Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations

Authors Georg Moser, Andreas Schnabl, Johannes Waldmann

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Georg Moser
Andreas Schnabl
Johannes Waldmann

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Georg Moser, Andreas Schnabl, and Johannes Waldmann. Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 304-315, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


For a given (terminating) term rewriting system one can often estimate its \emph{derivational complexity} indirectly by looking at the proof method that established termination. In this spirit we investigate two instances of the interpretation method: \emph{matrix interpretations} and \emph{context dependent interpretations}. We introduce a subclass of matrix interpretations, denoted as \emph{triangular matrix interpretations}, which induce polynomial derivational complexity and establish tight correspondence results between a subclass of context dependent interpretations and restricted triangular matrix interpretations. The thus obtained new results are easy to implement and considerably extend the analytic power of existing results. We provide ample numerical data for assessing the viability of the method.
  • Term Rewriting
  • Derivational Complexity
  • Termination
  • Automation


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