A simple non-termination test for the Knuth-Bendix method

  • David A. Plaisted
Term Rewriting Systems
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


We propose a simple test for nontermination in the Knuth-Bendix completion algorithm. This test has the property that if there exists a simplification ordering that can generate a completion S of a set R of rules, then S may be generated from R using this test. Also, this test is “user friendly” in that it does not require any detailed knowledge of termination orderings. However, this technique may generate completions S that are not terminating; therefore, traditional methods for proving termination need to be used on the locally confluent sets S of rewrite rules that are obtained. We show that this test may be implemented in reasonable time and space bounds.


Function Symbol Critical Pair Ground Term Reduction Sequence Constant Symbol 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • David A. Plaisted
    • 1
  1. 1.Department of Computer ScienceUniversity of North Carolina at Chapel HillChapel Hill

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