The Unification Problem for Confluent Right-Ground Term Rewriting Systems

  • Michio Oyamaguchi
  • Yoshikatsu Ohta
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2051)


The unification problem for term rewriting systems(TRSs) is the problem of deciding, for a given TRS R and two terms M and N, whether there exists a substitution θ such that and are congruent modulo R (i.e., \( M\theta \leftrightarrow *_R N\theta \) ). In this paper, the unification problem for con uent right-ground TRSs is shown to be decidable. To show this, the notion of minimal terms is introduced and a new unification algorithm of obtaining a substitution whose range is in minimal terms is proposed. Our result extends the decidability of unification for canonical (i.e., confluent and terminating) right-ground TRSs given by Hullot (1980) in the sense that the termination condition can be omitted. It is also exemplified that Hullot’s narrowing technique does not work in this case. Our result is compared with the undecidability of the word (and also unification) problem for terminating right-ground TRSs.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michio Oyamaguchi
    • 1
  • Yoshikatsu Ohta
    • 1
  1. 1.Faculty of EngineeringMie UniversityTsu-shiJapan

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