Dependency Pairs Revisited

Hirokawa, Nao; Middeldorp, Aart

doi:10.1007/978-3-540-25979-4_18

Cited by 55 publications

(98 citation statements)

References 20 publications

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“…Analogously, for a TRS P, the usable symbols and rules are defined as US(P, R) = s→t∈P US(t, R) and U(P, R) = s→t∈P U(t, R). Further refinements to reduce the set of usable rules can be found in [8,12,21].…”

Section: A Dp Processor Based On Ordersmentioning

confidence: 99%

The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs

Giesl

Thiemann

Schneider–Kamp

2005

Logic for Programming, Artificial Intelligence, and Reasoning

115

201

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Abstract. The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be combined and their modularity and power are increased significantly. We refer to this new concept as the "dependency pair framework " to distinguish it from the old "dependency pair approach". Moreover, this framework facilitates the development of new methods for termination analysis. To demonstrate this, we present several new techniques within the dependency pair framework which simplify termination problems considerably. We implemented the dependency pair framework in our termination prover AProVE and evaluated it on large collections of examples.

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Section: A Dp Processor Based On Ordersmentioning

confidence: 99%

The Dependency Pair Framework: Combining Techniques for Automated Termination Proofs

Giesl

Thiemann

Schneider–Kamp

2005

Logic for Programming, Artificial Intelligence, and Reasoning

115

201

View full text Add to dashboard Cite

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“…In contrast to the discussion about the applications of the argument filtering method in [19], we need not individually discuss application to each reduction order, and we can comb out some applied conditions. To reduce the number of constraints when proving the non-loopingness by reduction pairs, the notion of usable rules was introduced in TRSs [11], [15], [29]. We extended the notion onto STRSs [26].…”

Section: Foldl[ F Y Nil] → Y Foldl[ F Y Cons[x Xs]] → Foldl[ F mentioning

confidence: 99%

“…We next introduce the subterm criterion [22] and the strictly subterm criterion, which are slight improvements of the criterion in [15]. Although the original definition of the codomain of π (see the following definition) in [15] allows only positive integers, the improved definition allows sequences of positive integers [22].…”

Section: Proposition 319mentioning

confidence: 99%

“…Although the original definition of the codomain of π (see the following definition) in [15] allows only positive integers, the improved definition allows sequences of positive integers [22]. • u| π(root(u)) > esub v| π(root(v)) for some u → v ∈ C, and • the following conditions hold for any u → v ∈ C:…”

Section: Proposition 319mentioning

confidence: 99%

“…The notion of usable rules was introduced in TRSs [11], [15], [29], which is based on the technique of interpretation and the notion of C e -termination [13], [30]. Afterward we extended the method to STRSs [26].…”

Section: Usable Rules With Argument Filteringmentioning

confidence: 99%

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Static Dependency Pair Method for Simply-Typed Term Rewriting and Related Techniques

Kusakari

Sakai

2009

IEICE Trans. Inf. & Syst.

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Keiichirou KUSAKARI†a) and Masahiko SAKAI †b) , Members SUMMARY A static dependency pair method, proposed by us, can effectively prove termination of simply-typed term rewriting systems (STRSs). The theoretical basis is given by the notion of strong computability. This method analyzes a static recursive structure based on definition dependency. By solving suitable constraints generated by the analysis result, we can prove the termination. Since this method is not applicable to every system, we proposed a class, namely, plain function-passing, as a restriction. In this paper, we first propose the class of safe function-passing, which relaxes the restriction by plain function-passing. To solve constraints, we often use the notion of reduction pairs, which is designed from a reduction order by the argument filtering method. Next, we improve the argument filtering method for STRSs. Our argument filtering method does not destroy type structure unlike the existing method for STRSs. Hence, our method can effectively apply reduction orders which make use of type information. To reduce constraints, the notion of usable rules is proposed. Finally, we enhance the effectiveness of reducing constraints by incorporating argument filtering into usable rules for STRSs.

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