Termination of linear bounded term rewriting systems

Authors Irène Durand, Géraud Sénizergues, Marc Sylvestre

Thumbnail PDF


  • Filesize: 197 kB
  • 16 pages

Document Identifiers

Author Details

Irène Durand
Géraud Sénizergues
Marc Sylvestre

Cite AsGet BibTex

Irène Durand, Géraud Sénizergues, and Marc Sylvestre. Termination of linear bounded term rewriting systems. In Proceedings of the 21st International Conference on Rewriting Techniques and Applications. Leibniz International Proceedings in Informatics (LIPIcs), Volume 6, pp. 341-356, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting. We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse k-bounded problems are decidable. The k-bounded class (BO(k)) is, by definition, the set of linear systems for which every derivation can be replaced by a k-bounded derivation. In general, for BO(k) systems, the uniform (respectively inverse uniform) k-bounded termination problem is not equivalent to the uniform (resp. inverse uniform) termination problem, and the k-bounded (respectively inverse k-bounded) termination problem is not equivalent to the termination (respectively inverse termination) problem. This leads us to define more restricted classes for which these problems are equivalent: the classes BOLP(k) of k-bounded systems that have the length preservation property. By definition, a system is BOLP(k) if every derivation of length n can be replaced by a k-bounded derivation of length n. We define the class BOLP of bounded systems that have the length preservation property as the union of all the BOLP(k) classes. The class BOLP contains (strictly) several already known classes of systems: the inverse left-basic semi-Thue systems, the linear growing term rewriting systems, the inverse Linear-Finite-Path-Ordering systems, the strongly bottom-up systems.
  • Term rewriting
  • termination
  • rewriting strategy


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail