Abstract
One of the key results in the field of modularity for Term Rewriting Systems is the modularity of completeness for left-linear TRSs established by Toyama, Klop and Barendregt in [TKB89]. The proof, however, is quite long and involved. In this paper, a new proof of this basic result is given which is both short and easy, employing the powerful technique of ‘pile and delete’ already used with success in proving the modularity of UN→. Moreover, the same proof is shown to extend the result in [TKB89] proving modularity of termination for left-linear and consistent with respect to reduction TRSs.
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References
J.W. Klop. Term rewriting systems. In S. Abramsky, Dov M. Gabbay, and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, volume 2, chapter 1, pages 1–116. Clarendon Press, Oxford, 1992.
M. Marchiori. Modularity of UN→ for left-linear term rewriting systems. Draft, March 1993. Extended and revised version: Technical Report CS-R9433, CWI, Amsterdam.
A. Middeldorp. Modular Properties of Term Rewriting Systems. PhD thesis, Vrije Universiteit, Amsterdam, November 1990.
M. Schmidt-Schauß and S. Panitz. Modular termination of consistent and left-linear TRSs. Draft, May 1994.
Y. Toyama, J.W. Klop, and H.P. Barendregt. Termination for the direct sum of left-linear term rewriting systems. In N. Dershowitz, editor, Proceedings of the 3rd RTA, vol. 355 of LNCS, pp. 477–491, Springer, 1989. Extended version: Technical Report CS-R8923, CWI, Amsterdam.
Y. Toyama, J.W. Klop, and H.P. Barendregt. Termination for direct sums of left-linear complete term rewriting systems. JACM, 1994. To appear.
Y. Toyama. On the Church-Rosser property for the direct sum of term rewriting systems. JACM, 1(34):128–143, 1987.
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© 1995 Springer-Verlag Berlin Heidelberg
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Marchiori, M. (1995). Modularity of completeness revisited. In: Hsiang, J. (eds) Rewriting Techniques and Applications. RTA 1995. Lecture Notes in Computer Science, vol 914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-59200-8_43
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DOI: https://doi.org/10.1007/3-540-59200-8_43
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