Relating derivation lengths with the slow-growing hierarchy directly

Authors:
Georg Moser;Andreas Weiermann
Affiliations:
WWU Münster, Institut für Mathematische Logik und Grundlagenforschung, Münster, Germany;WWU Münster, Institut für Mathematische Logik und Grundlagenforschung, Münster, Germany
Venue:
RTA'03 Proceedings of the 14th international conference on Rewriting techniques and applications
Year:
2003

Citing 5
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Abstract

In this article we introduce the notion of a generalized system of fundamental sequences and we define its associated slow-growing hierarchy. We claim that these concepts are genuinely related to the classification of the complexity--the derivation length-- of rewrite systems for which termination is provable by a standard termination ordering. To substantiate this claim, we re-obtain multiple recursive bounds on the the derivation length for rewrite systems terminating under lexicographic path ordering, originally established by the second author.