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Summary: Dependency Pairs for Equational Rewriting ?
Jurgen Giesl 1 and Deepak Kapur 2
1 LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany,
giesl@informatik.rwth-aachen.de
2 Computer Science Dept., University of New Mexico, Albuquerque, NM 87131, USA
kapur@cs.unm.edu
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 [16, 18]. 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 ordinary term rewriting has been extensively studied (e.g., in
classical approaches based on simpli cation orderings [9, 23] and new powerful
techniques like dependency pairs [1{3]). There has also been signi cant progress
for termination of equational term rewrite systems whose equations only contain
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