Proving Termination of Ac-rewriting without Extended Rules

Polynomial interpretations and RPO-like orderings allow one to prove termination of Associative and Commutative (AC-)rewriting by only checking the rules of the given rewrite system without considering the so-called extended rules. However, these methods have important limitations as termination proving tools. To overcome these limitations, more powerful methods like the dependency pairs method have been extended to the AC-case. Unfortunately, in order to ensure AC-termination, the extended rules, which, in general, are hard to prove, must be added to the rewrite system. In this paper we present a new automatable ordering-based termination proving method for AC-rewriting which does not need to consider extended rules. Due to this, we can easily prove several non-trivial examples appearing in the literature that, to our knowledge, can be handled by no other automatic method.