Abstract
Termination is an important issue in the theory of term rewriting. In general termination is undecidable. There are nevertheless several methods successful in special cases. In [5] we introduced the notion of total termination: basically terms are interpreted compositionally in a total well-founded order, in such a way that rewriting chains map to descending chains. Total termination is thus a semantic notion. It turns out that most of the usual techniques for proving termination fall within the scope of total termination. This paper consists of two parts. In the first part we introduce a generalization of recursive path order presenting a new proof of its well-foundedness without using Kruskal's theorem. We also show that the notion of total termination covers this generalization. In the second part we present some syntactical characterizations of total termination that can be used to prove that many term rewriting systems are not totally terminating and hence outside the scope of the usual techniques. One of these characterizations can be considered as a sound and complete description of totality of orderings on terms.
Supported by NWO, the Dutch Organization for Scientific Research, under grant 612-316-041.
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Ferreira, M.C.F., Zantema, H. (1994). Syntactical analysis of total termination. In: Levi, G., RodrÃguez-Artalejo, M. (eds) Algebraic and Logic Programming. ALP 1994. Lecture Notes in Computer Science, vol 850. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58431-5_15
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DOI: https://doi.org/10.1007/3-540-58431-5_15
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