When quoting this document, please refer to the following
DOI: 10.4230/DagSemProc.07401.3
URN: urn:nbn:de:0030-drops-12469
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Thiemann, René ; Giesl, Jürgen ; Schneider-Kamp, Peter

Decision Procedures for Loop Detection

07401.ThiemannRene.Paper.1246.pdf (0.3 MB)


The dependency pair technique is a powerful modular method for automated termination proofs of term rewrite systems. We first show that dependency pairs are also suitable for disproving termination: loops can be detected more easily.

In a second step we analyze how to disprove innermost termination. Here, we present a novel procedure to decide whether a given loop is an innermost loop.

All results have been implemented in the termination prover AProVE.

BibTeX - Entry

  author =	{Thiemann, Ren\'{e} and Giesl, J\"{u}rgen and Schneider-Kamp, Peter},
  title =	{{Decision Procedures for Loop Detection}},
  booktitle =	{Deduction and Decision Procedures},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2007},
  volume =	{7401},
  editor =	{Franz Baader and Byron Cook and J\"{u}rgen Giesl and Robert Nieuwenhuis},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-12469},
  doi =		{10.4230/DagSemProc.07401.3},
  annote =	{Keywords: Non-Termination, Decision Procedures, Term Rewriting, Dependency Pairs}

Keywords: Non-Termination, Decision Procedures, Term Rewriting, Dependency Pairs
Collection: 07401 - Deduction and Decision Procedures
Issue Date: 2007
Date of publication: 29.11.2007

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