System S is a calculus providing the basic abstractions of term rewriting: matching and building terms, term traversal, combining computations and handling failure. The calculus forms a core language for implementation of a wide variety of rewriting languages, or more generally, languages for specifying tree transformations. In this paper we show how a conventional rewriting language based on c...

We define a transformation from term rewriting systems (TRSs) to context-sensitive TRSs in such a way that termination of the target system implies outermost termination of the original system. For the class of left-linear TRSs the transformation is complete. Thereby state-of-the-art termination methods and automated termination provers for context-sensitive rewriting become available for provi...

Theorem proving using term rewriting has been thoroughly explored for equational speciications; we look at the use of term rewriting for proving theorems in the process algebras of concurrency and conduct two experiments in this area. We use the LP theorem prover for proofs about CSP, and the RRL term rewriting system for reasoning about LOTOS. The results of these experiments provide informati...

In this invited talk, I will review five basic concepts of Axiomatic Rewriting Theory, an axiomatic and diagrammatic theory of rewriting started 25 years ago in a LICS paper with Georges Gonthier and Jean-Jacques Lévy, and developed along the subsequent years into a full-fledged 2-dimensional theory of causality and residuation in rewriting. I will give a contemporary view on the theory, inform...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...

rewriting systems on multisets (ARMS) are a simple construct in the context of Computational living systems, constituting a class of P systems that have been devised for modelling systems dynamics, with the belief that [177]: Environment + Computational living systems = Computation in agreement with the vision of living beings as computing entities whose computation purpose is keeping themselve...

We introduce rewriting with two sets of rules, the rst interpreted equa-tionally and the second not. A semantic view considers equational rules as deening an equational theory and reduction rules as deening a rewrite relation modulo this theory. An operational view considers both sets of rules as similar. We introduce suucient properties for these two views to be equivalent (up to diierent noti...

By reduction from the halting problem for Minsky’s two-register machines we prove that there is no algorithm capable of deciding the ∃∀∀∀-theory of one step rewriting of an arbitrary finite linear confluent finitely terminating term rewriting system (weak undecidability). We also present a fixed such system with undecidable ∃∀∗-theory of one step rewriting (strong undecidability). This improves...

Abstract rewriting systems are often defined as binary relations over a given set of objects. In this paper, we introduce a new notion of abstract rewriting system in the framework of categories. Then, we define the functoriality property of rewriting systems. This property is sometimes called vertical composition. We show that most graph transformation systems are functorial and provide a coun...