Syntactic Connuence Criteria for Positive/negative-conditional Term Rewriting Systems

We study the combination of the following already known ideas for showing connuence of unconditional or conditional term rewriting systems into practically more useful connuence criteria for conditional systems: Our syntactic separation into constructor and non-constructor symbols, Huet's introduction and Toyama's generalization of parallel closedness for non-noetherian unconditional systems, the use of shallow connuence for proving connuence of noetherian and non-noetherian conditional systems, the idea that certain kinds of limited connuence can be assumed for checking the fulllledness or infeasibility of the conditions of conditional critical pairs, and the idea that (when termination is given) only prime superpositions have to be considered and certain normalization restrictions can be applied for the substitutions fulllling the conditions of conditional critical pairs. Besides combining and improving already known methods, we present the following new ideas and results: We strengthen the criterion for overlay joinable noetherian systems, and, by using the expressiveness of our syntactic separation into constructor and non-constructor symbols, we are able to present criteria for level connuence that are not criteria for shallow connuence actually and also able to weaken the severe requirement of normality (stiiened with left-linearity) in the criteria for shallow connuence of noetherian and non-noetherian conditional systems to the easily satissed requirement of quasi-normality. Finally, the whole paper also gives a practically useful overview of the syntactic means for showing connuence of conditional term rewriting systems.