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Summary: To appear in the Journal of Symbolic Computation
Modular Termination Proofs for Rewriting
Using Dependency Pairs
J urgen Giesl 1 , Thomas Arts 2 and Enno Ohlebusch 3
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany,
giesl@informatik.rwth-aachen.de
2 Computer Science Laboratory, Ericsson, P.O. Box 1505, 125 25 Stockholm,
Sweden, thomas@cslab.ericsson.se
3 Faculty of Technology, University of Bielefeld, P.O. Box 10 01 31,
33501 Bielefeld, Germany, enno@TechFak.Uni-Bielefeld.DE
Abstract
Recently, Arts and Giesl developed the dependency pair approach which
allows automated termination and innermost termination proofs for many
term rewriting systems for which such proofs were not possible before. The
motivation for this approach was that virtually all previous techniques for
automated termination proofs of term rewriting systems were based on
simpli cation orderings. In practice, however, many rewrite systems are
not simply terminating, i.e., their termination cannot be veri ed by any
simpli cation ordering.
In this article we introduce a re nement of the dependency pair frame-
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