J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.  Home/Search   Document Not in Database   Summary   Related Articles   Check

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. J. Symbolic Computation, 34(1):21--58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

....principle with dependency pairs. In contrast to other recent techniques [4, 6] dependency pairs and size change graphs are both built from recursive calls which suggests to combine these approaches to benefit from their respective advantages. We recapitulate the concepts of dependency pairs; see [1, 7, 8] for refinements and motivations. Let f # D be a set of tuple symbols, where f has the same arity as f and we often write F for f , etc. If t = g(t 1 , t m ) with g we write t for g (t 1 , t m ) If l and t is a subterm of r with defined root, then ....

J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

....Jurgen Giesl, Rene Thiemann, Peter Schneider Kamp, Stephan Falke LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany giesl thiemann informatik.rwth aachen.de nowonder spf i2.informatik.rwth aachen.de Abstract. The dependency pair approach [2, 11, 12] is one of the most powerful techniques for termination and innermost termination proofs of term rewrite systems (TRSs) For any TRS, it generates inequality constraints that have to be satisfied by weakly monotonic well founded orders. We improve the dependency pair approach by considerably ....

....lexicographic or recursive path orders [7, 17] the Knuth Bendix order [18] and (most) polynomial orders [20] However, there are numerous important TRSs which are not simply terminating, i.e. their termination cannot be shown by simplification orders. Therefore, the dependency pair approach [2, 11, 12] was developed which allows the application of simplification orders to non simply terminating TRSs. In this way, the class of systems where termination is provable mechanically increases significantly. Example 1 The following TRS from [2] is not simply terminating, since in the last quot rule, ....

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

....Practically all known methods that are amenable to automation use simplifica tion orderings [Der79,Der87,Ste95b,MZ97] However, there exist numerous term rewrite systems for which termination cannot be proved by this kind of orderings. For that reason, Arts and Giesl [AG97a,AG97b,AG98,AG00,GA01,GAO01] developed the so called dependency pair approach. Given a TRS, the dependency pair technique automatically gen erates a set of constraints and the existence of a well founded (quasi )ordering satisfying these constraints is sufficient for termination. The advantage is that standard (automatic) ....

....to be familiar with the basic notions of term rewriting [DJ90,Klo92,BN98] In Section 2.1 we illustrate how dependency pairs are used for automatic termination proofs and in Section 2.2 we explain their use for innermost termination proofs. For motivations and further refinements see [AG00,GA01,GAO01] We adopt the notation of [GM00] and [KNT99] The root of a term f( is the leading function symbol f. For a TRS 7 over a signature Y, Z) root( l r C 7 is the set of the defined symbols and = Y Z) is the set of constructors of 7. Let Y denote the union of the signature Y and f [ f ....

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Submitted to the Journal of Symbolic Computation, 2001.

....reduction pair. 5 Comparison and Combination with Dependency Pairs Now we compare the size change principle with dependency pairs and show how to combine these approaches in order to bene t from their respective advantages. We brie y recapitulate the concepts of dependency pairs and refer to [1, 6, 7] for re nements and motivations. Let F = ff j f 2 Dg be a set of tuple symbols, where f has the same arity as f and we often write F for f , etc. If t = g(t 1 ; t m ) with g 2 D, we write t for g (t 1 ; t m ) If l r 2 R and t is a subterm of r with de ned ....

J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21-58, 2002.

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J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21-58, 2002.

....see e.g. Der87,Ste95b] Practically all known methods that are amenable to automation use simpli cation orderings [Der79,Der87,Ste95b,MZ97] However, there exist numerous term rewrite systems for which termination cannot be proved by this kind of orderings. For that reason, Arts and Giesl [AG97a,AG97b,AG98,AG00,GA01,GAO01] developed the so called dependency pair approach. Given a TRS, the dependency pair technique automatically generates a set of constraints and the existence of a well founded (quasi )ordering satisfying these constraints is sucient for termination. The advantage is that standard (automatic) ....

....the reader to be familiar with the basic notions of term rewriting [DJ90,Klo92,BN98] In Section 2.1 we illustrate how dependency pairs are used for automatic termination proofs and in Section 2.2 we explain their use for innermost termination proofs. For motivations and further re nements see [AG00,GA01,GAO01]. We adopt the notation of [GM00] and [KNT99] The root of a term f( is the leading function symbol f . For a TRS R over a signature F , D = froot(l)jl r 2 Rg is the set of the de ned symbols and C = F n D is the set of constructors of R. Let F denote the union of the signature F and ....

[Article contains additional citation context not shown here]

J. Giesl, T. Arts, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Submitted to the Journal of Symbolic Computation, 2001.

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T. Arts, J. Giesl, and E. Ohlebusch. Modular termination proofs for rewriting using dependency pairs. Journal of Symbolic Computation, 34(1):21--58, 2002.

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