Local Termination

  • Jörg Endrullis
  • Roel de Vrijer
  • Johannes Waldmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5595)


The characterization of termination using well-founded monotone algebras has been a milestone on the way to automated termination techniques, of which we have seen an extensive development over the past years. Both the semantic characterization and most known termination methods are concerned with global termination, uniformly of all the terms of a term rewriting system (TRS). In this paper we consider local termination, of specific sets of terms within a given TRS.

The principal goal of this paper is generalizing the semantic characterization of global termination to local termination. This is made possible by admitting the well-founded monotone algebras to be partial. We show that our results can be applied in the development of techniques for proving local termination. We give several examples, among which a verifiable characterization of the terminating S-terms in CL.


Normal Form Turing Machine Partial Model Global Termination Local Termination 
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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jörg Endrullis
    • 1
  • Roel de Vrijer
    • 1
  • Johannes Waldmann
    • 2
  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Hochschule für Technik, Wirtschaft und Kultur (FH) LeipzigLeipzigGermany

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