Published online by Cambridge University Press: 08 June 2015
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.
The research described in this paper is supported by the Austrian Science Fund (FWF) international project I963, the bilateral programs of the Japan Society for the Promotion of Science and the KAKENHI Grant No. 25730004.
This is an extended version of a paper presented at the Twelfth International Symposium on Functional and Logic Programming (FLOPS 2014), invited as a rapid publication in TPLP. The authors acknowledge the assistance of the conference chairs Michael Codish and Eijiro Sumii.