when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2008.1762
URN: urn:nbn:de:0030-drops-17626
URL: http://drops.dagstuhl.de/opus/volltexte/2008/1762/

Moser, Georg ; Schnabl, Andreas ; Waldmann, Johannes

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

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### Abstract

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.

### BibTeX - Entry

@InProceedings{moser_et_al:LIPIcs:2008:1762,
author =	{Georg Moser and Andreas Schnabl and Johannes Waldmann},
title =	{Complexity Analysis of Term Rewriting Based on  Matrix and Context Dependent Interpretations},
booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008)},
pages =	{304--315},
series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN =	{978-3-939897-08-8},
ISSN =	{1868-8969},
year =	{2008},
volume =	{2},
editor =	{Ramesh Hariharan and Madhavan Mukund and V Vinay},
publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},