Termination for the direct sum of left-linear term rewriting systems
The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that two term rewriting systems both are left-linear and complete if and only if the direct sum of these systems is so.
KeywordsInduction Hypothesis Function Symbol Modular Property Case Rank Preliminary Draft
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- G. Huet and D. C. Oppen, Equations and rewrite rules: a survey, in: R. Book, ed., Formal languages: perspectives and open problems (Academic Press, 1980) 349–393.Google Scholar
- N. Dershowitz. Termination of linear rewriting systems: Preliminary version, Lecture Notes in Comput. Sci. 115 (Springer-Verlag, 1981) 448–458.Google Scholar
- H. Ganzinger and R. Giegerich, A note on termination in combinations of heterogeneous term rewriting systems, EATCS Bulletin 31 (1987) 22–28.Google Scholar
- J. W. Klop and H. P. Barendregt, Private communication (January 19, 1986).Google Scholar
- A. Middeldorp, A sufficient condition for the termination of the direct sum of term rewriting systems, Preliminary Draft, Report IR-150, Free University, Amsterdam (1988).Google Scholar
- A. Middeldorp, Modular aspects of properties of term rewriting systems related to normal forms, Preliminary Draft, Free University, Amsterdam (September 1988).Google Scholar
- M. Rusinowitch, On termination of the direct sum of term rewriting systems, Inform. Process. Lett. 26 (1987) 65–70.Google Scholar
- Y. Toyama, On the Church-Rosser property for the direct sum of term rewriting systems, J. ACM 34 (1987) 128–143.Google Scholar
- Y. Toyama, Counterexamples to termination for the direct sum of term rewriting systems, Inform. Process. Lett. 25 (1987) 141–143.Google Scholar
- Y. Toyama, Commutativity of term rewriting systems, in: K. Fuchi and L. Kott, eds., Programming of Future Generation Computer II (Norht Holland 1988) 393–407.Google Scholar
- Y. Toyama, J.W. Klop, H.P. Barendregt, Termination for the direct sum of left-linear term rewriting systems: Preliminary draft, IEICE technical report COM88-30 (July 1988) 47–55.Google Scholar