Termination of Narrowing Using Dependency Pairs

  • María Alpuente
  • Santiago Escobar
  • José Iborra
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5366)


In this work, we extend the dependency pair approach for automated proofs of termination in order to prove the termination of narrowing. Our extension of the dependency pair approach generalizes the standard notion of dependency pairs by taking specifically into account the dependencies between the left-hand side of a rewrite rule and its own argument subterms. We demonstrate that the new narrowing dependency pairs exactly capture the narrowing termination behavior and provide an effective termination criterion which we prove to be sound and complete. Finally, we discuss how the problem of analyzing narrowing chains can be recast as a standard analysis problem for traditional (rewriting) chains, so that the proposed technique can be effectively mechanized by reusing the standard DP infrastructure.


Logic Program Logic Programming Dependency Graph Dependency Pair Reduction Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • María Alpuente
    • 1
  • Santiago Escobar
    • 1
  • José Iborra
    • 1
  1. 1.Technical University of Valencia (UPV)Spain

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