Middeldorp
Aart
Middeldorp, Aart
Neurauter
Friedrich
Neurauter, Friedrich
2011
Matrix interpretations are a powerful technique for proving termination of term rewrite systems, which is based on the well-known paradigm of interpreting terms into a domain equipped with a suitable well-founded order, such that every rewrite step causes a strict decrease. Traditionally, one uses vectors of non-negative numbers as domain, where two vectors are in the order relation if there is a strict decrease in the respective first components and a weak decrease in all other components. In this paper, we study various alternative well-founded orders on vectors of non-negative numbers based on vector norms and compare the resulting variants of matrix interpretations to each other and to the traditional approach. These comparisons are mainly theoretical in nature. We do, however, also identify one of these variants as a proper generalization of traditional matrix interpretations as a stand-alone termination method, which has the additional advantage that it gives rise to a more powerful implementation.
Computer Science, {}
Revisiting Matrix Interpretations for Proving Termination of Term Rewriting
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Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik GmbH, Wadern/Saarbruecken, Germany