well, if you are sure that the problem is NP-complete then we are sure that my algorithm sketch won't work
Are you sure that the problem to which those people referred is exactly the one you describe ?
I ask because your notion of "equivalence" of expressions is stronger then the intuitive notion of arithmetic equivalence; for example, you assume a+(b+b) and b+(a+b) or a(b+c) and ab+ac to be non-equivalent. This "strongness" could make the problem solvable in polynomial time.

>>..wrong?

those are good counterexamples...

now, certainly I could add new rules in order to make those examples work. The problem is that we could go on indefinitely (and I do not have indefinite time ). You should tackle the problem formally and rigorously define by structural induction the input forms and their equivalence condition in order to give a formal proof of (non)NP completeness.