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.KeywordsRecursive DecompositionReplacement PropertyGround SubstitutionRecursive PathDecomposition OrderingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.