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Abstract: Reduction orderings that are compatible with an equational theory E and total on (the E-equivalence classes of) ground terms play an important role in automated deduction. We present a general approach for combining such orderings. To be more precise, we show how E 1 -compatible reduction orderings total on \Sigma 1 -ground terms and E 2 -compatible reduction orderings total on \Sigma 2 -ground terms can be used to construct an (E 1 [E 2 )-compatible reduction ordering total on (\Sigma 1 [... (Update)
Context of citations to this paper: More
.... theory in practice is AC (Bachmair and Plaisted 1985, Delor and Puel 1993, Rubio and Nieuwenhuis 1995, Kapur and Sivakumar 1997, Baader 1997). Additionally, presenting the theory by a term rewriting system modulo E (Bachmair, Ganzinger and Stuber 1995, March e 1996, Stuber...
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BibTeX entry: (Update)
Baader, F. (1997). Combination of compatible reduction orderings that are total on ground terms. In 12th Ann. IEEE Symp. on Logic in Computer Science, Warsaw, pp. 2--13. IEEE Computer Society Press. http://citeseer.ist.psu.edu/article/baader97combination.html More
@inproceedings{ baader96combination,
author = "F. Baader",
title = "Combination of Compatible Reduction Orderings that are Total on Ground Terms",
booktitle = "Proceedings of the 10th International Workshop on Unification, {UNIF-96}, {CIS}-Report 96-91",
publisher = "CIS, Universit{\"a}t M{\"u}nchen",
pages = "97--106",
year = "1996",
url = "citeseer.ist.psu.edu/article/baader97combination.html" }
Citations (may not include all citations):384 Simple word problems in universal algebras (context) - Knuth, Bendix - 1970
214 Orderings for term-rewriting systems (context) - Dershowitz - 1982 DBLP
151 Proving termination with multiset orderings (context) - Dershowitz, Manna - 1979 ACM DBLP
103 Complete sets of reductions for some equational theories (context) - Peterson, Stickel - 1981 ACM DBLP
82 Two generalizations of the recursive path ordering (context) - Kamin, Levy - 1980
72 Completion without failure - Bachmair, Dershowitz et al. - 1989
58 Canonical Equational Proofs (context) - Bachmair - 1991 ACM
55 Completion of a set of rules modulo a set of equations (context) - Jouannaud, Kirchner - 1986 ACM DBLP
41 A precedence-based total AC-compatible ordering (context) - Rubio, Nieuwenhuis - 1993 ACM DBLP
37 Combining symbolic constraint solvers on algebraic domains - Kirchner, Ringeissen - 1994 ACM DBLP
34 Any ground associative-commutative theory has a finite canon.. - Narendran, Rusinowitch - 1991 ACM DBLP
33 Extension of the associative path ordering to a chain of ass.. (context) - Delor, Puel - 1993 ACM DBLP
30 Combining matching algorithms: The regular case (context) - Nipkow - 1989 ACM DBLP
22 Combination of constraint solving techniques: An algebraic p.. - Baader, Schulz - 1995 DBLP
20 A total AC-compatible ordering based on RPO - Rubio, Nieuwenhuis - 1995 ACM DBLP
18 A new method for proving termination of AC-rewrite systems (context) - Kapur, Sivakumar et al. - 1990 ACM DBLP
13 Associative-commutative reduction orderings (context) - Bachmair - 1992 ACM DBLP
11 Automatic Theorem Proving Project (context) - Lankford, Memo - 1975
10 Automated Deduction with Constrained Clauses (context) - Rubio - 1994
7 An algorithm for finding canonical sets of ground rewrite ru.. (context) - Gallier, Narendran et al. - 1993 ACM DBLP
7 Associative path orderings (context) - Bachmair, Plaisted - 1986 ACM DBLP
3 On ground AC-completion (context) - Marche - 1991 ACM DBLP
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