Well-foundedness for termination of term rewriting systems

Abstract

Well-foundedness is related to an important property of rewriting systems, namely termination. A well-known technique to prove well-foundedness on term orderings is Kruskal's theorem, which implies that a monotonic term ordering over a finite signature satisfying the subterm property is well-founded. However, it does not seem to work for a number of terminating term rewriting systems. In this paper, it is shown that a term ordering possessing subterm property and decomposability (in place of monotonicity) does yield a simpler proof of well-foundedness for terminating term rewriting systems than the techniques depending on Kruskal's theorem.