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Disproving Confluence of Term Rewriting Systems by Interpretation and Ordering

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Frontiers of Combining Systems (FroCoS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8152))

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Abstract

In order to disprove confluence of term rewriting systems, we develop new criteria for ensuring non-joinability of terms based on interpretation and ordering. We present some instances of the criteria which are amenable for automation, and report on an implementation of a confluence disproving procedure based on these instances. The experiments reveal that our method is successfully applied to automatically disprove confluence of some term rewriting systems, on which state-of-the-art automated confluence provers fail. A key idea to make our method effective is the introduction of usable rules—this allows one to decompose the constraint on rewrite rules into smaller components that depend on starting terms.

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Author information

Authors and Affiliations

  1. RIEC, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai, 980-8577, Japan

    Takahito Aoto

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  1. Takahito Aoto
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Editors and Affiliations

  1. LORIA, Inria Nancy Grand Est, Université de Lorraine, 615 rue du Jardin Botanique, 54602, Villers-les-Nancy, France

    Pascal Fontaine

  2. LORIA, Inria Nancy Grand Est, 615 rue du Jardin Botanique, 54602, Villers-lès-Nancy, France

    Christophe Ringeissen

  3. School of Computer Science, The University of Manchester, Oxford Rd, Kilburn Building, M13 9PL, Manchester, UK

    Renate A. Schmidt

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Aoto, T. (2013). Disproving Confluence of Term Rewriting Systems by Interpretation and Ordering. In: Fontaine, P., Ringeissen, C., Schmidt, R.A. (eds) Frontiers of Combining Systems. FroCoS 2013. Lecture Notes in Computer Science(), vol 8152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40885-4_22

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  • DOI: https://doi.org/10.1007/978-3-642-40885-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40884-7

  • Online ISBN: 978-3-642-40885-4

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