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New Abstract Criteria for Termination and Confluence of Conditional Rewrite Systems

  • We consider the problem of verifying confluence and termination of conditionalterm rewriting systems (TRSs). For unconditional TRSs the critical pair lemmaholds which enables a finite test for confluence of (finite) terminating systems.And for ensuring termination of unconditional TRSs a couple of methods forconstructing appropiate well-founded term orderings are known. If however ter-mination is not guaranteed then proving confluence is much more difficult. Re-cently we have obtained some interesting results for unconditional TRSs whichprovide sufficient criteria for termination plus confluence in terms of restrictedtermination and confluence properties. In particular, we have shown that anyinnermost terminating and locally confluent overlay system is complete, i.e. ter-minating and confluent. Here we generalize our approach to the conditional caseand show how to solve the additional complications due to the presence of con-ditions in the rules. Our main result can be stated as follows: Any conditionalTRS which is an innermost terminating semantical overlay system such that all(conditional) critical pairs are joinable is complete.

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Author:Bernhard Gramlich
Serie (Series number):SEKI Report (93,17)
Document Type:Preprint
Language of publication:English
Year of Completion:1999
Year of Publication:1999
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2000/04/03
Tag:Term rewriting systems; combined systems with sha; confluence; disjoint union; innermost termination; modularity; termination; weak termination
Faculties / Organisational entities:Fachbereich Informatik
DDC-Cassification:0 Allgemeines, Informatik, Informationswissenschaft / 004 Informatik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011