Vademecum of Divergent Term Rewriting Systems

This paper presents two structural patterns to detect divergence of the completion procedure, followed by a detailed overview of diierent examples of divergent rewrite systems. Further it introduces ve different empirical methods to avoid divergence, applicable during a session with a rewrite rule laboratory.

[1]  Ursula Martin,et al.  How to Choose Weights in the Knuth Bendix Ordering , 1987, RTA.

[2]  Michaël Rusinowitch.  Path of Subterms Ordering and Recursive Decomposition Ordering Revisited , 1985, RTA.

[3]  Jean-Pierre Jouannaud,et al.  Automatic Proofs by Induction in Theories without Constructors , 1989, Inf. Comput..

[4]  Françoise Bellegarde,et al.  Transformation Ordering , 1987, TAPSOFT, Vol.1.

[5]  Hélène Kirchner,et al.  Completion of a Set of Rules Modulo a Set of Equations , 1986, SIAM J. Comput..

[6]  Jean-Marie Hullot,et al.  Canonical Forms and Unification , 1980, CADE.

[7]  Nachum Dershowitz,et al.  Completion for Rewriting Modulo a Congruence , 1987, Theor. Comput. Sci..

[8]  Deepak Kapur,et al.  On Proving Uniform Termination and Restricted Termination of Rewriting Systems , 1983, SIAM J. Comput..

[9]  J. Siekmann,et al.  A Noetherian and confluent rewrite system for idempotent semigroups , 1982 .

[10]  Nachum Dershowitz,et al.  Existence, Uniqueness, and Construction of Rewrite Systems , 1988, SIAM J. Comput..

[11]  Françoise Bellegarde,et al.  Rewriting Systems on FP Expressions to Reduce the Number of Sequences Yielded , 1986, Science of Computer Programming.

[12]  Nachum Dershowitz,et al.  Completion and Its Applications , 1989 .

[13]  Gérard P. Huet,et al.  Proofs by induction in equational theories with constructors , 1980, 21st Annual Symposium on Foundations of Computer Science (sfcs 1980).

[14]  Miki Hermann,et al.  On Nontermination of Knuth-Bendix Algorithm , 1986, ICALP.

[15]  Pierre Lescanne.  Divergence of the Knuth-Bendix Completion Procedure and Termination Orderings , 1986, Bull. EATCS.

[16]  D. Knuth,et al.  Simple Word Problems in Universal Algebras , 1983 .

[17]  Mark A Ardis.  Data Abstraction Transformations. , 1980 .

[18]  Pierre Lescanne,et al.  Computer experiments with the REVE term rewriting system generator , 1983, POPL '83.

[19]  Paliath Narendran,et al.  It is Undecidable Whether the Knuth-Bendix Completion Procedure Generates a Crossed Pair , 1989, STACS.

[20]  Pierre Lescanne,et al.  Termination of Rewriting Systems by Polynomial Interpretations and Its Implementation , 1987, Sci. Comput. Program..

[21]  N. A C H U M D E R S H O W I T Z.  Termination of Rewriting' , 2022 .

[22]  Ralf-Detlef Kutsche,et al.  Proving Inductive Theorems Based on Term Rewriting Systems , 1988, ALP.

[23]  James R. Slagle,et al.  Automated Theorem-Proving for Theories with Simplifiers Commutativity, and Associativity , 1974, JACM.

[24]  Gérard Huet,et al.  On the Uniform Halting Problem for Term Rewriting Systems , 1978 .

[25]  Laurent Fribourg,et al.  A Strong Restriction of the Inductive Completion Procedure , 1986, J. Symb. Comput..

[26]  Deepak Kapur,et al.  Proof by Consistency , 1987, Artif. Intell..

[27]  Leo Bachmair,et al.  Proof by consistency in equational theories , 1988, [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science.

[28]  Nachum Dershowitz,et al.  Orderings for Equational Proofs , 1986, LICS.

[29]  Gérard P. Huet,et al.  A Complete Proof of Correctness of the Knuth-Bendix Completion Algorithm , 1981, J. Comput. Syst. Sci..

[30]  Pierre Lescanne,et al.  Completion Procedures as Transition Rules + Control , 1989, TAPSOFT, Vol.1.

[31]  Nachum Dershowitz,et al.  Commutation, Transformation, and Termination , 1986, CADE.

[32]  Michaël Rusinowitch,et al.  On Word Problems in Equational Theories , 1987, ICALP.