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Matrix Interpretations on Polyhedral Domains

Author Johannes Waldmann

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Johannes Waldmann

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Johannes Waldmann. Matrix Interpretations on Polyhedral Domains. In 26th International Conference on Rewriting Techniques and Applications (RTA 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 36, pp. 318-333, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


We refine matrix interpretations for proving termination and complexity bounds of term rewrite systems we restricting them to domains that satisfy a system of linear inequalities. Admissibility of such a restriction is shown by certificates whose validity can be expressed as a constraint program. This refinement is orthogonal to other features of matrix interpretations (complexity bounds, dependency pairs), but can be used to improve complexity bounds, and we discuss its relation with the usable rules criterion. We present an implementation and experiments.
  • termination of term rewriting
  • matrix interpretations
  • constraint programming
  • linear inequalities


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