@MISC{Dershowitz82orderingsfor, author = {Nachum Dershowitz}, title = { ORDERINGS FOR TERM-REWRITING SYSTEMS}, year = {1982} }

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Abstract

Methods of proving that a term-rewriting system terminates are presented. They are based on the intuitive notion of 'simplification orderings'. orderings in which any term that is syntactically simpler than another is smaller than the other. M a consequence of Kruskal's Tree Theorem, any nonterminating system must be self-embedding in the sense that it allows for the derivation of some term from a simpler one; thus termination is guaranteed jf every rule in the system as a reduction in some simplification ordering. Most 01 the orderings that have been used for proving tennination are indeed simplication orderings; using this notion often allows for much easier proofs. A particularly useful class of simplification orderings, the 'recursive path orderings', is defined. Examples of the use of simplification orderings in termination proofs are given.