Testing for termination with monotonicity constraints

Michael Codish, Vitaly Lagoon, Peter J. Stuckey

Research output: Contribution to journalConference articlepeer-review

37 Scopus citations


Termination analysis is often performed over the abstract domains of monotonicity constraints or of size change graphs. First, the transition relation for a given program is approximated by a set of descriptions. Then, this set is closed under a composition operation. Finally, termination is determined if all of the idempotent loop descriptions in this closure have (possibly different) ranking functions. This approach is complete for size change graphs: An idempotent loop description has a ranking function if and only if it has one which indicates that some specific argument decreases in size. In this paper we generalize the size change criteria for size change graphs which are not idempotent. We also illustrate that proving termination with monotonicity constraints is more powerful than with size change graphs and demonstrate that the size change criteria is incomplete for monotonicity constraints. Finally, we provide a complete termination test for monotonicity constraints.

Original languageEnglish
Pages (from-to)326-340
Number of pages15
JournalLecture Notes in Computer Science
StatePublished - 1 Jan 2005
Event21st International Conference on Logic Programming, ICLP 2005 - Sitges, Spain
Duration: 2 Oct 20055 Oct 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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