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Decreasing Diagrams and Relative Termination

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Abstract

In this article we use the decreasing diagrams technique to show that a left-linear and locally confluent term rewrite system \(\mathcal{R}\) is confluent if the critical pair steps are relatively terminating with respect to \(\mathcal{R}\). We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem. Experimental data for both methods are presented.

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Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Ishikawa, 923-1292, Japan

    Nao Hirokawa

  2. Institute of Computer Science, University of Innsbruck, 6020, Innsbruck, Austria

    Aart Middeldorp

Authors
  1. Nao Hirokawa
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  2. Aart Middeldorp
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Correspondence to Nao Hirokawa.

Additional information

The research described in this paper is supported by FWF (Austrian Science Fund) project P22467 and the Grant-in-Aid for Young Scientists (B) 22700009 of the Japan Society for the Promotion of Science.

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Hirokawa, N., Middeldorp, A. Decreasing Diagrams and Relative Termination. J Autom Reasoning 47, 481–501 (2011). https://doi.org/10.1007/s10817-011-9238-x

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  • DOI: https://doi.org/10.1007/s10817-011-9238-x

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