Certification of Nontermination Proofs Using Strategies and Nonlooping Derivations

  • Julian Nagele
  • René Thiemann
  • Sarah Winkler
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8471)


The development of sophisticated termination criteria for term rewrite systems has led to powerful and complex tools that produce (non)termination proofs automatically. While many techniques to establish termination have already been formalized—thereby allowing to certify such proofs—this is not the case for nontermination. In particular, the proof checker Open image in new window  was so far limited to (innermost) loops. In this paper we present an Isabelle/HOL formalization of an extended repertoire of nontermination techniques. First, we formalized techniques for nonlooping nontermination. Second, the available strategies include (an extended version of) forbidden patterns, which cover in particular outermost and context-sensitive rewriting. Finally, a mechanism to support partial nontermination proofs further extends the applicability of our proof checker.


Inference Rule Recursive Call Critical Pair Proof Assistant Identity Problem 
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The authors are listed in alphabetical order regardless of individual contributions or seniority.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institute of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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