This paper presents on-going researches on theoretical and practical issues of combining rewriting based automated theorem proving and user-guided proof development, with the strong constraint of safe cooperation of both. In practice, we instantiate the theoretical study on the Coq proof assistant and the ELAN rewriting based system, focusing first on equational and then on inductive proofs. Di...

Context-sensitive rewriting is a refined form of rewriting that explores a smaller reduction space by imposing some fixed restrictions on the replacements. Any Term Rewriting System (TRS) can be given a context-sensitive rewrite relation. In this paper, we review the theory of context-sensitive rewriting and formulate conditions to guarantee the confluence of this relation. Also, for left-linea...

We are concerned with the verification of behavioural equivalences for CCS specifications. We consider their axiomatic presentations thus relying on a term rewriting approach to verify the equivalence. In this framework it happens that, while some behavioural equivalences do admit a fmite canonical term rewriting system, the completion of observational congruence diverges. In the paper we prese...

Orderings on polynomial interpretations of operators represent a powerful technique for proving the termination of rewriting systems. One of the main problems of polynomial orderings concerns the choice of the right interpretation for a given rewriting system. Here, we present two new heuristic approaches: (i) guidelines for dealing with special classes of rewriting systems as well as (ii) an a...

We describe an algorithm which takes as input a finitely presented group F, a finite confluent rewriting system for a quotient G and a prime p, and returns as output a finite confluent rewriting system for the largest extension of an elementary abelian group in characteristic p by G which is still an epimorphic image of F.

CARIBOO is a termination proof tool for rule-based programming languages, where a program is a rewrite system and query evaluation consists in rewriting a ground expression [3]. It applies to languages such as ASF+SDF, Maude, Cafe-OBJ, or ELAN. By contrast with most of the existing tools, which prove in general termination of standard rewriting (rewriting without strategy) on the free term alge...

We show that confluence of shallow and right-linear term rewriting systems is decidable. This class of rewriting system is expressive enough to include nontrivial nonground rules such as commutativity, identity, and idempotence. Our proof uses the fact that this class of rewrite systems is known to be regularity-preserving, which implies that its reachability and joinability problems are decida...