J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems (FroCoS '98), volume 7 of Studies in Logic and Computation, pages 141160, Amsterdam, The Netherlands, 2000. Research Studies Press, John Wiley & Sons.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....property of TRSs to which traditional techniques cannot be applied. Since this method compares rewrite rules and dependency pairs by a weak reduction pair instead of a reduction order, to nd an appropriate weak reduction pair for a given TRS is necessary. The argument ltering method introduced [4, 8] allows us to make a weak reduction pair from an arbitrary reduction order. In this paper, we rst extend the argument ltering method by combining subterm relation. Next, we study the relation between the argument ltering method and various elimination methods. The key of our result is the ....

....s t by s R t, and s t by s R C[t] for some C. Then, it is trivial that ( is a weak reduction pair such that 8l r 2 R: l r and 8hu; vi 2 DP (R) u v. 2 ) 3) It is easily shown by identifying f # with f . 3 ) 1) This case has already been shown in [1 4, 8]. Note that the proofs for (2 ) 1) and for (1 ) 3) have already been shown in [10, 14] and [4] 1 , respectively. The above theorem shows that the weak reduction pair plays an important role. To design a weak reduction pair, the argument ltering method introduced in [4, 8] is very useful, ....

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J.Giesl, E.Ohlebusch, Pushing the Frontiers of Combining Rewrite Systems Farther Outwards, In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCos '98, Applied Logic Series, Amsterdam, The Netherlands, October 1998.

....the notion of dependency pairs [1, 2, 3] Since this method compares rewrite rules and dependency pairs by a weak reduction order instead of a reduction order, to find an appropriate weak reduction order for a given TRS is necessary. For this purpose, the argument filtering method was introduced [4, 8, 12], which allows us to make a weak reduction order from an arbitrary reduction order. In this paper, we study the relation between the argument filtering method and various elimination methods. The key of our result is the observation that the argument filtering method combining with the dependency ....

.... that satisfies l r for all l r 2 R. A TRS R is simply terminating iff there exists a simplification order that satisfies l r for all l r 2 R. 3 Soundness Conditions for Transformation In this section, we first explain the dependency pair [1, 2, 3] and the argument filtering method [4, 8, 12], whose notions have been greatly extended to the provable class of termination. The set of dependency pairs itself is a term rewriting system. Thus, so is the union of a term rewriting system and its dependency pairs. We discuss the relations about the termination property between a term ....

[Article contains additional citation context not shown here]

J.Giesl, E.Ohlebusch, Pushing the Frontiers of Combining Rewrite Systems Farther Outwards, In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCos '98, Applied Logic Series, Amsterdam, The Netherlands, October 1998.

....ordering p such that (a) wp( p wp(r) for all rules I r in , p(t) t p, c) p(s) p p(t) for at least one dependency pair s t from P. The information that systems are DP quasi simple terminating can be used when combining these systems and proving termination of the resulting TRS [GO00,GAO01] Theorem 6 (Modulity of DP quasi simple termination) Let 1 and be two TRSs over disjoint signatures 1 and , respectively. Then their union = is DP quasi simply teinating if and only if both 1 and are DP quasi simply teinating. For DP simple termination the modularity result for ....

J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems far- ther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCoS-98, volume 7 of Studies in Logic and Computation, pages 141-160, Amsterdam, The Netherlands, 2000. Research Studies Press, John Wiley 85 Sons.

.... P such that (b) P (s) P P (t) for all dependency pairs s t from P, and (c) P (s) P P (t) for at least one dependency pair s t from P. The information that systems are DP quasi simple terminating can be used when combining these systems and proving termination of the resulting TRS [GO00,GAO01]. Theorem 6 (Modularity of DP quasi simple termination) Let R 1 and R 2 be two TRSs over disjoint signatures F 1 and F 2 , respectively. Then their union R = R 1 [ R 2 is DP quasi simply terminating if and only if both R 1 and R 2 are DP quasi simply terminating. 7 For DP simple termination ....

J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCoS-98, volume 7 of Studies in Logic and Computation, pages 141-160, Amsterdam, The Netherlands, 2000. Research Studies Press, John Wiley & Sons.

....is therefore well suited to be used for more general rewriting problems, too. For example, the framework of dependency pairs can easily be extended for termination modulo associativity and commutativity [39] Moreover, several well known and new modularity results can be derived in this framework [5,7,26]. Acknowledgement We would like to thank Hans Zantema, Aart Middeldorp, Thomas Kolbe, and Bernhard Gramlich for constructive criticism and many helpful comments. This work was partially supported by the Deutsche Forschungsgemeinschaft under grants no. Wa 652 7 1,2 as part of the focus program ....

J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCoS '98, Applied Logic Series, Amsterdam, The Netherlands, October 1998. Kluwer Academic Publishers, Amsterdam.

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J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems (FroCoS '98), volume 7 of Studies in Logic and Computation, pages 141160, Amsterdam, The Netherlands, 2000. Research Studies Press, John Wiley & Sons.

No context found.

Giesl, J. and E. Ohlebusch: 2000, `Pushing the Frontiers of Combining Rewrite Systems Farther Outwards'. In: Proceedings of the Second International Workshop on Frontiers of Combining Systems (FroCoS '98), Vol. 7 of Studies in Logic and Computation. Amsterdam, The Netherlands, pp. 141--160.

No context found.

J. Giesl and E. Ohlebusch. Pushing the frontiers of combining rewrite systems farther outwards. In Proceedings of the Second International Workshop on Frontiers of Combining Systems (FroCoS '98), Logic and Computation Series, pages 141--160, Amsterdam, The Netherlands, 1998. Research Studies Press, John Wiley & Sons.

No context found.

J.Giesl, E.Ohlebusch, Pushing the Frontiers of Combining Rewrite Systems Farther Outwards, In Proceedings of the Second International Workshop on Frontiers of Combining Systems, FroCos '98, Applied Logic Series, Amsterdam, The Netherlands, October 1998.

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