## Syntactic Confluence Criteria for Positive/Negative-Conditional Term Rewriting Systems

• We study the combination of the following already known ideas for showing confluence ofunconditional or conditional term rewriting systems into practically more useful confluence criteria forconditional systems: Our syntactic separation into constructor and non-constructor symbols, Huet's intro-duction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, theuse of shallow confluence for proving confluence of noetherian and non-noetherian conditional systems, theidea that certain kinds of limited confluence can be assumed for checking the fulfilledness or infeasibilityof the conditions of conditional critical pairs, and the idea that (when termination is given) only primesuperpositions have to be considered and certain normalization restrictions can be applied for the sub-stitutions fulfilling the conditions of conditional critical pairs. Besides combining and improving alreadyknown methods, we present the following new ideas and results: We strengthen the criterion for overlayjoinable noetherian systems, and, by using the expressiveness of our syntactic separation into constructorand non-constructor symbols, we are able to present criteria for level confluence that are not criteria forshallow confluence actually and also able to weaken the severe requirement of normality (stiffened withleft-linearity) in the criteria for shallow confluence of noetherian and non-noetherian conditional systems tothe easily satisfied requirement of quasi-normality. Finally, the whole paper also gives a practically usefuloverview of the syntactic means for showing confluence of conditional term rewriting systems.

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Author: Claus-Peter Wirth urn:nbn:de:hbz:386-kluedo-3501 SEKI Report (95,9) Preprint English 1995 1995 Technische Universität Kaiserslautern 2000/04/03 Fachbereich Informatik 0 Informatik, Informationswissenschaft, allgemeine Werke / 00 Informatik, Wissen, Systeme / 004 Datenverarbeitung; Informatik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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