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AProVE: A System for Proving Termination Jurgen Giesl, Rene Thiemann, Peter SchneiderKamp, Stephan Falke

Summary: AProVE: A System for Proving Termination
J˜urgen Giesl, Ren’e Thiemann, Peter Schneider­Kamp, Stephan Falke
LuFG Informatik II, RWTH Aachen, Ahornstr. 55, 52074 Aachen, Germany
1 Introduction
The system AProVE (Automated Program Verification Environment) can be used for
automated termination and innermost termination proofs of (conditional) term rewrite
systems (TRSs). AProVE currently o#ers the techniques of recursive path orders pos­
sibly with status [3] (Sect. 2), dependency pairs including recent refinements such as
narrowing, rewriting, and instantiation of dependency pairs [1, 4, 5] (Sect. 3), and the
size­change principle, also in combination with dependency pairs [7, 9] (Sect. 4). The
tool is written in Java and proofs can be performed both in a fully automated or in an
interactive mode via a graphical user interface (Sect. 5)
2 Direct Termination Proofs
In a direct termination proof, the system tries to find a reduction order such that all
rules of a TRS are decreasing. Currently, the following path orders are implemented in
AProVE: the embedding order (EMB), the lexicographic path order (LPO, [6]), the LPO
with status which compares subterms lexicographically according to arbitrary permu­
tations (LPOS), the recursive path order which compares subterms as multisets (RPO,


Source: Ábrahám, Erika - Fachgruppe Informatik, Rheinisch Westfälische Technische Hochschule Aachen (RWTH)


Collections: Computer Technologies and Information Sciences