Ordinals and knuth-bendix orders

Authors:
Sarah Winkler;Harald Zankl;Aart Middeldorp
Affiliations:
Institute of Computer Science, University of Innsbruck, Innsbruck, Austria;Institute of Computer Science, University of Innsbruck, Innsbruck, Austria;Institute of Computer Science, University of Innsbruck, Innsbruck, Austria
Venue:
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Year:
2012

Citing 14
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Abstract

In this paper we consider a hierarchy of three versions of Knuth-Bendix orders. (1) We show that the standard definition can be (slightly) simplified without affecting the ordering relation. (2) For the extension of transfinite Knuth-Bendix orders we show that transfinite ordinals are not needed as weights, as far as termination of finite rewrite systems is concerned. (3) Nevertheless termination proving benefits from transfinite ordinals when used in the setting of general Knuth-Bendix orders defined over a weakly monotone algebra. We investigate the relationship to polynomial interpretations and present experimental results for both termination analysis and ordered completion. For the latter it is essential that the order is totalizable on ground terms.