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Mechanizing and Improving Dependency Pairs # Jurgen Giesl (giesl@informatik.rwthaachen.de),

Summary: Mechanizing and Improving Dependency Pairs #
J˜urgen Giesl (giesl@informatik.rwth­aachen.de),
Ren’e Thiemann (thiemann@informatik.rwth­aachen.de) and
Peter Schneider­Kamp (psk@informatik.rwth­aachen.de)
LuFG Informatik 2, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
Stephan Falke (spf@cs.unm.edu)
Computer Science Dept., University of New Mexico, Albuquerque, NM 87131, USA
Abstract. The dependency pair technique [1, 11, 12] is a powerful method for
automated termination and innermost termination proofs of term rewrite systems
(TRSs). For any TRS, it generates inequality constraints that have to be satisfied
by well­founded orders. We improve the dependency pair technique by considerably
reducing the number of constraints produced for (innermost) termination proofs.
Moreover, we extend transformation techniques to manipulate dependency pairs
which simplify (innermost) termination proofs significantly. In order to fully mech­
anize the approach, we show how transformations and the search for suitable or­
ders can be mechanized e#ciently. We implemented our results in the automated
termination prover AProVE and evaluated them on large collections of examples.
Keywords: termination, term rewriting, dependency pairs
1. Introduction
Termination is an essential property of term rewrite systems. Before


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


Collections: Computer Technologies and Information Sciences