( alpha : 2 <= i2 <= 511 && 2 <= o3 <= 509 && o1 <= 256 && 3+i1+o3 <= i3+o1 && 2o1+o3 <= 511+2alpha && 2 <= i3 && i1+2o1+o3 <= i3+3alpha && 255i3+511alpha <= i1+510o1+255o3 && 1 <= i1)}
+
+# 
+#  
+#  T1 compose T2;
+
+{[i1,i2,i3] -> [o1,i2,o3] : Exists ( alpha,beta,gamma : 2 <= i2 <= 511 && 2 <= gamma <= 509 && o1 <= 256 && o3 <= 511 && o3+alpha <= o1+gamma && o1+255gamma <= 255o3+alpha && gamma+2alpha <= 511+2beta && 1 <= i1 && 255i3+511beta <= i1+255gamma+510alpha && i1+gamma+2alpha <= i3+3beta && 2 <= i3 && 3+i1+gamma <= i3+alpha)}
+
+# 
diff --git a/omega/examples/old_test/wielage b/omega/examples/old_test/wielage
new file mode 100644
index 0000000..f2e3911
--- /dev/null
+++ b/omega/examples/old_test/wielage
@@ -0,0 +1,13 @@
+{[k1,k2,k3] :
+15+k1+2k2+3k3 = 0
+ && k2+k3 <= 0
+ && 0 <= 5+k2+k3
+ && k3 <= 0
+ && 0 <= 5+k3
+ && k1+k2+k3 <= 0
+ && 0 <= 5+k1+k2+k3
+};
+
+
+{[x] : exists (a,b : 0 <= x+4a <= 2 && 0 <= x+8b <= 6)};
+
diff --git a/omega/examples/old_test/wielage.oc-rt b/omega/examples/old_test/wielage.oc-rt
new file mode 100644
index 0000000..6c4b10a
--- /dev/null
+++ b/omega/examples/old_test/wielage.oc-rt
@@ -0,0 +1,22 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# {[k1,k2,k3] :
+# 15+k1+2k2+3k3 = 0
+#  && k2+k3 <= 0
+#  && 0 <= 5+k2+k3
+#  && k3 <= 0
+#  && 0 <= 5+k3
+#  && k1+k2+k3 <= 0
+#  && 0 <= 5+k1+k2+k3
+# };
+
+{[0,0,-5]}
+
+# 
+# 
+# 
+# {[x] : exists (a,b : 0 <= x+4a <= 2 && 0 <= x+8b <= 6)};
+
+{[x]: Exists ( alpha,beta : -4alpha <= x <= -4alpha+2, -8beta+6 && alpha <= 2beta)}
+
+# 
+# 
diff --git a/omega/examples/old_test/wild b/omega/examples/old_test/wild
new file mode 100644
index 0000000..7c43e3c
--- /dev/null
+++ b/omega/examples/old_test/wild
@@ -0,0 +1,13 @@
+symbolic L,M;
+
+I := {[j,i] : 1 <= j <= 100 && j-L <= i <= j};
+
+D := I*I intersection {[j1,i1] -> [j2,i2] : i1+j1 = i2+M};
+I;
+D;
+range D;
+(range D) - (range D);
+E := I - range D;
+sample := {[-M+3,-M+3]: L = 0 && -97 <= M <= 2};
+sample intersection range D;
+sample intersection E;
diff --git a/omega/examples/old_test/wild.oc-rt b/omega/examples/old_test/wild.oc-rt
new file mode 100644
index 0000000..811519b
--- /dev/null
+++ b/omega/examples/old_test/wild.oc-rt
@@ -0,0 +1,43 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic L,M;
+# 
+# 
+# I := {[j,i] : 1 <= j <= 100 && j-L <= i <= j};
+# 
+# 
+# D := I*I intersection {[j1,i1] -> [j2,i2] : i1+j1 = i2+M};
+# 
+# I;
+
+{[j,i]: 1, i <= j <= 100 && j <= L+i}
+
+# 
+# D;
+
+{[In_1,In_2] -> [Out_1,In_1-M+In_2] : 1, In_2 <= In_1 <= 100 && 1 <= Out_1 <= 100 && In_1 <= L+In_2 && M+Out_1 <= L+In_1+In_2 && In_1+In_2 <= M+Out_1}
+
+# 
+# range D;
+
+{[In_1,In_2]: Exists ( alpha : 1, In_2 <= In_1 <= 100 && M <= -In_2+200 && 2 <= M+L+In_2 && M+In_2 <= L+2alpha && 2alpha <= M+In_2 && In_1 <= L+In_2)}
+
+# 
+# (range D) - (range D);
+
+{[In_1,In_2]  : FALSE }
+
+# 
+# E := I - range D;
+# 
+# sample := {[-M+3,-M+3]: L = 0 && -97 <= M <= 2};
+# 
+# sample intersection range D;
+
+{[In_1,In_2]  : FALSE }
+
+# 
+# sample intersection E;
+
+{[-M+3,-M+3]: L = 0 && -97 <= M <= 2}
+
+# 
diff --git a/omega/examples/old_test/wrap b/omega/examples/old_test/wrap
