Abstract
In this paper, we give a generalization of the associative path ordering. This ordering has been introduced by Bachmair and Plaisted [5] and is a restricted variant of the recursive path ordering which can be used for proving the termination of associative-commutative term rewriting systems. This ordering requires strong conditions on the precedence on the alphabet. In this article, we treat the case of a precedence which contains a chain of AC symbols. We also introduce some unary symbols comparable with AC symbols.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Leo Bachmair. Proof Methods for Equational Theories. PhD thesis, University of Illinois at Urbana-Champaign, 1987.
Leo Bachmair. Associative-commutative reduction orderings. Info Proc. Letters, 1992.
Leo Bachmair and Nachum Dershowitz. Commutation, transformation, and termination. In Jorg H. Siekmann, editor, Proc. 8th Int. Conf. on Automated Deduction, Oxford, England, LNCS 230, pages 5–20, July 1986.
Leo Bachmair and Nachum Dershowitz. Completion for rewriting modulo a congruence. In Pierre Lescanne, editor, Proceedings of the Second International Conference on Rewriting Techniques and Applications, pages 192–203, Bordeaux, France, May 1987. Vol. 256 of Lecture Notes in Computer Science, Springer, Berlin.
Leo Bachmair and David A. Plaisted. Termination orderings for associative-commutative rewriting systems. Journal of Symbolic Computation, 1(4):329–349, December 1985.
Ahlem Ben Cherifa and Pierre Lescanne. Termination of rewriting systems by polynomial interpretations and its implementation. Research Report 677, INRIA, June 1987.
Hubert Comon and Catherine Delor. Equational formulas with membership constraints. Technical report, Laboratoire de Recherche en informatique, March 1991. To appear in Information and Computation.
Paliath Narendran and Michaël Rusinowitch. Any ground associative-commutative theory has a finite canonical system. In Ronald V. Book, editor, Proc. 4th Rewriting Techniques and Applications, Como, LNCS 488. Springer-Verlag, April 1991.
Joachim Steinbach. AC-termination of rewrite systems: a modified Knuth-Bendix ordering. In H. Kirchner and W. Wechler, editors, Proc. 2nd Int. Conf. on Algebraic and Logic Programming, LNCS 463, pages 372–386, October 1990.
Joachim Steinbach. Improving associative path orderings. In Proc. 10th Int. Conf. on Automated Deduction, Kaiserslautern, LNCS 449. Springer-Verlag, July 1990.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Delor, C., Puel, L. (1993). Extension of the associative path ordering to a chain of associative commutative symbols. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_29
Download citation
DOI: https://doi.org/10.1007/978-3-662-21551-7_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56868-1
Online ISBN: 978-3-662-21551-7
eBook Packages: Springer Book Archive