The Tyrolean Termination Tool (T T T for short) is a powerful tool for automatically proving termination of rewrite systems. It incorporates several new refinements of the dependency pair method that are easy to implement, increase the power of the method, result in simpler termination proofs, and make the method more efficient. T T T employs polynomial… (More)
In this paper we present some new refinements of the dependency pair method for automatically proving the termination of term rewrite systems. These refinements are very easy to implement, increase the power of the method, result in simpler termination proofs, and make the method more efficient.
Developing automatable methods for proving termination of term rewrite systems that resist traditional techniques based on simplification orders has become an active research area in the past few years. The dependency pair method of Arts and Giesl is one of the most popular such methods. However, there are several obstacles that hamper its automation. In… (More)
In this paper, we present a variant of the dependency pair method for analysing runtime complexities of term rewrite systems automatically. This method is easy to implement, but signicantly extends the analytic power of existing direct methods. Our ndings extend the class of TRSs whose linear or quadratic runtime complexity can be detected automatically. We… (More)
First-order applicative term rewrite systems provide a natural framework for modeling higher-order aspects. In this paper we present a transformation from untyped applicative term rewrite systems to functional term rewrite systems that preserves and reflects termination. Our transformation is less restrictive than other approaches. In particular, head… (More)
We present a tool for automatically proving termination of first-order rewrite systems. The tool is based on the dependency pair method of Arts and Giesl . It incorporates several new ideas that make the method more efficient. The tool produces high-quality output and has a convenient web interface. If T T T succeeds in proving termination, it outputs a… (More)
In this paper we use the decreasing diagrams technique to show that a left-linear term rewrite system R is confluent if all its critical pairs are joinable and the critical pair steps are relatively terminating with respect to R. We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem. Experimental data… (More)
Polynomial interpretations are a useful technique for proving termination of term rewrite systems. We show how polynomial interpretations with negative coefficients, like x − 1 for a unary function symbol or x − y for a binary function symbol, can be used to extend the class of rewrite systems that can be automatically proved terminating.
This paper builds on recent eorts (Hirokawa and Moser, 2008) to exploit the dependency pair method for verifying feasible, i.e., polynomial runtime complexities of term rewrite systems automatically. We extend our earlier results by revisiting dependency graphs in the context of complexity analysis. The obtained new results are easy to implement and… (More)