Decidability of Termination for Semi-constructor TRSs, Left-Linear Shallow TRSs and Related Systems

  • Yi Wang
  • Masahiko Sakai
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


We consider several classes of term rewriting systems and prove that termination is decidable for these classes. By showing the cycling property of infinite dependency chains, we prove that termination is decidable for semi-constructor case, which is a superclass of right-ground TRSs. By analyzing argument propagation cycles in the dependency graph, we show that termination is also decidable for left-linear shallow TRSs. Moreover we extend these by combining these two techniques.


Decision Procedure Dependency Graph Function Symbol Label Function Smoothness Condition 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yi Wang
    • 1
  • Masahiko Sakai
    • 1
  1. 1.Graduate School of Information ScienceNagoya UniversityFuro-cho, Chikusa-ku, NagoyaJapan

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