Article

Termination by quasi-periodic interpretations

Authors:

Hans Zantema,

Johannes WaldmannAuthors Info & Claims

RTA'07: Proceedings of the 18th international conference on Term rewriting and applications

Pages 404 - 418

Published: 26 June 2007 Publication History

Abstract

We present a new method for automatically proving termination of term rewriting and string rewriting. It is based on the well-known idea of interpretation of terms in natural numbers where every rewrite step causes a decrease. In the dependency pair setting only weak monotonicity is required for these interpretations. For these we use quasi-periodic functions. It turns out that then the decreasingness for rules only needs to be checked for finitely many values, which is easy to implement.

Using this technique we automatically prove termination of over ten string rewriting systems in TPDB for which termination was open until now.

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Cited By

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Koprowski AWaldmann J(2009)Max/plus tree automata for termination of term rewritingActa Cybernetica10.5555/1774732.177473819:2(357-392)Online publication date: 1-Feb-2009
https://dl.acm.org/doi/10.5555/1774732.1774738
Zankl HHirokawa NMiddeldorp A(2009)KBO OrientabilityJournal of Automated Reasoning10.1007/s10817-009-9131-z43:2(173-201)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1007/s10817-009-9131-z
Zankl HMiddeldorp A(2009)Increasing interpretationsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-009-9144-756:1(87-108)Online publication date: 1-May-2009
https://dl.acm.org/doi/10.1007/s10472-009-9144-7
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Termination by quasi-periodic interpretations
1. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms

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RTA'07: Proceedings of the 18th international conference on Term rewriting and applications

June 2007

419 pages

ISBN:3540734473

Editor:
Franz Baader
TU Dresden, Theoretical Computer Science, Dresden, Germany

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 26 June 2007

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Koprowski AWaldmann J(2009)Max/plus tree automata for termination of term rewritingActa Cybernetica10.5555/1774732.177473819:2(357-392)Online publication date: 1-Feb-2009
https://dl.acm.org/doi/10.5555/1774732.1774738
Zankl HHirokawa NMiddeldorp A(2009)KBO OrientabilityJournal of Automated Reasoning10.1007/s10817-009-9131-z43:2(173-201)Online publication date: 1-Aug-2009
https://dl.acm.org/doi/10.1007/s10817-009-9131-z
Zankl HMiddeldorp A(2009)Increasing interpretationsAnnals of Mathematics and Artificial Intelligence10.1007/s10472-009-9144-756:1(87-108)Online publication date: 1-May-2009
https://dl.acm.org/doi/10.1007/s10472-009-9144-7
Zankl HMiddeldorp A(2008)Increasing InterpretationsProceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics10.1007/978-3-540-85110-3_16(191-205)Online publication date: 28-Jul-2008
https://dl.acm.org/doi/10.1007/978-3-540-85110-3_16
Marché CZantema H(2007)The termination competitionProceedings of the 18th international conference on Term rewriting and applications10.5555/1779782.1779805(303-313)Online publication date: 26-Jun-2007
https://dl.acm.org/doi/10.5555/1779782.1779805

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Decidability of Innermost Termination and Context-Sensitive Termination for Semi-Constructor Term Rewriting Systems

Termination of non-simple rewrite systems

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