Abstract
Various methods for proving the termination of term rewriting systems have been suggested. Most of them are based on the notion of a simplification ordering. In this paper, a collection of well-known simplification orderings will be briefly presented including path orderings and decomposition orderings. A satisfactory application to examples often found in practice is an essential requirement concerning such orderings. We describe a detailed empirical study of their time complexities with respect to comparable pairs of terms.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Avenhaus, Jürgen, Madlener, Klaus E., and Steinbach, Joachim, ‘COMTES — An experimental environment for the completion of term rewriting systems’, in N. Dershowitz (Ed.),Proc. 3rd RTA (LNCS 355), pp. 542–546. Chapel Hill (North Carolina), April 1989.
Dershowitz, Nachum, ‘Orderings for term rewriting systems’,J. TCS,17(3), 279–301 (March 1982).
Dershowitz, Nachum, ‘Termination of rewriting’,JSC,3, 69–116 (1987).
Huet, Gérard and Oppen, Derek, C., ‘Equations and rewrite rules: A survey’, in R. Book (Ed.),Formal Languages — Perspectives and Open Problems, pp. 349–405. Academic Press, 1980.
Jouannaud, Jean-Pierre, Lescanne, Pierre and Reinig, Fernand, ‘Recursive decomposition ordering’, in D. Bjørner (Ed.),Working Conference on Formal Description of Programming Concepts II (IFIP), pp. 331–348, Garmisch-Partenkirchen (Germany), 1982.
Kamin, Sam and Lévy, Jean-Jacques, ‘Attempts for generalizing the recursive path orderings’, Urbana (Illinois), February 1980.
Kapur, Deepak, Narendran, Paliath and Sivakumar, G., ‘A path ordering for proving termination of term rewriting systems’, InProc. 10th CAAP (LNCS 185), pp. 173–187, Berlin (Germany), March 1985.
Knuth, Donald E. and Bendix, Peter B., ‘Simple word problems in universal algebras’, in J. Leech (Ed.),Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, 1970.
Krishnamoorthy, M. S. and Narendran, Paliath, ‘Note on recursive path ordering’,J. TCS,40, 323–328 (1985).
Lescanne, Pierre, ‘On the recursive decomposition ordering with lexicographical status and other related orderings’,JAR,6, 39–49 (1990).
Plaisted, David Alan, ‘A recursively defined ordering for proving the termination of term rewriting systems’, internal report UIUCDCS-R-87-943, University of Illinois at Urbana-Champaign, Urbana (Illinois), September 1978.
Rusinowitch, Michaël, ‘Path of subterms ordering and recursive decomposition ordering revisited,JSC,3, 117–131 (1987).
Steinbach, Joachim, ‘Extensions and comparison of simplification orderings’, in N. Dershowitz (Ed.),Proc. 3rd RTA (LNCS 355), pp. 434–448, Chapel Hill (North Carolina), April 1989.
Steinbach, Joachim, ‘On the complexity of simplification orderings’,SEKI-Report, University of Kaiserslautern, Kaiserslautern (Germany), 1993.
Author information
Authors and Affiliations
Additional information
This research was supported by the Deutsche Forschungsgemeinschaft, SFB 314 (D4-Projekt).
Rights and permissions
About this article
Cite this article
Steinbach, J. Simplification orderings: Putting them to the test. J Autom Reasoning 10, 389–397 (1993). https://doi.org/10.1007/BF00881798
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00881798