Certifying Proofs in the First-Order Theory of Rewriting

The first-order theory of rewriting is a decidable theory for linear variable-separated rewrite systems. The decision procedure is based on tree automata techniques and recently we completed a formalization in the Isabelle proof assistant. In this paper we present a certificate language that enables the output of software tools implementing the decision procedure to be formally verified. To show the feasibility of this approach, we present FORT-h, a reincarnation of the decision tool FORT with certifiable output, and the formally verified certifier FORTify.