Derived Pairs, Overlap Closures, and Rewrite Dominoes: New Tools for Analyzing Term Rewriting Systems

Abstract

Starting from the seminal work of Knuth and Bendix, we develop several notions useful in the study of term rewriting systems. In particular we introduce the notions of "derived pairs" and "overlap closure" and show that they are useful in analyzing sets of rewrite rules for various properties related to termination. We also introduce a new representation, based on rewrite dominoes, for rewrite rules and sequences of rewrites.