new file mode 100644
index 0000000..895c51b
--- /dev/null
+++ b/omega/examples/old_test/wrap
@@ -0,0 +1,12 @@
+symbolic n;
+I := {[i,j,k] : 1 <= i,j,k <= n};
+R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+R1;
+R1+;
+R1+ within I;
+R2 := {[i,n,n] -> [i+1,1,1] : 1 <= i,i+1 <= n}
+	union R1;
+R2;
+R2+;
+R2+ within I;
diff --git a/omega/examples/old_test/wrap.oc-rt b/omega/examples/old_test/wrap.oc-rt
new file mode 100644
index 0000000..0729e41
--- /dev/null
+++ b/omega/examples/old_test/wrap.oc-rt
@@ -0,0 +1,50 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# I := {[i,j,k] : 1 <= i,j,k <= n};
+# 
+# R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+# 	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+# 
+# R1;
+
+{[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n} union
+ {[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n}
+
+# 
+# R1+;
+
+{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
+# R1+ within I;
+
+{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
+# R2 := {[i,n,n] -> [i+1,1,1] : 1 <= i,i+1 <= n}
+# 	union R1;
+# 
+# R2;
+
+{[i,n,n] -> [i+1,1,1] : 1 <= i < n} union
+ {[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n} union
+ {[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n}
+
+# 
+# R2+;
+
+{[i,j,k] -> [i',j',k'] : 1 <= i < i' <= n && 1 <= j <= n && 1 <= k <= n && 1 <= j' <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
+# R2+ within I;
+
+{[i,j,k] -> [i',j',k'] : 1 <= i < i' <= n && 1 <= j <= n && 1 <= k <= n && 1 <= j' <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
diff --git a/omega/examples/old_test/wrap0 b/omega/examples/old_test/wrap0
new file mode 100644
index 0000000..ca914af
--- /dev/null
+++ b/omega/examples/old_test/wrap0
@@ -0,0 +1,7 @@
+symbolic n;
+I := {[i,j,k] : 1 <= i,j,k <= n};
+R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+R1;
+R1+ within I;
+R1+;
diff --git a/omega/examples/old_test/wrap0.oc-rt b/omega/examples/old_test/wrap0.oc-rt
new file mode 100644
index 0000000..d9c7d34
--- /dev/null
+++ b/omega/examples/old_test/wrap0.oc-rt
@@ -0,0 +1,26 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# I := {[i,j,k] : 1 <= i,j,k <= n};
+# 
+# R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+# 	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+# 
+# R1;
+
+{[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n} union
+ {[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n}
+
+# 
+# R1+ within I;
+
+{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
+# R1+;
+
+{[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
diff --git a/omega/examples/old_test/wrap1 b/omega/examples/old_test/wrap1
new file mode 100644
index 0000000..d862a5a
--- /dev/null
+++ b/omega/examples/old_test/wrap1
@@ -0,0 +1,8 @@
+symbolic n;
+I := {[i,j,k] : 1 <= i,j,k <= n};
+R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+R2 := {[i,n,n] -> [i+1,1,1] : 1 <= i,i+1 <= n}
+	union R1;
+R2;
+R2+ within I;
diff --git a/omega/examples/old_test/wrap1.oc-rt b/omega/examples/old_test/wrap1.oc-rt
new file mode 100644
index 0000000..9e43201
--- /dev/null
+++ b/omega/examples/old_test/wrap1.oc-rt
