Increasing Interpretations

Authors:
Harald Zankl;Aart Middeldorp
Affiliations:
Institute of Computer Science, University of Innsbruck, Innsbruck, Austria 6020;Institute of Computer Science, University of Innsbruck, Innsbruck, Austria 6020
Venue:
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Year:
2008

Citing 16
Cited 0

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Abstract

The paper 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. The 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 natural interpretations. Furthermore, this generalization perfectly fits the recursive SCC decomposition algorithm which is implemented in virtually every termination prover dealing with term rewrite systems.