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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.

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Comparing and putting together recursive path ordering, simplification orderings and Non-Ascending Property for termination proofs of term rewriting systems