Beyond Dependency Graphs

Korp, Martin; Middeldorp, Aart

doi:10.1007/978-3-642-02959-2_26

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Theorem 3 (Usable Rule Processor1

Example 7 Consider the Cdp Problem Of Example 6 And Let N1

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2011

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Cited by 2 publications

(2 citation statements)

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“…e.g. [2,20,25]. In our example, these estimations would even yield the exact innermost dependency graph.…”

Section: Theorem 3 (Usable Rule Processormentioning

confidence: 99%

Proving Termination by Dependency Pairs and Inductive Theorem Proving

et al. 2011

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Current techniques and tools for automated termination analysis of term rewrite systems (TRSs) are already very powerful. However, they fail for algorithms whose termination is essentially due to an inductive argument. Therefore, we show how to couple the dependency pair method for termination of TRSs with inductive theorem proving. As confirmed by the implementation of our new approach in the tool AProVE, now TRS termination techniques are also successful on this important class of algorithms.

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“…e.g. [2,20,25]. In our example, these estimations would even yield the exact innermost dependency graph.…”

Section: Theorem 3 (Usable Rule Processormentioning

confidence: 99%

Proving Termination by Dependency Pairs and Inductive Theorem Proving

et al. 2011

View full text Add to dashboard Cite

show abstract

“…e.g. [10,9,15]). By the definition of the dependency graph, every DP-chain corresponds to a path in this graph and also every FP-CDP chain corresponds to a path in the DP graph and thus also in every (over-)approximation of this graph.…”

Section: Example 7 Consider the Cdp Problem Of Example 6 And Let Nmentioning

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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Beyond Dependency Graphs

Cited by 2 publications

References 14 publications

Proving Termination by Dependency Pairs and Inductive Theorem Proving

Proving Termination by Dependency Pairs and Inductive Theorem Proving

Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

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