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References
A. Aiken, D. Kozen, and E. Wimmers. Decidability of systems of set constraints with negative constraints. Technical Report 93-1362, Computer Science Department, Cornell University, 1993.
A. Aiken and E. Wimmers. Solving systems of set constraints. In Proceedings of the Seventh Symposium on Logic in Computer Science, pages 329–340, Santa Cruz, CA, June 1992. IEEE.
F. Baader. Rewrite systems for varieties of semigroups. In M. Stickel, editor, Proceedings of the Tenth International Conference on Automated Deduction (Kaiserslautern, West Germany), volume 449 of Lecture Notes in Computer Science, pages 381–395, Berlin, July 1990. Springer-Verlag.
F. Baader and K. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. In D. Kapur, editor, Proceedings of the Eleventh International Conference on Automated Deduction (Saratoga Springs, NY), volume 607 of Lecture Notes in Artificial Intelligence, Berlin, June 1992. Springer-Verlag.
F. Baader and K. Schulz. Combination techniques and decision problems for disunification. In C. Kirchner, editor, Proceedings of the Fifth International Conference on Rewriting Techniques and Applications (Montreal, Canada), volume 690 of Lecture Notes in Computer Science, Berlin, 1993. Springer-Verlag.
L. Bachmair, H. Ganzinger, and U. Waldmann. Set constraints are the monadic class. In Proceedings of the Symposium on Logic in Computer Science (Montreal, Canada), pages 75–83. IEEE, 1993.
F. Barbanera. Combining term rewriting and type assignment systems. IJFCS, 1:165–184, 1990.
F. Barbanera and M. Fernández. Combining first and higher order rewrite systems with type assignment systems. In Proceedings of the International Conference on Typed Lambda Calculi and Applications, Utrecht, Holland, 1993.
F. Barbanera and M. Fernández. Modularity of termination and confluence in combinations of rewrite systems with λω. In Proceedings of the 20th International Colloquium on Automata, Languages, and Programming, 1993.
F. Barbanera, M. Fernández, and H. Geuvers. Modularity of strong normalization and confluence in the λ-algebraic-cube. In lics94, 1994.
H. P. Barendregt. Lambda calculi with types. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science. Oxford University Press, Oxford, 1991. To appear.
A. Boudet. Unification in order-sorted algebras with overloading. In D. Kapur, editor, Proceedings of the Eleventh International Conference on Automated Deduction (Saratoga Springs, NY), volume 607 of Lecture Notes in Artificial Intelligence, Berlin, June 1992. Springer-Verlag.
A. Boudet and H. Comon. About the theory of tree embedding. In J.-P. Jouannaud, editor, Proceedings of the Colloquium on Trees in Algebra and Programming (Orsay, France), Lecture Notes in Computer Science, Berlin, April 1993. Springer-Verlag.
A. Boudet and E. Contejean. “Syntactic” AC-unification. In J.-P. Jouannaud, editor, Proc. CCL, pages 136–151, Munich, September 1994. Springer-Verlag.
V. Breazu-Tannen and J. Gallier. Polymorphic rewriting conserves algebraic strong normalization. In Proceedings of the Sixteenth International Colloquium on Automata, Languages and Programming (Stresa, Italy), volume 372 of Lecture Notes in Computer Science, pages 137–150, Berlin, July 1989. European Association of Theoretical Computer Science, Springer-Verlag.
F. Bronsard. Using Term Orders to Control Deductions. PhD thesis, University of Illinois, 1995. Forthcoming.
F. Bronsard and U. S. Reddy. Conditional rewriting in Focus. In M. Okada, editor, Proceedings of the Second International Workshop on Conditional and Typed Rewriting Systems (Montreal, Canada), volume 516 of Lecture Notes in Computer Science, Berlin, 1991. Springer-Verlag.
F. Bronsard and U. S. Reddy. Reduction techniques for first-order reasoning. In M. Rusinowitch and J. L. Rémy, editors, Proceedings of the Third International Workshop on Conditional Rewriting Systems (Pont-a-Mousson, France, July 1992), volume 656 of Lecture Notes in Computer Science, pages 242–256. Springer-Verlag, Berlin, January 1993.
A.-C. Caron, J.-L. Coquidé, and M. Dauchet. Encompassment properties and automata with constraints. In C. Kirchner, editor, Proceedings of the Fifth International Conference on Rewriting Techniques and Applications (Montreal, Canada), volume 690 of Lecture Notes in Computer Science, Berlin, 1993. Springer-Verlag.
