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+# 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;