Tyrolean Complexity Tool: Features and Usage

The Tyrolean Complexity Tool, TCT for short, is an open source complexity analyser for term rewrite systems. Our tool TCT features a majority of the known techniques for the automated characterisation of polynomial complexity of rewrite systems and can investigate derivational and runtime complexity, for full and innermost rewriting. This system description outlines features and provides a short introduction to the usage of TCT

SAT Solving for Argument Filterings

This paper introduces a propositional encoding for lexicographic path orders in connection with dependency pairs. This facilitates the application of SAT solvers for termination analysis of term rewrite systems based on the dependency pair method. We address two main inter-related issues and encode them as satisfiability problems of propositional formulas that can be efficiently handled by SAT solving: (1) the combined search for a lexicographic path order together with an \emph{argument filtering} to orient a set of inequalities; and (2) how the choice of the argument filtering influences the set of inequalities that have to be oriented. We have implemented our contributions in the termination prover AProVE. Extensive experiments show that by our encoding and the application of SAT solvers one obtains speedups in orders of magnitude as well as increased termination proving power

CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates

Termination is an important property of programs; notably required for programs formulated in proof assistants. It is a very active subject of research in the Turing-complete formalism of term rewriting systems, where many methods and tools have been developed over the years to address this problem. Ensuring reliability of those tools is therefore an important issue. In this paper we present a library formalizing important results of the theory of well-founded (rewrite) relations in the proof assistant Coq. We also present its application to the automated verification of termination certificates, as produced by termination tools

The Certification Problem Format

We provide an overview of CPF, the certification problem format, and explain some design decisions. Whereas CPF was originally invented to combine three different formats for termination proofs into a single one, in the meanwhile proofs for several other properties of term rewrite systems are also expressible: like confluence, complexity, and completion. As a consequence, the format is already supported by several tools and certifiers. Its acceptance is also demonstrated in international competitions: the certified tracks of both the termination and the confluence competition utilized CPF as exchange format between automated tools and trusted certifiers.Comment: In Proceedings UITP 2014, arXiv:1410.785

Automated verification of termination certificates

In order to increase user confidence, many automated theorem provers provide certificates that can be independently verified. In this paper, we report on our progress in developing a standalone tool for checking the correctness of certificates for the termination of term rewrite systems, and formally proving its correctness in the proof assistant Coq. To this end, we use the extraction mechanism of Coq and the library on rewriting theory and termination called CoLoR