Proving termination of associative commutative rewriting systems by rewriting

  • Isabelle Gnaedig
  • Pierre Lescanne
Term Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


We propose in this paper a special reduction ordering for proving termination of Associative Commutative (AC in short) rewriting systems. This ordering is based on a transformation of the terms by a rewriting system with rules similar to distributivity. We show this is a reduction ordering which works in the AC case since it is AC-commuting, and which provides an automatizable termination tool, since it is stable by instantiation. Thereafter, we show cases where this ordering fails, and propose an extension of this method to other transformation rules such as endomorphism.


Normal Form Word Problem Transformation Rule Distributivity Rule Closed Substitution 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Isabelle Gnaedig
    • 1
  • Pierre Lescanne
    • 1
  1. 1.CrinVandoeuvre CedexFrance

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