@@ -0,0 +1,25 @@
+# Omega Calculator v1.2 (based on Omega Library 1.2, August, 2000):
+# symbolic n;
+# 
+# I := {[i,j,k] : 1 <= i,j,k <= n};
+# 
+# R1 := {[i,j,n] -> [i,j+1,1] : 1 <= i,j,j+1 <= n}
+# 	 union {[i,j,k] -> [i,j,k'] : 1 <= i,j,k,k' <= n && k' = k+1};
+# 
+# R2 := {[i,n,n] -> [i+1,1,1] : 1 <= i,i+1 <= n}
+# 	union R1;
+# 
+# R2;
+
+{[i,n,n] -> [i+1,1,1] : 1 <= i < n} union
+ {[i,j,k] -> [i,j,k+1] : 1 <= i <= n && 1 <= j <= n && 1 <= k < n} union
+ {[i,j,n] -> [i,j+1,1] : 1 <= i <= n && 1 <= j < n}
+
+# 
+# R2+ within I;
+
+{[i,j,k] -> [i',j',k'] : 1 <= i < i' <= n && 1 <= j <= n && 1 <= k <= n && 1 <= j' <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j',k'] : 1 <= j < j' <= n && 1 <= i <= n && 1 <= k <= n && 1 <= k' <= n} union
+ {[i,j,k] -> [i,j,k'] : 1 <= k < k' <= n && 1 <= i <= n && 1 <= j <= n}
+
+# 
diff --git a/omega/examples/old_test/x b/omega/examples/old_test/x
new file mode 100644
index 0000000..56c23ca
--- /dev/null
+++ b/omega/examples/old_test/x
@@ -0,0 +1,9 @@
+old_IS:= {[i,j]: 1 <= i <= 8 & 1 <= j <= 4};
+T1:={[i,j] -> [j-i+8,i,0]};
+T2:={[i,j] -> [i+j-1,i,1]};
+n1:= T1 \ old_IS;
+n1;
+n2:= T2 \ old_IS;
+n2;
+codegen T1:old_IS,T2:old_IS;
+codegen 2 T1:old_IS,T2:old_IS;
diff --git a/omega/examples/old_test/x.oc-rt b/omega/examples/old_test/x.oc-rt
new file mode 100644
index 0000000..fc77e1a
--- /dev/null
+++ b/omega/examples/old_test/x.oc-rt
@@ -0,0 +1,84 @@
+>>> old_IS:= {[i,j]: 1 <= i <= 8 & 1 <= j <= 4};
+>>> T1:={[i,j] -> [j-i+8,i,0]};
+>>> T2:={[i,j] -> [i+j-1,i,1]};
+>>> n1:= T1 \ old_IS;
+>>> n1;
+{[i,j] -> [j-i+8,i,0] : 1 <= i <= 8 && 1 <= j <= 4}
+>>> n2:= T2 \ old_IS;
+>>> n2;
+{[i,j] -> [i+j-1,i,1] : 1 <= i <= 8 && 1 <= j <= 4}
+>>> codegen T1:old_IS,T2:old_IS;
+for(t1 = 1; t1 <= 11; t1++) {
+  for(t2 = max(t1-3,1); t2 <= min(t1,-t1+8); t2++) {
+    s2(t2,t1-t2+1);
+  }
+  for(t2 = max(-t1+9,1); t2 <= min(-t1+12,t1-4); t2++) {
+    s1(t2,t1+t2-8);
+  }
+  for(t2 = max(-t1+9,t1-3); t2 <= min(-t1+12,t1); t2++) {
+    s1(t2,t1+t2-8);
+    s2(t2,t1-t2+1);
+  }
+  for(t2 = max(-t1+9,t1+1); t2 <= min(-t1+12,8); t2++) {
+    s1(t2,t1+t2-8);
+  }
+  for(t2 = max(t1-3,-t1+13); t2 <= min(t1,8); t2++) {
+    s2(t2,t1-t2+1);
+  }
+}
+
+>>> codegen 2 T1:old_IS,T2:old_IS;
+for(t1 = 1; t1 <= 3; t1++) {
+  for(t2 = 1; t2 <= t1; t2++) {
+    s2(t2,t1-t2+1);
+  }
+  for(t2 = -t1+9; t2 <= 8; t2++) {
+    s1(t2,t1+t2-8);
+  }
+}
+for(t2 = 1; t2 <= 4; t2++) {
+  s2(t2,-t2+5);
+}
+for(t2 = 5; t2 <= 8; t2++) {
+  s1(t2,t2-4);
+}
+for(t2 = 2; t2 <= 3; t2++) {
+  s2(t2,-t2+6);
+}
+for(t2 = 4; t2 <= 5; t2++) {
+  s1(t2,t2-3);
+  s2(t2,-t2+6);
+}
+for(t2 = 6; t2 <= 7; t2++) {
+  s1(t2,t2-3);
+}
+for(t2 = 3; t2 <= 6; t2++) {
+  s1(t2,t2-2);
+  s2(t2,-t2+7);
+}
+for(t2 = 2; t2 <= 3; t2++) {
+  s1(t2,t2-1);
+}
+for(t2 = 4; t2 <= 5; t2++) {
+  s1(t2,t2-1);
+  s2(t2,-t2+8);
+}
+for(t2 = 6; t2 <= 7; t2++) {
+  s2(t2,-t2+8);
+}
+for(t2 = 1; t2 <= 4; t2++) {
+  s1(t2,t2);
+}
+for(t2 = 5; t2 <= 8; t2++) {
+  s2(t2,-t2+9);
+}
+for(t1 = 9; t1 <= 11; t1++) {
+  for(t2 = 1; t2 <= -t1+12; t2++) {
+    s1(t2,t1+t2-8);
+  }
+  for(t2 = t1-3; t2 <= 8; t2++) {
+    s2(t2,t1-t2+1);
+  }
+}
+
+