Slothrop: Knuth–Bendix completion with a modern termination checker. A Knuth-Bendix completion procedure is parametrized by a reduction ordering used to ensure termination of intermediate and resulting rewriting systems. While in principle any reduction ordering can be used, modern completion tools typically implement only Knuth-Bendix and path orderings. Consequently, the theories for which completion can possibly yield a decision procedure are limited to those that can be oriented with a single path order. In this paper, we present a variant on the Knuth-Bendix completion procedure in which no ordering is assumed. Instead we rely on a modern termination checker to verify termination of rewriting systems. The new method is correct if it terminates; the resulting rewrite system is convergent and equivalent to the input theory. Completions are also not just ground-convergent, but fully convergent. We present an implementation of the new procedure, Slothrop, which automatically obtains such completions for theories that do not admit path orderings.
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References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
- Sato, Haruhiko; Winkler, Sarah: Encoding dependency pair techniques and control strategies for maximal completion (2015)
- Bofill, Miquel; Rubio, Albert: Paramodulation with non-monotonic orderings and simplification (2013)
- Winkler, Sarah; Sato, Haruhiko; Middeldorp, Aart; Kurihara, Masahito: Multi-completion with termination tools (2013)
- Winkler, Sarah; Middeldorp, Aart: AC completion with termination tools (2011)
- Nishida, Naoki; Sakai, Masahiko: Proving injectivity of functions via program inversion in term rewriting (2010)
- Winkler, Sarah; Sato, Haruhiko; Middeldorp, Aart; Kurihara, Masahito: Optimizing $\textmkb_\textTT$ (2010)
- Nishida, Naoki; Sakai, Masahiko: Completion after program inversion of injective functions (2009)
- Sato, Haruhiko; Winkler, Sarah; Kurihara, Masahito; Middeldorp, Aart: Multi-completion with termination tools. (System description) (2008)
- Wehrman, Ian; Stump, Aaron; Westbrook, Edwin: Slothrop: Knuth-Bendix completion with a modern termination checker (2006)