Summary: Improving Dependency Pairs #
J˜urgen Giesl, Ren’e Thiemann, Peter Schneider­Kamp, Stephan Falke
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
{giesl|thiemann}@informatik.rwth­aachen.de
{nowonder|spf}@i2.informatik.rwth­aachen.de
Abstract. The dependency pair approach is one of the most powerful
techniques for termination and innermost termination proofs of term re­
write systems (TRSs). For any TRS, it generates inequality constraints
that have to be satisfied by weakly monotonic well­founded orders. We
improve the dependency pair approach by considerably reducing the
number of constraints produced for (innermost) termination proofs.
Moreover, we extend transformation techniques to manipulate depen­
dency pairs which simplify (innermost) termination proofs significantly.
In order to fully automate the dependency pair approach, we show how
transformation techniques and the search for suitable orders can be mech­
anized e#ciently. We implemented our results in the automated termina­
tion prover AProVE and evaluated them on large collections of examples.
1 Introduction
Most traditional methods to prove termination of TRSs (automatically) use
simplification orders [7, 24], where a term is greater than its proper subterms.

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

Collections: Computer Technologies and Information Sciences