Abstract
Well-foundedness is the essential property of orderings for proving termination. We introduce a simple criterion on term orderings such that any term ordering possessing the subterm property and satisfying this criterion is well-founded. The usual path orders fulfil this criterion, yielding a much simpler proof of well-foundedness than the classical proof depending on Kruskal's theorem. Even more, our approach covers non-simplification orders like spo and gpo which can not be dealt with by Kruskal's theorem.
For finite alphabets we present completeness results, i. e., a term rewriting system terminates if and only if it is compatible with an order satisfying the criterion. For infinite alphabets the same completeness results hold for a slightly different criterion.
Supported by NWO, the Dutch Organization for Scientific Research, under grant 612-316-041.
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© 1995 Springer-Verlag Berlin Heidelberg
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Ferreira, M.C.F., Zantema, H. (1995). Well-foundedness of term orderings. In: Dershowitz, N., Lindenstrauss, N. (eds) Conditional and Typed Rewriting Systems. CTRS 1994. Lecture Notes in Computer Science, vol 968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60381-6_7
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DOI: https://doi.org/10.1007/3-540-60381-6_7
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