We propose an extension of rewriting techniques to derive inclusion relations a ⊆ b between terms built from monotonic operators. Instead of using only a rewriting relation ⊆ −→ and rewriting a to b, we use another rewriting relation ⊇ −→ as well and seek a common expression c such that a ⊆ −→ ∗ c and b ⊇ −→ ∗ c. Each component of the bi-rewriting system 〈 ⊆ −→, ⊇ −→〉 is allowed to be a subset ...

This paper proposes rewriting modulo SMT, a new technique that combines the power of SMT solving, rewriting modulo theories, and model checking. Rewriting modulo SMT is ideally suited to model and analyze reachability properties of infinite-state open systems, i.e., systems that interact with a nondeterministic environment. Such systems exhibit both internal nondeterminism, which is proper to t...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for locally confluent overlay term rewriting systems and we give the example as application of this result. Furthermore we obtain that co...

Rewriting induction (Reddy, 1990) is an automated proof method for inductive theorems of term rewriting systems. Reasoning by the rewriting induction is based on the noetherian induction on some reduction order and the original rewriting induction is not capable of proving theorems which are not orientable by that reduction order. To deal with such theorems, Bouhoula (1995) as well as Dershowit...

We address the problem of an efficient rewriting strategy for general term rewriting systems. Several strategies have been proposed over the last two decades for rewriting, the most efficient of all being the natural rewriting strategy [9]. All the strategies so far, including natural rewriting, assume that the given term rewriting system is a left-linear constructor system. Although these rest...

A simple method is proposed for testing equivalence in a restricted domain of two given term rewriting systems. By using the Church-Rosser property and the teachability of term rewriting systems, the method allows us to prove equivalence of these systems without the explicit use of induction; this proof usually requires some kind of induction. The method proposed is a general extension of induc...

A property is called persistent if for any manysorted term rewriting system , has the property if and only if term rewriting system , which results from by omitting its sort information, has the property . In this paper, we show that termination is persistent for right-linear overlay term rewriting systems and we give the example as application of this result. Furthermore we obtain that termina...

This paper places concurrent rewriting in the perspective of supporting the development and use of computational systems. We brieey recall the usefulness of computational systems (i.e. a rewriting theory with strategies) as a logical framework. We then show that the right implementation model for concurrent rewriting allows us to give a meaning to the concurrent rewrite of overlapping redexes. ...