Comparing and putting together recursive path ordering, simplification orderings and Non-Ascending Property for termination proofs of term rewriting systems
We give a sufficient condition for proving strong termination in Combinatory Logic and Rewriting Systems which solves an open problem [Böh 77]. We also compare, in the context of general rewriting systems, the power of that condition and other known methods, as the recursive path orderings and simplification orderings, presenting original results.
A new technique for proving strong termination, called Diagram of Matchings, is also introduced. In many cases it allows to combine together the strength of various methods of proof.
KeywordsStrong Termination Combinatory Logic Axiom Schema Rewrite System Basic Combinator
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