Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

Details Termination of Rewriting with and Automated Synthesis of Forbidden Patterns Termination of Rewriting with and Automated Synthesis of Forbidden Patterns

2010-12-27

arxiv.org/abs/1012.5562v1

EPTCS 44, 2010, pp. 35-50

Computer Science

Logic in Computer Science

In Proceedings IWS 2010, arXiv:1012.5337

Scientific paper

10.4204/EPTCS.44.3

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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