Nagoya Termination Tool

Yamada, Akihisa; Kusakari, Keiichirou; Sakabe, Toshiki

doi:10.1007/978-3-319-08918-8_32

Cited by 28 publications

(20 citation statements)

References 28 publications

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“…We also apply partial status for KBO as in [26] but not for LPO, since LPO does not benefit from partial statuses because weights are not considered. The power of WPO is much more significant in this setting, and WPO(MSum) is about 30% stronger than any other existing techniques.…”

Section: Results For Reduction Pairsmentioning

confidence: 99%

“…We implemented a simple form of the DP framework as the Nagoya Termination Tool (NaTT) and incorporated WPO as a DP processor [48]. The encodings presented in Section 5 and optimizations presented in Section 6 are implemented.…”

Section: Methodsmentioning

confidence: 99%

“…In this paper, we fully revise this approach and directly define a reduction pair by incorporating partial statuses [26] into WPO. A partial status is a generalization of status that admits non-permutations.…”

Section: Wpo With Partial Statusmentioning

confidence: 99%

“…Next we extend WPO to a reduction pair by incorporating partial statuses [26]. This extension further relaxes the weak simplicity condition, and arbitrary weakly monotone interpretations can be used for weight computation.…”

Section: Introductionmentioning

confidence: 99%

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A unified ordering for termination proving

Yamada

Kusakari

Sakabe

2015

Science of Computer Programming

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We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of interpretations. We investigate summations, polynomials and maximums for such interpretations. We show that KBO is a restricted case of WPO induced by summations, the polynomial order (POLO) is subsumed by WPO induced by polynomials, and the lexicographic path order (LPO) is a restricted case of WPO induced by maximums. By combining these interpretations, we obtain an instance of WPO that unifies KBO, LPO and POLO. In order to fit WPO in the modern dependency pair framework, we further provide a reduction pair based on WPO and partial statuses. As a reduction pair, WPO also subsumes matrix interpretations. We finally present SMT encodings of our techniques, and demonstrate the significance of our work through experiments.

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Section: Results For Reduction Pairsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Wpo With Partial Statusmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A unified ordering for termination proving

Yamada

Kusakari

Sakabe

2015

Science of Computer Programming

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“…For term rewrite systems (TRSs), termination analysis has attracted considerable attention (see , 1 e.g., the survey of Zantema [31] and the termination portal 1 ), and various automated termination provers for TRSs have been developed, e.g. AProVE [9], T T T 2 [20], and NaTT [28]. Among them the dependency pair (DP) method [2,12] and its successor the DP framework [10] became a modern standard.…”

Section: Introductionmentioning

confidence: 99%

Reducing Relative Termination to Dependency Pair Problems

Iborra

Nishida

Vidal

et al. 2015

Automated Deduction - CADE-25

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Relative termination, a generalized notion of termination, has been used in a number of different contexts like proving the confluence of rewrite systems or analyzing the termination of narrowing. In this paper, we introduce a new technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. The practical significance of our method is illustrated by means of an experimental evaluation.

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Reachability Analysis for Termination and Confluence of Rewriting

Sternagel

Yamada

2019

Tools and Algorithms for the Construction and Analysis of Systems

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In term rewriting, reachability analysis is concerned with the problem of deciding whether or not one term is reachable from another by rewriting. Reachability analysis has several applications in termination and confluence analysis of rewrite systems. We give a unified view on reachability analysis for rewriting with and without conditions by means of what we call reachability constraints. Moreover, we provide several techniques that fit into this general framework and can be efficiently implemented. Our experiments show that these techniques increase the power of existing termination and confluence tools.

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Nagoya Termination Tool

Cited by 28 publications

References 28 publications

A unified ordering for termination proving

A unified ordering for termination proving

Reducing Relative Termination to Dependency Pair Problems

Reachability Analysis for Termination and Confluence of Rewriting

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