2026-08-10T17:36:40Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:2662 2024-03-06T10:33:30Z ddc:004 open_access

Termination of linear bounded term rewriting systems Durand, Irène Sénizergues, Géraud Sylvestre, Marc Term rewriting termination rewriting strategy For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting. We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse k-bounded problems are decidable. The k-bounded class (BO(k)) is, by definition, the set of linear systems for which every derivation can be replaced by a k-bounded derivation. In general, for BO(k) systems, the uniform (respectively inverse uniform) k-bounded termination problem is not equivalent to the uniform (resp. inverse uniform) termination problem, and the k-bounded (respectively inverse k-bounded) termination problem is not equivalent to the termination (respectively inverse termination) problem. This leads us to define more restricted classes for which these problems are equivalent: the classes BOLP(k) of k-bounded systems that have the length preservation property. By definition, a system is BOLP(k) if every derivation of length n can be replaced by a k-bounded derivation of length n. We define the class BOLP of bounded systems that have the length preservation property as the union of all the BOLP(k) classes. The class BOLP contains (strictly) several already known classes of systems: the inverse left-basic semi-Thue systems, the linear growing term rewriting systems, the inverse Linear-Finite-Path-Ordering systems, the strongly bottom-up systems. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Irène Durand and Géraud Sénizergues and Marc Sylvestre 2010 Is Part Of LIPIcs, Volume 6, Proceedings of the 21st International Conference on Rewriting Techniques and Applications (2010) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.RTA.2010.341 urn:nbn:de:0030-drops-26625 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.RTA.2010.341 eng https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode