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Termination of term rewriting using dependency pairs

Summary: Termination of term rewriting using
dependency pairs
Thomas Arts a , J¨urgen Giesl b
a Department of Computer Science, Utrecht University, P.O. Box 80.089,
3508 TB Utrecht, The Netherlands, E­mail: thomas@cs.ruu.nl
b Department of Computer Science, Darmstadt University of Technology,
Alexanderstraße 10, 64283 Darmstadt, Germany, E­mail:
We present techniques to prove termination and innermost termination of term
rewriting systems automatically. In contrast to previous approaches, we do not
compare left­ and right­hand sides of rewrite rules, but introduce the notion of
dependency pairs to compare left­hand sides with special subterms of the right­
hand sides. This results in a technique which allows to apply existing methods
for automated termination proofs to term rewriting systems where they failed up
to now. In particular, there are numerous term rewriting systems where a direct
termination proof with simplification orderings is not possible, but in combination
with our technique, well­known simplification orderings (such as the recursive path
ordering, polynomial orderings, or the Knuth­Bendix ordering) can now be used to
prove termination automatically.


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


Collections: Computer Technologies and Information Sciences