Improving associative path orderings

Abstract

The effective computation with term rewriting systems modulo a theory E presumes E-termination. We will give a classification of the methods guaranteeing AC-termination based on the recursive path ordering. Furthermore, we will show that these techniques [called associative path orderings] cannot use quasi-orderings on operators. Above all, this report will deal with two new orderings applicable to AC-theories. We apply the concept of the associative path ordering to the recursive path ordering with status [RPOS] and the improved recursive decomposition ordering with status [IRDS]. Since these orderings are stronger than the recursive path ordering, the corresponding orderings restricted to AC-theories are more powerful than the associative path ordering. From a practical point of view the associative-commutative IRDS is more interesting than the associative path ordering because the detection of an admissible precedence for orienting the rules of a given system is easier.

This research was supported by the Deutsche Forschungsgemeinschaft. SFB 314