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Increasing interpretations

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Abstract

The article at hand introduces a refinement of interpretation-based termination criteria for term rewrite systems in the dependency pair setting. Traditional methods share the property that—in order to be successful—all rewrite rules must (weakly) decrease with respect to some measure. One novelty of our approach is that we allow some rules to increase the interpreted value. These rules are found by simultaneously searching for adequate polynomial interpretations while considering the information of the dependency graph. We prove that our method extends the termination proving power of linear interpretations. Furthermore, this generalization perfectly fits the dependency pair framework which is implemented in virtually every termination prover dealing with term rewrite systems. We present two dependency pair processors for increasing interpretations. The novelty of the second one is that it can be used to eliminate single edges from the dependency graph.

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Authors and Affiliations

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

    Harald Zankl & Aart Middeldorp

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  1. Harald Zankl
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  2. Aart Middeldorp
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Correspondence to Harald Zankl.

Additional information

This research is supported by FWF (Austrian Science Fund) project P18763.

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Zankl, H., Middeldorp, A. Increasing interpretations. Ann Math Artif Intell 56, 87–108 (2009). https://doi.org/10.1007/s10472-009-9144-7

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