W. Charatonik and L. Pacholski. Negative set constraints with equality. In Proceedings of 9th IEEE Symposium on Logic in Computer Science, Paris, 1994. in press.
P. Chew. Unique normal forms in term rewriting systems with repeated variables. In Proceedings of the Thirteenth Annual Symposium on Theory of Computing, pages 7–18. ACM, 1981.
J. Christian. Problem corner: An experiment with Grau's ternary Boolean algebra. Submitted.
E. A. Cichon. Bounds on derivation lengths from termination proofs. Technical Report CSD-TR-622, Department of Computer Science, University of London, Surrey, England, June 1990.
D. Cohen and P. Watson. An efficient representation of arithmetic for term rewriting. In R. Book, editor, Proceedings of the Fourth International Conference on Rewriting Techniques and Applications (Como, Italy), volume 488 of Lecture Notes in Computer Science, pages 240–251, Berlin, April 1991. Springer-Verlag.
H. Comon. Solving inequations in term algebras (Preliminary version). In Proceedings of the Fifth Annual Symposium on Logic in Computer Science, pages 62–69, Philadelphia, PA, June 1990. IEEE.
H. Comon. Complete axiomatizations of some quotient term algebras. Theoretical Computer Science, 118(2), September 1993.
H. Comon and R. Treinen. The first-order theory of lexicographic path orderings is undecidable. Rapport de Recherche 867, Laboratoire de Recherche en Informatique, Universite de Paris-Sud, Orsay, France, November 1993.
E. Contejean. Eléments pour la Décidabilité de l'Unification modulo la Distributivité. PhD thesis, Univ. Paris-Sud, Orsay, France, April 1992.
E. Contejean. A partial solution for D-unification based on a reduction to ACl-unification. In Proceedings of the EATCS International Conference on Automata, Languages and Programming, pages 621–632, Lund, Sweden, July 1993. Springer-Verlag.
E. Contejean. Solving linear Diophantine constraints incrementally. In D. S. Warren, editor, Proc. of the Tenth Int. Conf. on Logic Programming, Logic Programming, pages 532–549, Budapest, Hungary, June 1993. MIT Press.
P.-L. Curien, T. Hardin, and J.-J. Lévy. Confluence properties of weak and strong calculi of explicit substitutions. RR 1617, Institut National de Rechereche en Informatique et en Automatique, Rocquencourt, February 1992.
M. Dauchet. Simulation of Turing machines by a regular rewrite rule. Theoretical Computer Science, 103(2):409–420, 1992.
M. Dauchet, T. Heuillard, P. Lescanne, and S. Tison. Decidability of the confluence of finite ground term rewriting systems and of other related term rewriting systems. Information and Computation, 88(2):187–201, October 1990.
M. Dauchet and S. Tison. The theory of ground rewrite systems is decidable. In Proceedings of the Fifth Symposium on Logic in Computer Science, pages 242–248, Philadelphia, PA, June 1990.
N. Dershowitz and J.-P. Jouannaud. Rewrite systems. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, volume B: Formal Methods and Semantics, chapter 6, pages 243–320. North-Holland, Amsterdam, 1990.
N. Dershowitz, J.-P. Jouannaud, and J. W. Klop. Open problems in rewriting. In R. Book, editor, Proceedings of the Fourth International Conference on Rewriting Techniques and Applications (Como, Italy), volume 488 of Lecture Notes in Computer Science, pages 445–456, Berlin, April 1991. Springer-Verlag.
N. Dershowitz, J.-P. Jouannaud, and J. W. Klop. More problems in rewriting. In C. Kirchner, editor, Proceedings of the Fifth International Conference on Rewriting Techniques and Applications (Montreal, Canada), volume 690 of Lecture Notes in Computer Science, pages 468–487, Berlin, June 1993. Springer-Verlag.
N. Dershowitz and M. Okada. A rationale for conditional equational programming. Theoretical Computer Science, 75:111–138, 1990.
D. Dougherty. Adding algebraic rewriting to the untyped lambda calculus (extended abstract). In R. Book, editor, Proceedings of the Fourth International Conference on Rewriting Techniques and Applications (Como, Italy), volume 488 of Lecture Notes in Computer Science, pages 37–48, Berlin, April 1991. Springer-Verlag.
M. Fernández. AC-complement problems: Validity and negation elimination. In C. Kirchner, editor, Proceedings of the Fifth International Conference on Rewriting Techniques and Applications (Montreal, Canada), volume 690 of Lecture Notes in Computer Science, Berlin, 1993. Springer-Verlag.
