Lazy abstraction for size-change termination

Michael Codish, Carsten Fuhs, Jürgen Giesl, Peter Schneider-Kamp

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations


Size-change termination is a widely used means of proving termination where source programs are first abstracted to size-change graphs which are then analyzed to determine if they satisfy the size-change termination property. Here, the choice of the abstraction is crucial to the success of the method, and it is an open problem how to choose an abstraction such that no critical loss of precision occurs. This paper shows how to couple the search for a suitable abstraction and the test for size-change termination via an encoding to a single SAT instance. In this way, the problem of choosing the right abstraction is solved en passant by a SAT solver. We show that for the setting of term rewriting, the integration of this approach into the dependency pair framework works smoothly and gives rise to a new class of size-change reduction pairs. We implemented size-change reduction pairs in the termination prover AProVE and evaluated their usefulness in extensive experiments.

Original languageEnglish GB
Title of host publicationLogic for Programming, Artificial Intelligence, and Reasoning - 17th International Conference, LPAR-17, Proceedings
EditorsChristian G. Fermuller
PublisherSpringer Verlag
Number of pages16
ISBN (Print)364216241X, 9783642162411
StatePublished - 1 Jan 2010
Event17th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-17 - Yogyakarta, Indonesia
Duration: 10 Oct 201015 Oct 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6397 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference17th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR-17

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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