Nao Hirokawa

Tyrolean termination tool

This paper describes the Tyrolean Termination Tool (

Automating the dependency pair method

\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}

Tyrolean termination tool: Techniques and features

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.

Dependency Pairs Revisited

\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}

Polynomial Interpretations with Negative Coefficients

is a tool for automatically proving termination of rewrite systems based on the dependency pair method of Arts and Giesl [3]. It produces high-quality output and has a convenient web interface. The tool is available at http://cl2-informatik.uibk.ac.at/ttt

KBO Orientability

\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}

Uncurrying for Termination

incorporates several new improvements to the dependency pair method. In addition, it is now possible to run the tool in fully automatic mode on a collection of rewrite systems. Moreover, besides ordinary (first-order) rewrite systems, the tool accepts simply-typed applicative rewrite systems which are transformed into ordinary rewrite systems by the recent method of Aoto and Yamada [2]. In the next section we describe the differences between the semi automatic mode and the Tsukuba Termination Tool. Section 3 describes the fully automatic mode. In Section 4 we show a termination proof of a simply-typed applicative system obtained by

Tsukuba termination tool

\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}

Decreasing diagrams and relative termination

. In Section 5 we describe how to input a collection of rewrite systems and how to interpret the resulting output. Some implementation details are given in Section 6. The final section contains a short comparison with other tools for automatically proving termination.

Uncurrying for Termination and Complexity

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 this paper we present new ideas to overcome these obstacles. We provide ample numerical data supporting our ideas.