Goal-Directed and Relative Dependency Pairs for Proving the Termination of Narrowing

  • José Iborra
  • Naoki Nishida
  • Germán Vidal
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6037)


In this work, we first consider a goal-oriented extension of the dependency pair framework for proving termination w.r.t. a given set of initial terms. Then, we introduce a new result for proving relative termination in terms of a dependency pair problem. Both contributions put together allow us to define a simple and powerful approach to analyzing the termination of narrowing, an extension of rewriting that replaces matching with unification in order to deal with logic variables. Our approach could also be useful in other contexts where considering termination w.r.t. a given set of terms is also natural (e.g., proving the termination of functional programs).


Logic Program Dependency Graph Initial Goal Usable Rule Extra Variable 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • José Iborra
    • 1
  • Naoki Nishida
    • 2
  • Germán Vidal
    • 1
  1. 1.DSICUniversidad Politécnica de ValenciaSpain
  2. 2.Graduate School of Information ScienceNagoya UniversityNagoyaJapan

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