Adss example for non-equivalence of two non-deterministic insert operations

examples/equivalent_operations/NDInsert.curry

+--- Example to show the non-equivalence of two versions of a
+--- non-deterministic insert operation.
+
+import Test.Prop
+
+-- Non-deterministic defined by overlapping rules:
+ndinsert1 :: a -> [a] -> [a]
+ndinsert1 x ys     = x : ys
+ndinsert1 x (y:ys) = y : ndinsert1 x ys
+
+-- Non-deterministic defined by non-overlapping rules:
+ndinsert2 :: a -> [a] -> [a]
+ndinsert2 x []     = [x]
+ndinsert2 x (y:ys) = x : y : ys  ?  y : ndinsert2 x ys
+
+-- The equality of both ndinsert operations on ground values always succeeds:
+ndinsert_groundequiv x xs = ndinsert1 x xs <~> ndinsert2 x xs
+
+-- Actually, ndinsert1 and ndinsert2 are not equivalent, as can be seen
+-- by evaluating `head (ndinsert 1 failed)`.
+-- Thus, we check the equivalence with CurryCheck:
+
+-- In PAKCS, the counter example is reported by the 7th test:
+ndinsert_equiv = ndinsert1 <=> ndinsert2
+