AProVE 1.2: Automatic Termination Proofs in the Dependency Pair Framework

Giesl, Jürgen; Schneider–Kamp, Peter; Thiemann, René

doi:10.1007/11814771_24

Cited by 191 publications

(253 citation statements)

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“…Here, T T T 2 uses only the techniques of this paper in the combination TC, whereas in TC + all supported techniques are tried, including usable rules and nontermination. We compare to CiME/Coccinelle using AProVE [10] or CiME [5] as provers (ACC,CCC), and to Rainbow/CoLoR using AProVE or Matchbox [18] (ARC,MRC) where we take the results of the latest certified termination competition in Nov 2008 7 involving 1391 TRSs from the termination problem database.…”

Section: Error Messagesmentioning

confidence: 99%

Certification of Termination Proofs Using CeTA

Thiemann

Sternagel

2009

Lecture Notes in Computer Science

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105

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Abstract. There are many automatic tools to prove termination of term rewrite systems, nowadays. Most of these tools use a combination of many complex termination criteria. Hence generated proofs may be of tremendous size, which makes it very tedious (if not impossible) for humans to check those proofs for correctness. In this paper we use the theorem prover Isabelle/HOL to automatically certify termination proofs. To this end, we first formalized the required theory of term rewriting including three major termination criteria: dependency pairs, dependency graphs, and reduction pairs. Second, for each of these techniques we developed an executable check which guarantees the correct application of that technique as it occurs in the generated proofs. Moreover, if a proof is not accepted, a readable error message is displayed. Finally, we used Isabelle's code generation facilities to generate a highly efficient and certified Haskell program, CeTA, which can be used to certify termination proofs without even having Isabelle installed.

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Section: Error Messagesmentioning

confidence: 99%

Certification of Termination Proofs Using CeTA

Thiemann

Sternagel

2009

Lecture Notes in Computer Science

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105

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“…We tested our algorithms within our certifier CeTA (version 2.3) in combination with the termination analyzer AProVE [18], which is (as far as we know) currently the only tool, that can prove innermost nontermination of term rewrite systems. Through our experiments, a major soundness bug in AProVE was revealed: one of the two loop-finding methods completely ignored the strategy.…”

Section: Discussionmentioning

confidence: 99%

Certification of Nontermination Proofs

Sternagel

Thiemann

2012

Interactive Theorem Proving

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Automatic tools for proving (non)termination of term rewrite systems, if successful, deliver proofs as justification. In this work, we focus on how to certify nontermination proofs. Besides some techniques that allow to reduce the number of rules, the main way of showing nontermination is to find a loop, a finite derivation of a special shape that implies nontermination. For standard termination, certifying loops is easy. However, it is not at all trivial to certify whether a given loop also implies innermost nontermination. To this end, a complex decision procedure has been developed in [1]. We formalized this decision procedure in Isabelle/HOL and were able to simplify some parts considerably. Furthermore, from our formalized proofs it is easy to obtain a low complexity bound. Along the way of presenting our formalization, we report on generally applicable ideas that allow to reduce the formalization effort and improve the efficiency of our certifier.

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“…For these latter rules, obtaining ℓ ≈ Pol r with a useful max-polynomial interpretation is impossible, since division and modulo are no max-polynomials. 15 …”

Section: Integer Dependency Pair Frameworkmentioning

confidence: 99%

“…Thus, in the example above the termination proof is trivial by using the interpretation with G Pol = x2 and cons Pol = x2 + 1. 15 In principle, one could also permit interpretations f Pol containing divisions. But existing implementations to search for interpretations cannot handle division or modulo.…”

Section: Now [N/m]mentioning

confidence: 99%