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Mechanically Proving Termination Using Polynomial Interpretations

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Abstract

For a long time, term orderings defined by polynomial interpretations were scarcely used in computer-aided termination proof of TRSs. But recently, the introduction of the dependency pairs approach achieved considerable progress w.r.t. automated termination proof, in particular by requiring from the underlying ordering much weaker properties than the classical approach. As a consequence, the noticeable power of a combination dependency pairs/polynomial orderings yielded a regain of interest for these interpretations. We describe criteria on polynomial interpretations for them to define weakly monotonic orderings. From these criteria, we obtain new techniques both for mechanically checking termination using a given polynomial interpretation and for finding such interpretations with full automation. With regard to automated search, we propose an original method for solving Diophantine constraints. We implemented these techniques into the CiME rewrite tool, and we provide some experimental results that show how useful polynomial orderings actually are in practice.

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Authors and Affiliations

  1. PCRI-LRI (CNRS UMR 8623) & INRIA Futurs Bât. 490, Université Paris-Sud, Centre d'Orsay, 91405, Orsay, Cedex, France

    Evelyne Contejean & Claude Marché

  2. DCC-FC & LIACC, University of Porto, R. do Campo Alegre 823, 4150-180, Porto, Portugal

    Ana Paula Tomás

  3. CEDRIC, IIE, Conservatoire National des Arts et Métiers, 18 allée Jean Rostand, 91025, Evry, Cedex, France

    Xavier Urbain

Authors
  1. Evelyne Contejean
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  2. Claude Marché
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  3. Ana Paula Tomás
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  4. Xavier Urbain
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Correspondence to Evelyne Contejean.

Additional information

★ This research was supported in part by the EWG CCL II, the cooperation CNRS-ICCTI, projects 4312, 5518 and 6777, and the “ATIP CiME du département STIC du CNRS”.

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Contejean, E., Marché, C., Tomás, A.P. et al. Mechanically Proving Termination Using Polynomial Interpretations. J Autom Reasoning 34, 325–363 (2005). https://doi.org/10.1007/s10817-005-9022-x

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