M. C. F. Ferreira and H. Zantema. Total termination of term rewriting. In C. Kirchner, editor, Proceedings of the Fifth Conference on Rewriting Techniques and Applications, volume 690 of Lecture Notes in Computer Science, pages 213–227. Springer, 1993.
R. Gilleron, S. Tison, and M. Tommasi. Solving systems of set constraints using tree automata. In Proceedings of the Symposium on Theoretical Aspects of Computer Science (Würzburg, Germany), Lecture Notes in Computer Science, Berlin, 1993. Springer-Verlag.
R. Gilleron, S. Tison, and M. Tommasi. Solving systems of set constraints with negated subset relationships. In Proc. 34th Symposium on Foundations of Computer Science, pages 372–380, Palo Alto, CA, November 1993. IEEE Computer Society Press.
N. Heintze and J. Jaffar. A decision procedure for a class of set constraints. In Proceedings of the Fifth Symposium on Logic in Computer Science (Philadelphia, PA), pages 42–51. IEEE, June 1990.
J. Hsiang and M. Rusinowitch. A new method for establishing refutational completeness in theorem proving. In J. H. Siekmann, editor, Proceedings of the Eighth International Conference on Automated Deduction (Oxford, England), volume 230 of Lecture Notes in Computer Science, pages 141–152, Berlin, July 1986. Springer-Verlag.
G. Huet. Confluent reductions: Abstract properties and applications to term rewriting systems. J. of the Association for Computing Machinery, 27(4):797–821, October 1980.
G. Huet. A complete proof of correctness of the Knuth-Bendix completion algorithm. J. Computer and System Sciences, 23(1):11–21, 1981.
G. Huet, editor. Logical Foundations of Functional Programming. University of Texas at Austin Year of Programming. Addison-Wesley, Reading, MA, 1990.
G. Huet and D. S. Lankford. On the uniform halting problem for term rewriting systems. Rapport laboria 283, Institut de Recherche en Informatique et en Automatique, Le Chesnay, France, March 1978.
G. Huet and J.-J. Lévy. Call by need computations in non-ambiguous linear term rewriting systems. Rapport Laboria 359, Institut National de Recherche en Informatique et en Automatique, Le Chesnay, France, August 1979.
G. Huet and J.-J. Lévy. Computations in orthogonal rewriting systems, I and II. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson, pages 395–443. MIT Press, Cambridge, MA, 1991. This is a revision of [50].
G. Huet and J.-J. Lévy. Computations in orthogonal rewriting systems, II. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson, chapter 12, pages 415–443. MIT Press, Cambridge, MA, 1991.
J.-P. Jouannaud and C. Kirchner. Solving equations in abstract algebras: A rule-based survey of unification. In J.-L. Lassez and G. Plotkin, editors, Computational Logic: Essays in Honor of Alan Robinson. MIT-Press, 1991.
J.-P. Jouannaud and H. Kirchner. Construction d'un plus petit ordre de simplification. RAIRO Theoretical Informatics, 18(3):191–207, 1984.
J.-P. Jouannaud and E. Kounalis. Automatic proofs by induction in equational theories without constructors. Information and Computation, 81(1):1–33, 1989.
J.-P. Jouannaud and M. Okada. Executable higher-order algebraic specification languages. In Proceedings of the Sixth Symposium on Logic in Computer Science, pages 350–361, Amsterdam, The Netherlands, 1991. IEEE.
J.-P. Jouannaud and M. Okada. Satisfiability of systems of ordinal notations with the subterm property is decidable. In J. L. Albert, B. Monien, and M. R. Artalejo, editors, Proceedings of the Eighteenth EATCS Colloquium on Automata, Languages and Programming (Madrid, Spain), volume 510 of Lecture Notes in Computer Science, pages 455–468, Berlin, July 1991. Springer-Verlag.
J.-P. Jouannaud and W. Sadfi. Strong sequentially of left-linear overlapping rewrite systems. In N. Dershowitz and N. Lindenstrauss, editors, Proceedings of the Fourth International Workshop on Conditional Rewriting Systems (Jerusalem, Israel, July 1994), Berlin, 1995. Springer-Verlag. To appear.
D. Kapur, P. Narendran, and H. Zhang. On sufficient completeness and related properties of term rewriting systems. Acta Informatica, 24(4):395–415, August 1987.
L. Kirby and J. Paris. Accessible independence results for Peano arithmetic. Bulletin London Mathematical Society, 14:285–293, 1982.
