Confluence Proofs of Term Rewriting Systems Based on Persistency

Abstract

Since the confluence property of term rewrite systems is persistent, a term rewriting system R is confluent if it is decomposed into small subsystems by introducing appropriate many-sorted types and each of them is confluent. However, if introducing types does not decompose R into small subsystems, this proof method does not work. In this paper we propose a new method for confluence proof based on persistency, which can be applied to non-left-linear term rewriting systems not decomposed into subsystems by introducing types.