An actual implementation of a procedure that mechanically proves termination of rewriting systems based on inequalities between polynomial interpretations

Cherifa, Ahlem Ben; Lescanne, Pierre

doi:10.1007/3-540-16780-3_78

Cited by 12 publications

(2 citation statements)

References 7 publications

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“…For general notions on orderings and termination, we refer to (Dershowitz, 1987). For definitions of AC-compatible orderings, see (Bachmair and Plaisted, 1985;Ben Cherifa and Lescanne, 1986;Narendran and Rusinowitch, 1991;Nieuwenhuis and Rubio, 1993;Delor and Puel, 1993).…”

Section: Termination Of Normalized Rewritingmentioning

confidence: 99%

Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

Marché

1996

Journal of Symbolic Computation

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In the first part of this paper, we introduce normalized rewriting, a new rewrite relation. It generalizes former notions of rewriting modulo a set of equations E, dropping some conditions on E. For example, E can now be the theory of identity, idempotence, the theory of Abelian groups or the theory of commutative rings. We give a new completion algorithm for normalized rewriting. It contains as an instance the usual AC completion algorithm, but also the well-known Buchberger algorithm for computing Gröbner bases of polynomial ideals.In the second part, we investigate the particular case of completion of ground equations. In this case we prove by a uniform method that completion modulo E terminates, for some interesting theories E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories, including the AC-ground case (a result known since 1991), the ACUI-ground case (a new result to our knowledge), and the cases of ground equations modulo the theory of Abelian groups and commutative rings, which is already known when the signature contains only constants, but is new otherwise.Finally, we give implementation results which show the efficiency of normalized completion with respect to completion modulo AC.

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Section: Termination Of Normalized Rewritingmentioning

confidence: 99%

Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

Marché

1996

Journal of Symbolic Computation

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“…The Termination Proof System CEC supports two concepts for proving the termination of rewrite systems, recursive path orderings in the version of Kapur, Narendran and Sivakumar [3] and polynomial interpretation with the techniques described by Ben Cherifa and Lescanne [4].…”

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CEC: A system for the completion of conditional equational specifications

Bertling¹,

Ganzinger²,

Schäfers³

1988

Esop '88

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The CEC-system has been developed to support various operational aspects of software specifications by conditional equations. It is part of the efforts in the PROSPECTRA-project to support the development of programs from specifications. CEC is implemented in Prolog and runs under CProlog 1.5 and Quintus-Prolog 1.6 and 2.0. The present system is a successor of a system that has been presented at STACS '87, Passau, and at the Workshop on Conditional Term Rewriting, Orsay 1987. The old version was based on a concept of completion relative to constraints as described in [1] whereas the new version is based on ideas investigated in [2]. The Specification LanguageA specification consists of a many-sorted signature and conditional equations. Operators may be specified as constructors, with the understanding that different constructor ground terms must not be identified in the equational theory. Linear notation of terms as in C-Prolog is possible. Additional parsing and pretty-printing functions can be provided by the user. The Termination Proof SystemCEC supports two concepts for proving the termination of rewrite systems, recursive path orderings in the version of Kapur, Narendran and Sivakumar [3] and polynomial interpretation with the techniques described by Ben Cherifa and Lescanne [4]. The Completion ProcedureThe main feature of CEC is a completion procedure for conditional equations. The theory behind the procedure is described in [2]. It can handle nonreductive conditional equations by a kind of narrowing technique in which nonreductive conditions are superposed by reductive rewrite rules.In order to make completion terminate on nontrivial examples, CEC has implemented two powerful techniques for simplifying critical pair peaks and superposition instances of nonreductive conditional equations. One technique we call rewriting in contexts, meaning that the equations of a condition are oriented into rules as far as possible, and these (skolemized) rules are used when reducing a conditional equation to normal form. The second technique uses the nonreductive equations for simplification of other equations by a forward chaining derivation. If the condition of a nonreductive equation is instance of a subset of the condition of an equation to be considered for simplification, the corresponding instance of the conclusion is added as a further condition to the equation to be simplified. This forward chaining is allowed as long as the complexity of the resulting equation does not exceed a bound that is defined during the creation of the equation to be simplified. Accompanied by a subsumption test and by rewriting in these enriched contexts, the procedure is therefore able to detect a quite large class of loops in the narrowing process.The completion can be run automatically or through manual guidance of the user. For that purpose, CEC makes the basic completion inference rules visible at the user level. The system automatically keeps t This work is partially supported by the ESPRIT-project PROSPECTRA, ref#390.

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Proving termination of associative commutative rewriting systems by rewriting

Gnaedig¹,

Lescanne²

1986

8th International Conference on Automated Deduction

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An actual implementation of a procedure that mechanically proves termination of rewriting systems based on inequalities between polynomial interpretations

Cited by 12 publications

References 7 publications

Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

CEC: A system for the completion of conditional equational specifications

Proving termination of associative commutative rewriting systems by rewriting

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