Generalizing Newman’s Lemma for Left-Linear Rewrite Systems

  • Bernhard Gramlich
  • Salvador Lucas
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


Confluence criteria for non-terminating rewrite systems are known to be rare and notoriously difficult to obtain. Here we prove a new result in this direction. Our main result is a generalized version of Newman’s Lemma for left-linear term rewriting systems that does not need a full termination assumption. We discuss its relationships to previous confluence criteria, its restrictions, examples of application as well as open problems. The whole approach is developed in the (more general) framework of context-sensitive rewriting which thus turns out to be useful also for ordinary (context-free) rewriting.


Normal Form Reduction Step Critical Pair Reduction Graph Critical Peak 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Bernhard Gramlich
    • 1
  • Salvador Lucas
    • 2
  1. 1.Fakultät für InformatikTechnische Universität WienWienAustria
  2. 2.DSIC, Universidad Politécnica de ValenciaValenciaSpain

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