AC-KBO revisited

KIHISA YAMADA, Research Institute for Secure Systems, AIST, Japan
SARAH WINKLER, Institute of Computer Science, University of Innsbruck, Austria
NAO HIROKAWA, School of Information Science, JAIST, Japan
AART MIDDELDORP Institute of Computer Science, University of Innsbruck, Austria


Equational theories that contain axioms expressing associativity and commutativity (AC) of certain operators are ubiquitous. Theorem proving methods in such theories rely on well-founded orders that are compatible with the AC axioms. In this paper we consider various definitions of AC-compatible Knuth-Bendix orders. The orders of Steinbach and of Korovin and Voronkov are revisited. The former is enhanced to a more powerful version, and we modify the latter to amend its lack of monotonicity on non-ground terms. We further present new complexity results. An extension reflecting the recent proposal of subterm coefficients in standard Knuth-Bendix orders is also given. The various orders are compared on problems in termination and completion.