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Published in:
2009 | OriginalPaper | Chapter
Local Termination
Authors : Jörg Endrullis, Roel de Vrijer, Johannes Waldmann
Published in: Rewriting Techniques and Applications
Publisher: Springer Berlin Heidelberg
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The characterization of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic characterization and most known termination methods are concerned with
global
termination, uniformly of all the terms of a term rewriting system (TRS). In this paper we consider
local
termination, of specific sets of terms within a given TRS.
The principal goal of this paper is generalizing the semantic characterization of global termination to local termination. This is made possible by admitting the well-founded monotone algebras to be partial. We show that our results can be applied in the development of techniques for proving local termination. We give several examples, among which a verifiable characterization of the terminating
S
-terms in CL.