VMTL–A Modular Termination Laboratory

Schernhammer, Felix; Gramlich, Bernhard

doi:10.1007/978-3-642-02348-4_20

Cited by 15 publications

(11 citation statements)

References 13 publications

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“…Available tools for proving operational termination of conditional rewriting (AProVE [10] or VMTL [16]) rely on transformations U that map each operational termination problem for the CTRS R into a termination problem for a…”

Section: Introductionmentioning

confidence: 99%

2D Dependency Pairs for Proving Operational Termination of CTRSs

Lucas

Meseguer

2014

Rewriting Logic and Its Applications

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Abstract. The notion of operational termination captures nonterminating computations due to subsidiary processes that are necessary to issue a single 'main' step but which often remain 'hidden' when the main computation sequence is observed. This highlights two dimensions of nontermination: one for the infinite sequencing of computation steps, and the other that concerns the proof of some single steps. For conditional term rewriting systems (CTRSs), we introduce a new dependency pair framework which exploits the bidimensional nature of conditional rewriting (rewriting steps + satisfaction of the conditions as reachability problems) to obtain a powerful and more expressive framework for proving operational termination of CTRSs.

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Section: Introductionmentioning

confidence: 99%

2D Dependency Pairs for Proving Operational Termination of CTRSs

Lucas

Meseguer

2014

Rewriting Logic and Its Applications

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“…which is obtained from R by removing the conditional part of the rules (see [6, page 324] and [36,Definition 7.1.2], for instance), is terminating. However, R is not operationally terminating: we have an infinite proof tree for the inference system for CTRSs in Figure 1 (substitutions provide the necessary match of rules against the different goals; the labels indicating the applied rules have been conveniently shortened): Available tools for proving operational termination of CTRSs R (e.g., AProVE [18] or VMTL [38]) rely on transformations U that prove operational termination of R as termination of the TRS U(R). However, this transformational approach has substantial limitations.…”

Section: Termination V -Termination and Operational Termination Of Ctrssmentioning

confidence: 99%

Dependency pairs for proving termination properties of conditional term rewriting systems

Lucas

Meseguer

2017

Journal of Logical and Algebraic Methods in Programming

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The notion of operational termination provides a logic-based definition of termination of computational systems as the absence of infinite inferences in the computational logic describing the operational semantics of the system. For Conditional Term Rewriting Systems we show that operational termination is characterized as the conjunction of two termination properties. One of them is traditionally called termination and corresponds to the absence of infinite sequences of rewriting steps (a horizontal dimension). The other property, that we call V -termination, concerns the absence of infinitely many attempts to launch the subsidiary processes that are required to perform a single rewriting step (a vertical dimension). We introduce appropriate notions of dependency pairs to characterize termination, V -termination, and operational termination of Conditional Term Rewriting Systems. This can be used to obtain a powerful and more expressive framework for proving termination properties of Conditional Term Rewriting Systems.

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“…We implemented the CDP framework and the context processors in the termination tool VMTL (cf. [19]). In order to evaluate the practical power of this approach we tested this implementation on the TRSs of the outermost category of the TPDB 2 .…”

Section: Implementation and Evaluationmentioning

confidence: 99%

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

Gramlich

Schernhammer

2010

Electron. Proc. Theor. Comput. Sci.

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We introduce a modified version of the well-known dependency pair framework that is suitable for the termination analysis of rewriting under forbidden pattern restrictions. By attaching contexts to dependency pairs that represent the calling contexts of the corresponding recursive function calls, it is possible to incorporate the forbidden pattern restrictions in the (adapted) notion of dependency pair chains, thus yielding a sound and complete approach to termination analysis. Building upon this contextual dependency pair framework we introduce a dependency pair processor that simplifies problems by analyzing the contextual information of the dependency pairs. Moreover, we show how this processor can be used to synthesize forbidden patterns suitable for a given term rewriting system on-the-fly during the termination analysis.

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VMTL–A Modular Termination Laboratory

Cited by 15 publications

References 13 publications

2D Dependency Pairs for Proving Operational Termination of CTRSs

2D Dependency Pairs for Proving Operational Termination of CTRSs

Dependency pairs for proving termination properties of conditional term rewriting systems

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

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