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+# 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 }
+
+#