Nao Hirokawa

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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 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.
This paper describes the Tyrolean Termination Tool (TTT in the sequel), the successor of the Tsukuba Termination Tool [12]. We describe the differences between the two and explain the new features, some of which are not (yet) available in any other termination tool, in some detail. TTT is a tool for automatically proving termination of rewrite systems based(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 [1]. It incorporates several new ideas that make the method more efficient. The tool produces high-quality output and has a convenient web interface. If TTT succeeds in proving termination, it outputs a(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)
This paper builds on recent e orts (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)
First-order applicative rewrite systems provide a natural framework for modeling higher-order aspects. In this article 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)
In this article we use the decreasing diagrams technique to show that a left-linear and locally confluent term rewrite system $\mathcal{R}$ is confluent if the critical pair steps are relatively terminating with respect to $\mathcal{R}$ . We further show how to encode the rule-labeling heuristic for decreasing diagrams as a satisfiability problem.(More)