Order-sorted termination: The unsorted way

  • Peter Csaba Ölveczky
  • Olav Lysne
Term Rewriting
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1139)


We consider the problem of proving termination of order-sorted rewrite systems. The dominating method for proving termination of order-sorted systems has been to simply ignore sort information, and use the techniques developed for unsorted rewriting. The problem with this approach is that many order-sorted rewrite systems terminate because of the structure of the set of sorts. In these cases the corresponding unsorted system would not terminate.

In this paper we approach the problem of order-sorted termination by mapping the order-sorted rewrite system into an unsorted one such that termination of the latter implies termination of the former. By encoding sort information into the unsorted mapping, we are able to use general purpose termination orderings to prove termination of order-sorted rewrite systems whose termination depend on the sort hierarchy. We present a sequence of gradually stronger methods, and show that a previously published method is contained in ours as a special case.


Order-sortedness Termination 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Peter Csaba Ölveczky
    • 1
  • Olav Lysne
    • 2
  1. 1.Department of InformaticsUniversity of Bergen, The High Technology CenterBergenNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

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