Tyrolean Termination Tool 2

Abstract

This paper describes the second edition of the Tyrolean Termination Tool -a fully automatic termination analyzer for first-order term rewrite systems. The main features of this tool are its (non-)termination proving power, its speed, its flexibility due to a strategy language, and the fact that the source code of the whole project is freely available. The clean design together with a stand-alone OCaml library for term rewriting, make it a perfect starting point for other tools concerned with rewriting as well as experimental implementations of new termination methods.

Well-Definedness of Streams by Termination

“…Together with the rules not(0) → 1 and not(1) → 0 from R d this TRS is terminating as can easily be proved fully automatically by AProVE [4] or TTT2 [7]. As a consequence, the result of this paper states that the specification uniquely defines a stream for every ground term of type s, in particular for morse.…”

“…It turns out that for several interesting cases termination of the observational variant of a specification can be proved by termination tools like AProVE [4] or TTT2 [7]. This provides a new technique to prove well-definedness of stream specifications fully automatically, applying for cases where earlier approaches fail.…”

A Tool Proving Well-Definedness of Streams Using Termination Tools

“…-Several stream specifications, including Fibonacci stream, Thue-Morse stream and Kolakoski stream are predefined. For all of these examples termination of the observational variant can be proved fully automatically both by AProVE [2] and TTT2 [3], proving well-definedness of the given stream specification.…”

“…Both AProVE [2] and TTT2 [3] are able to prove termination each of the resulting TRSs within a few seconds, in this way proving well-definedness of all three original specifications. Unfortunately the generated proofs of both tools are quite long and not easily readable.…”

“…The main result of [5] states that if the TRS Obs(S) is terminating, then the stream specification S admits a unique solution. As for proving termination of TRSs automatically during the last ten years strong tools have been developed like AProVE [2] and TTT2 [3], our approach to prove welldefinedness of a stream specification S simply consists of proving termination of Obs(S) by a tool like AProVE or TTT2. It is not even required to download such a termination tool: both tools admit a web interface in which any TRS is easily entered.…”