C. Kirchner. Computing unification algorithms. In Proceedings of the First Symposium on Logic in Computer Science, pages 206–216, Cambridge, Massachussets, June 1986. IEEE.
J. W. Klop. Combinatory Reduction Systems, volume 127 of Mathematical Centre Tracts. Mathematisch Centrum, Amsterdam, 1980.
G. Kucherov and M. Rusinowitch. On the ground reducibility problem for word rewriting systems with variables. Information Processing Letters, 1994. To appear. Earlier version appeared in the Proceedings of 1994 ACM/SIGAPP Symposium on Applied Computing, Phoenix, AZ.
P. Lescanne. On termination of one rule rewrite systems. Theoretical Computer Science, 132:395–401, 1994.
P. Lescanne and J. Rouyer-Degli. The calculus of explicit substitutions λν. Technical Report RR-2222, INRIA-Lorraine, January 1994.
L. Fribourg. A superposition oriented theorem prover. Theoretical Computer Science, 35:161, 1985.
D. Lugiez and J.-L. Moysset. Complement problems and tree automata in AC-like theories. In Proceedings of the Symposium on Theoretical Aspects of Computer Science (Würzburg, Germany), Lecture Notes in Computer Science, Berlin, 1993. Springer-Verlag.
K. Mano, September 1993. Personal communication.
K. Mano and M. Ogawa. A new proof of Chew's theorem. Technical report, IPSJ PRG94-19-7, 1994.
M. Marchiori. Modularity of UN→ for left-linear term rewriting systems. Technical report, CWI, Amsterdam, 1994.
A. Martelli and G. Rossi. Efficient unification with infinite terms in logic programming. In International conference on fifth generation computer systems, pages 202–209, 1984.
P.-A. Melliès. Typed λ-calculi with explicit substitutions may not terminate, 1995. To appear.
A. Middeldorp. Modular aspects of properties of term rewriting systems related to normal forms. In N. Dershowitz, editor, Proceedings of the Third International Conference on Rewriting Techniques and Applications (Chapel Hill, NC), volume 355 of Lecture Notes in Computer Science, pages 263–277, Berlin, April 1989. Springer-Verlag.
A. Middeldorp and B. Gramlich. Simple termination is difficult. Applicable Algebra in Engineering, Communication and Computing, 6(2):115–128, 1995.
D. Miller. A logic programming language with lambda-abstraction, function variables, and simple unification. In P. Schroeder-Heister, editor, Extensions of Logic Programming, volume 690 of Lecture Notes in Computer Science. Springer-Verlag, 1991.
M. Oyamaguchi. On the word problem for right-ground term-rewriting systems. In Trans. IEICE, volume E73-5, pages 718–723, 1990.
F. Müller. Confluence of the lambda calculus with left-linear algebraic rewriting. Information Processing Letters, 41:293–299, April 1992.
A. Nerode and Y. V. Matiyasevich, editors. Logical Foundations of Computer Science, Third International Symposium, LFCS'94, St. Petersburg, Russia, July 1994, Proceedings, volume 813 of Lecture Notes in Computer Science. Springer-Verlag, 1994.
R. Nieuwenhuis and F. Orejas. Clausal rewriting. In S. Kaplan and M. Okada, editors, Extended Abstracts of the Second International Workshop on Conditional and Typed Rewriting Systems, pages 81–88, Montreal, Canada, June 1990. Concordia University. Revised version to appear in Lecture Notes in Computer Science, Springer-Verlag, Berlin.
T. Nipkow. Higher-order critical pairs. In Proceedings of the Sixth Symposium on Logic in Computer Science, pages 342–349, Amsterdam, The Netherlands, 1991. IEEE.
M. Ogawa and S. Ono. On the uniquely converging property of nonlinear term rewriting systems. Technical report, IEICE COMP89-7, 1989.
E. Ohlebusch. On the modularity of confluence of constructor-sharing term rewriting systems. In Proceedings of the Colloquium on Trees in Algebra and Programming, 1994.
Y. Ohta, M. Oyamaguchi, and Y. Toyama. On the Church-Rosser property of simple-right-linear term rewriting systems. Trans. IEICE, to appear.
V. v. Oostrom. Confluence by decreasing diagrams. IR 298, Vrije Universiteit, Amsterdam, The Netherlands, August 1992. To appear in Theoretical Computer Science.
V. v. Oostrom. Confluence for Abstract and Higher-Order Rewriting. PhD thesis, Vrije Universiteit, Amsterdam, March 1994.
