Abstract

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.

BibTeX Entry

@article{YWHM-TPLP16,
 author    = "Akihisa Yamada and Sarah Winkler and Nao Hirokawa and Aart
              Middeldorp",
 title     = "{AC-KBO} Revisited",
 journal   = "Theory and Practice of Logic Programming",
 volume    = 16,
 number    = 2, 
 pages     = "163--188",
 year      = 2016,
 doi       = "10.1017/S1471068415000083"
}