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102
SAT Solving for Termination Analysis with Polynomial Interpretations
, 2007
"... Polynomial interpretations are one of the most popular techniques for automated termination analysis and the search for such interpretations is a main bottleneck in most termination provers. We show that one can obtain speedups in orders of magnitude by encoding this task as a SAT problem and by a ..."
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Cited by 54 (22 self)
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Polynomial interpretations are one of the most popular techniques for automated termination analysis and the search for such interpretations is a main bottleneck in most termination provers. We show that one can obtain speedups in orders of magnitude by encoding this task as a SAT problem and by applying modern SAT solvers.
Automated termination analysis for logic programs with cut
, 2010
"... Termination is an important and wellstudied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas realworld Prolog programs typically use the cut operator. We introduce a novel preprocessing method which automatica ..."
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Cited by 32 (14 self)
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Termination is an important and wellstudied property for logic programs. However, almost all approaches for automated termination analysis focus on definite logic programs, whereas realworld Prolog programs typically use the cut operator. We introduce a novel preprocessing method which automatically transforms Prolog programs into logic programs without cuts, where termination of the cutfree program implies termination of the original program. Hence after this preprocessing, any technique for proving termination of definite logic programs can be applied. We implemented this preprocessing in our
TyroleanTermination Tool 2
 In Proc. of the Int. Conf. on Rewriting Techniques and Applications (RTA
, 2009
"... Abstract. This paper describes the second edition of the Tyrolean Termination Tool—a fully automatic termination analyzer for firstorder term rewrite systems. The main features of this tool are its (non)termination proving power, its speed, its flexibility due to a strategy language, and the fa ..."
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Cited by 29 (8 self)
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Abstract. This paper describes the second edition of the Tyrolean Termination Tool—a fully automatic termination analyzer for firstorder term rewrite systems. The main features of this tool are its (non)termination proving power, its speed, its flexibility due to a strategy language, and the fact that the source code of the whole project is freely available. The clean design together with a standalone OCaml library for term rewriting, make it a perfect starting point for other tools concerned with rewriting as well as experimental implementations of new termination methods. Key words: term rewriting, termination, automation 1
G.: Automated Complexity Analysis Based on the Dependency Pair Method
 IJCAR 2008. LNCS (LNAI
, 2008
"... Abstract. In this paper, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically. This method is easy to implement, but signi cantly extends the analytic power of existing direct methods. Our ndings extend the class of TRSs whose li ..."
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Cited by 26 (9 self)
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Abstract. In this paper, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically. This method is easy to implement, but signi cantly extends the analytic power of existing direct methods. Our ndings extend the class of TRSs whose linear or quadratic runtime complexity can be detected automatically. We provide ample numerical data for assessing the viability of the method. 1
Certification of automated termination proofs
 In Proc. FroCoS’07
, 2007
"... 2 CÉDRIC – Conservatoire national des arts et métiers Abstract. Nowadays, formal methods rely on tools of different kinds: proof assistants with which the user interacts to discover a proof step by step; and fully automated tools which make use of (intricate) decision procedures. But while some pro ..."
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Cited by 26 (6 self)
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2 CÉDRIC – Conservatoire national des arts et métiers Abstract. Nowadays, formal methods rely on tools of different kinds: proof assistants with which the user interacts to discover a proof step by step; and fully automated tools which make use of (intricate) decision procedures. But while some proof assistants can check the soundness of a proof, they lack automation. Regarding automated tools, one still has to be satisfied with their answers Yes/No/Donotknow, the validity of which can be subject to question, in particular because of the increasing size and complexity of these tools. In the context of rewriting techniques, we aim at bridging the gap between proof assistants that yield formal guarantees of reliability and highly automated tools one has to trust. We present an approach making use of both shallow and deep embeddings. We illustrate this approach with a prototype based on the CiME rewriting toolbox, which can discover involved termination proofs that can be certified by the COQ proof assistant, using the COCCINELLE library for rewriting. 1
CoLoR: a Coq library on wellfounded rewrite relations and its application to the automated verification of termination certificates
, 2010
"... ..."
Proving termination of integer term rewriting
 In Proc. RTA ’09, LNCS 5595
, 2009
"... Abstract. When using rewrite techniques for termination analysis of programs, a main problem are predefined data types like integers. We extend term rewriting by builtin integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically. 1 ..."
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Cited by 18 (11 self)
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Abstract. When using rewrite techniques for termination analysis of programs, a main problem are predefined data types like integers. We extend term rewriting by builtin integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically. 1
Proving Termination using Recursive Path Orders and SAT solving
 IN PROC. FROCOS ’07, LNAI 4720
, 2007
"... We introduce a propositional encoding of the recursive path order with status (RPO). RPO is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. Our encoding allows us to apply SAT solvers in order to d ..."
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Cited by 17 (8 self)
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We introduce a propositional encoding of the recursive path order with status (RPO). RPO is a combination of a multiset path order and a lexicographic path order which considers permutations of the arguments in the lexicographic comparison. Our encoding allows us to apply SAT solvers in order to determine whether a given term rewrite system is RPOterminating. Furthermore, to apply RPO within the dependency pair framework, we combined our novel encoding for RPO with an existing encoding for argument filters. We implemented our contributions in the termination prover AProVE. Our experiments show that due to our encoding, combining termination provers with SAT solvers improves the performance of RPOimplementations by orders of magnitude.
Better termination proving through cooperation
"... Abstract. One of the difficulties of proving program termination is managing the subtle interplay between the finding of a termination argument and the finding of the argument’s supporting invariant. In this paper we propose a new mechanism that facilitates better cooperation between these two types ..."
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Cited by 17 (5 self)
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Abstract. One of the difficulties of proving program termination is managing the subtle interplay between the finding of a termination argument and the finding of the argument’s supporting invariant. In this paper we propose a new mechanism that facilitates better cooperation between these two types of reasoning. In an experimental evaluation we find that our new method leads to dramatic performance improvements. 1
Proving Termination by Bounded Increase
, 2007
"... Most methods and tools for termination analysis of term rewrite systems (TRSs) essentially try to find arguments of functions that decrease in recursive calls. However, they fail if the reason for termination is that an argument is increased in recursive calls repeatedly until it reaches a bound. ..."
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Cited by 16 (8 self)
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Most methods and tools for termination analysis of term rewrite systems (TRSs) essentially try to find arguments of functions that decrease in recursive calls. However, they fail if the reason for termination is that an argument is increased in recursive calls repeatedly until it reaches a bound. In this paper, we solve that problem and present a method to prove innermost termination of TRSs with bounded increase automatically.