V. v. Oostrom and F. v. Raamsdonk. Weak orthogonality implies confluence: the higher-order case. In [78, pp. 379–392], 1994.
M. Oyamaguchi. The Church-Rosser property for ground term rewriting systems is decidable. Theoretical Computer Science, 49(1):43–79, 1987.
M. Oyamaguchi and Y. Ohta. On the confluent property of right-ground term rewriting systems. Trans. IEICE, J76-D-I:39–45, 1993.
Z. Quian and K. Wang. Modular ac-unification of higher-order patterns. In J.-P. Jouannaud, editor, CCL94, pages 105–120, Munich, September 1994. Springer-Verlag.
C. Ringeissen. Unification in a combination of equational theories with shared constants and its application to primal algebras. In A. Voronkov, editor, Proceedings of the Conference on Logic Programming and Automated Reasoning (St. Petersburg, Russia), volume 624 of Lecture Notes in Artificial Intelligence, Berlin, July 1992. Springer-Verlag.
C. Ringeissen. Combinaison de résolutions de contraintes. Master's thesis, Nancy, December 1993. Thèse.
A. Rubio. Automated deduction with constrained clauses. PhD thesis, Univ. de Catalunya, 1994.
A. Sattler-Klein. About changing the ordering during Knuth-Bendix completion. In Proceedings of the Symposium on Theoretical Aspects of Computer Science, pages 175–186, 1994.
M. Schmidt-Shauß. An algorithm for distributive unification. Research report 13/94, Fachbereich Informatik, Universität Franckfurt, Germany, December 1994.
M. Schmidt-Shauß. Unification of stratified second-order terms. Research report 12/94, Fachbereich Informatik, Universität Franckfurt, Germany, December 1994.
M. Takahashi. λ-calculi with conditional rules. In M. Bezem and J. F. Groote, editors, Proceedings of the International Conference on Typed Lambda Calculi and Applications (Utrecht, The Netherlands), volume 664 of Lecture Notes in Computer Science, pages 406–417, Berlin, 1993. Springer-Verlag.
E. Tiden and S. Arnborg. Unification problems with one-sided distributivity. J. Symbolic Computation, 3:183–202, 1987.
Y. Toyama. Strong sequentiality of left linear overlapping term rewriting systems. In Proc. 7th IEEE Symp. on Logic in Computer Science, Santa Cruz, CA, 1992.
Y. Toyama and M. Oyamaguchi. Church-Rosser property and unique normal form property of non-duplicating term rewriting systems. In N. Dershowitz and N. Lindenstrauss, editors, Workshop on Conditional Term Rewriting Systems (Jerusalem, July 1994), Lecture Notes in Computer Science. Springer-Verlag, to appear.
R. Treinen. A new method for undecidability proofs of first order theories. In K. V. Nori and C. E. V. Madhavan, editors, Proceedings of the Tenth Conference on Foundations of Software Technology and Theoretical Computer Science, volume 472 of Lecture Notes in Computer Science, pages 48–62. Springer-Verlag, 1990.
R. Treinen. A new method for undecidability proofs of first order theories. J. Symbolic Computation, 14(5):437–458, November 1992.
K. N. Venkataraman. Decidability of the purely existential fragment of the theory of term algebras. J. of the Association for Computing Machinery, 34(2):492–510, 1987.
H. R. Walters and H. Zantema. Rewrite systems for integer arithmetic. In J. Hsiang, editor, Proceedings of the 6th Conference on Rewriting Techniques and Applications (this proceedings), Lecture Notes in Computer Science. Springer, 1995.
A. Weiermann. Bounding derivation lengths with functions from the slow growing hierarchy. Preprint Münster, 1993.
J. B. Wells. Typability and type checking in the second-order λ-calculus are equivalent and undecidable. In Proceedings of 9th IEEE Symposium on Logic in Computer Science, Paris, 1994.
B. Werner. Méta-théorie du Calcul des Constructions Inductives. Thèse Univ. Paris VII, France, 1994.
L. Wos. Automated reasoning: 33 basic research problems.
H. Zantema. Termination of term rewriting: interpretation and type elimination. Journal of Symbolic Computation, 17:23–50, 1994.
H. Zantema. Total termination of term rewriting is undecidable. Technical Report UU-CS-1994-55, Utrecht University, December 1994.
J. Zhang. A 3-place commutative operator from TBA. AAR Newsletters, to appear.
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Dershowitz, N., Jouannaud, JP., Klop, J.W. (1995). Problems in rewriting III. 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_82
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