This chapter focuses on rewrite systems, which are directed equations used to compute by repeatedly replacing sub-terms of a given formula with equal terms until the simplest form possible is obtained.Expand

Methods for proving that systems of rewrite rules are terminating programs are described, including polynomial interpretations and path orderings, which are used in termination proofs of various kinds of orderings on terms.Expand

Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable… Expand

Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable… Expand

The multiset ordering enables the use of relatively simple and intuitive termination functions in otherwise difficult termination proofs, and is used to prove the termination of production systems, programs defined in terms of sets of rewriting rules.Expand

This paper outlines the application of transforms—mappings from terms to terms—to termination in general, and describes various specific transforms, including transforms for associative-commutative rewrite systems.Expand

The application of proof orderings to various rewrite-based theorem-proving methods, including refinements of the standard Knuth-Bendix completion procedure based on critical pair criteria, and Huet's procedure for rewriting modulo a congruence are described.Expand

A term-rewriting system P over a set of terms T is a finite set of rewrite rules of the form Q,(g) + ri(@, u here the & are variables ranging over I’.Expand