Tyrolean Termination Tool

  • Nao Hirokawa
  • Aart Middeldorp
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3467)


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

\(\mathsf{T}\!_{\mbox{\sf T}}\!\mathsf{T}\) 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.


Dependency Graph Automatic Mode Usable Rule Termination Proof Termination Tool 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Nao Hirokawa
    • 1
  • Aart Middeldorp
    • 1
  1. 1.Institute of Computer ScienceUniversity of InnsbruckInnsbruckAustria

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