Abstract
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 
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.
This research was supported by the Austrian Science Fund (FWF): P22767 and I963.
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Notes
- 1.
In the literature (e.g., in [7]) a nonterminating DP problem is also called infinite. This is the reason why in
this property is defined as infinite-dpp. - 2.
More precisely, \(n_0\) can be set to \(0\) if \(p=\varepsilon \) and to
otherwise.
- 3.
Rules (i)–(iv) in [22, Definition 5], which are omitted here for brevity.
this property is defined as infinite-dpp.
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Nagele, J., Thiemann, R., Winkler, S. (2014). Certification of Nontermination Proofs Using Strategies and Nonlooping Derivations. In: Giannakopoulou, D., Kroening, D. (eds) Verified Software: Theories, Tools and Experiments. VSTTE 2014. Lecture Notes in Computer Science(), vol 8471. Springer, Cham. https://doi.org/10.1007/978-3-319-12154-3_14
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