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Mechanizing and Improving Dependency Pairs

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Abstract

The dependency pair technique is a powerful method for automated termination and innermost termination proofs of term rewrite systems (TRSs). For any TRS, it generates inequality constraints that have to be satisfied by well-founded orders. We improve the dependency pair technique by considerably reducing the number of constraints produced for (innermost) termination proofs. Moreover, we extend transformation techniques to manipulate dependency pairs that simplify (innermost) termination proofs significantly. To fully mechanize the approach, we show how transformations and the search for suitable orders can be mechanized efficiently. We implemented our results in the automated termination prover AProVE and evaluated them on large collections of examples.

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Authors and Affiliations

  1. LuFG Informatik 2, RWTH Aachen, Ahornstr. 55, 52074, Aachen, Germany

    Jürgen Giesl, René Thiemann & Peter Schneider-Kamp

  2. Computer Science Department, University of New Mexico, Albuquerque, NM, 87131, USA

    Stephan Falke

Authors
  1. Jürgen Giesl
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  2. René Thiemann
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  3. Peter Schneider-Kamp
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  4. Stephan Falke
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Correspondence to Jürgen Giesl.

Additional information

Supported by the Deutsche Forschungsgemeinschaft DFG, grant GI 274/5-1.

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Giesl, J., Thiemann, R., Schneider-Kamp, P. et al. Mechanizing and Improving Dependency Pairs. J Autom Reasoning 37, 155–203 (2006). https://doi.org/10.1007/s10817-006-9057-7

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