Orderings for term-rewriting systems

Methods of proving that a term-rewriting system terminates are presented. They are based on the notion of "simplification orderings", orderings in which any term that is homeomorphically embeddable in another is smaller than the other. A particularly useful class of simplification orderings, the "recursive path orderings", is defined. Several examples of the use of such orderings in termination proofs are given.

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