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KBO Orientability

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Abstract

This article presents three new approaches to prove termination of rewrite systems with the Knuth–Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic or linear arithmetic and the resulting formula is tested for satisfiability using dedicated solvers. Any satisfying assignment represents a weight function and a precedence such that the induced Knuth–Bendix order orients the rules of the encoded rewrite system from left to right. This means that in contrast to the dedicated methods our approach does not directly solve the problem but transforms it to equivalent formulations for which sophisticated back-ends exist. In order to make all approaches complete we present a method to compute upper bounds on the weights. Furthermore, our encodings take dependency pairs into account to increase the applicability of the order.

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Authors and Affiliations

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

    Harald Zankl & Aart Middeldorp

  2. School of Information Science, Japan Advanced Institute of Science and Technology, Nomi, Japan

    Nao Hirokawa

Authors
  1. Harald Zankl
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  2. Nao Hirokawa
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  3. Aart Middeldorp
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Correspondence to Harald Zankl.

Additional information

The first and third authors are supported by FWF (Austrian Science Fund) project P18763 and the second author is supported by the Grant-in-Aid for Young Scientists 20800022 of the Ministry of Education, Culture, Sports, Science and Technology of Japan.

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Zankl, H., Hirokawa, N. & Middeldorp, A. KBO Orientability. J Autom Reasoning 43, 173–201 (2009). https://doi.org/10.1007/s10817-009-9131-z

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