A confluence criterion based on the generalised Newman Lemma

  • Wolfgang Küchlin
Rewrite Rules And The Completion Procedure
Part of the Lecture Notes in Computer Science book series (LNCS, volume 204)


In order to improve the efficiency of the Knuth-Bendix Algorithm by eliminating unnecessary reductions, a criterion predicting confluence of critical pairs was given by Winkler in 1983. Subsequently, Winkler and Buchberger also presented a more general form of Newman's Lemma. We derive a more general confluence criterion directly from the Generalised Newman Lemma and integrate it into the Knuth-Bendix Algorithm with the aim of generating fewer critical pairs. With the new criterion it is possible to give a concise justification for the removal of reducible rules in the KB-algorithm. A slightly specialised version of this criterion needs only a single match to test for; empirical results substantiate the claim of a considerable gain in efficiency for the Knuth-Bendix Algorithm.


Step Stone Reducible Rule Critical Pair Confluence Criterion Completion Process 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Wolfgang Küchlin
    • 1
  1. 1.Mathematics, ETH (Swiss Federal Institute of Technology)Zürich

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