The dependency pair technique 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 well-founded 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 that simplify (innermost) termination proofs significantly. To fully mechanize the approach, we show how transformations and the search for suitable orders can be mechanized efficiently. We implemented our results in the automated termination prover AProVE and evaluated them on large collections of examples.

AProVE 1.2 is one of the most powerful systems for automated termination proofs of term rewrite systems (TRSs). It is the first tool which automates the new dependency pair framework [8] and therefore permits a completely flexible combination of different termination proof techniques. Due to this framework, AProVE 1.2 is also the first termination prover which can be fully configured by the user.

Abstract. The dependency pair approach is one of the most powerful techniques for automated termination proofs of term rewrite systems. Up to now, it was regarded as one of several possible methods to prove termination. In this paper, we show that dependency pairs can instead be used as a general concept to integrate arbitrary techniques for termination analysis. In this way, the benefits of different techniques can be combined and their modularity and power are increased significantly. We refer to this new concept as the "dependency pair framework " to distinguish it from the old "dependency pair approach". Moreover, this framework facilitates the development of new methods for termination analysis. To demonstrate this, we present several new techniques within the dependency pair framework which simplify termination problems considerably. We implemented the dependency pair framework in our termination prover AProVE and evaluated it on large collections of examples.

Abstract. Polynomial interpretations are one of the most popular techniques for automated termination analysis and the search for such interpretations is a main bottleneck in most termination provers. We show that one can obtain speedups in orders of magnitude by encoding this task as a SAT problem and by applying modern SAT solvers.