Summary: Improving Dependency Pairs #
J˜urgen Giesl, Ren’e Thiemann, Peter SchneiderKamp, Stephan Falke
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
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.
Most traditional methods to prove termination of TRSs (automatically) use
simplification orders [7, 24], where a term is greater than its proper subterms.