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Dependency Pairs for Equational Rewriting ? Jurgen Giesl 1 and Deepak Kapur 2

Summary: Dependency Pairs for Equational Rewriting ?
Jurgen Giesl 1 and Deepak Kapur 2
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany,
2 Computer Science Dept., University of New Mexico, Albuquerque, NM 87131, USA
Abstract. The dependency pair technique of Arts and Giesl [1{3] for
termination proofs of term rewrite systems (TRSs) is extended to rewrit-
ing modulo equations. Up to now, such an extension was only known in
the special case of AC-rewriting [15, 17]. In contrast to that, the pro-
posed technique works for arbitrary non-collapsing equations (satisfying
a certain linearity condition). With the proposed approach, it is now pos-
sible to perform automated termination proofs for many systems where
this was not possible before. In other words, the power of dependency
pairs can now also be used for rewriting modulo equations.
1 Introduction
Termination of term rewriting (e.g., [1{3, 9, 22]) and termination of rewriting
modulo associativity and commutativity equations (e.g., [8, 13, 14, 20, 21]) have
been extensively studied. For equations other than AC-axioms, however, there
are only a few techniques available to prove termination (e.g., [6, 10, 16, 18]).


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences