Recursive Derivational Length Bounds for Confluent Term Rewrite Systems Research Paper

Abstract

Let F be a signature and \( \mathcal{R} \) a term rewrite system on ground terms of F. We define the concepts of a context-free potential redex in a term and of bounded confluent terms. We bound recursively the lengths of derivations of a bounded confluent term t by a function of the length of derivations of context-free potential redexes of this term. We define the concept of inner redex and we apply the recursive bounds that we obtained to prove that, whenever \( \mathcal{R} \) is a confluent overlay term rewrite system, the derivational length bound for arbitrary terms is an iteration of the derivational length bound for inner redexes.