Tyrolean termination tool

• Authors: Nao Hirokawa;Aart Middeldorp
• Venue: RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
• Year: 2005

This paper describes the Tyrolean Termination Tool ($\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}$ 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. $\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}$ 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 $\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}$ 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 $\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}$. 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.