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Decreasing Diagrams and Relative Termination

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Automated Reasoning (IJCAR 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6173))

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Abstract

In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system \({\mathcal{R}}\) is confluent if all its critical pairs are joinable and 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.

The research described in this paper is the starting point of 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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Author information

Authors and Affiliations

  1. School of Information Science, Japan Advanced Institute of Science and Technology, Japan

    Nao Hirokawa

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

    Aart Middeldorp

Authors
  1. Nao Hirokawa
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  2. Aart Middeldorp
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Editors and Affiliations

  1. RWTH Aachen, LuFG Informatik, 2, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl

  2. Department of Computer Science, Chalmers University of Technology, 41296, Gothenburg, Sweden

    Reiner Hähnle

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Hirokawa, N., Middeldorp, A. (2010). Decreasing Diagrams and Relative Termination. In: Giesl, J., Hähnle, R. (eds) Automated Reasoning. IJCAR 2010. Lecture Notes in Computer Science(), vol 6173. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14203-1_41

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  • DOI: https://doi.org/10.1007/978-3-642-14203-1_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14202-4

  • Online ISBN: 978-3-642-14203-1

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