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C.: Loops under Strategies
 Proc. of the 20th International Conference on Rewriting Techniques and Applications, RTA’09. LNCS
, 2009
"... Abstract. Most techniques to automatically disprove termination of term rewrite systems search for a loop. Whereas a loop implies nontermination for full rewriting, this is not necessarily the case if one considers rewriting under strategies. Therefore, in this paper we first generalize the notion o ..."
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Abstract. Most techniques to automatically disprove termination of term rewrite systems search for a loop. Whereas a loop implies nontermination for full rewriting, this is not necessarily the case if one considers rewriting under strategies. Therefore, in this paper we first generalize the notion of a loop to a loop under a given strategy. In a second step we present two novel decision procedures to check whether a given loop is a contextsensitive or an outermost loop. We implemented and successfully evaluated our method in the termination prover T T T 2. 1
Certification of nontermination proofs
 In Proc. ITP 2012, volume 7406 of LNCS
, 2012
"... Abstract 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 t ..."
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Abstract 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.
Loops under Strategies... Continued
"... Termination is an important property of term rewrite systems (TRSs). Therefore, much effort has been spent on developing and automating techniques for showing termination of TRSs. But in order to detect bugs, it is at least as important to prove nontermination of TRSs. Note that for rewriting under ..."
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Termination is an important property of term rewrite systems (TRSs). Therefore, much effort has been spent on developing and automating techniques for showing termination of TRSs. But in order to detect bugs, it is at least as important to prove nontermination of TRSs. Note that for rewriting under strategies, one cannot ignore the strategy, since a nonterminating TRS may still be terminating due to the strategy.
DOI: 10.1007/9783540958918_48 · Source: DBLP
, 2009
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.