Slothrop: Knuth-Bendix Completion with a Modern Termination Checker

  • Ian Wehrman
  • Aaron Stump
  • Edwin Westbrook
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ian Wehrman
    • 1
  • Aaron Stump
    • 1
  • Edwin Westbrook
    • 1
  1. 1.Dept. of Computer Science and EngineeringWashington University in St. LouisSt. LouisUSA

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