There are properties of rewriting systems that are characterized by means of some syntactic conditions (e.g., requiring left-linear and non-overlapping rules for ensuring confluence). Sometimes, though, a given property might hold but the syntactic conditions are not met. This is particularly true when the systems are obtained by some automated transformation. In this paper, we introduce a tech...

Term rewriting systems with rules of different priority are introduced. The semantics are exp}ained in detail and several examples are discussed. Note: Partial support received from the European Communities under Esprit contract no. 432, Meteor (An integrated formal approach to industrial software development).

abstract: Recently, dependency pairs have greatly extended the provable class of terminating of term rewriting systems. The set of dependency pairs itself makes a term rewriting system. However, a term rewriting system and its dependency pairs do not accurately agree on the termination property. In this paper, we study the relation for the termination property between a term rewriting system, t...

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...

The class of orthogonal rewriting systems (rewriting systems where rewrite steps cannot depend on one another) is the main class of not-necessarily-terminating rewriting systems for which connuence is known to hold. Huet and Toyama have shown that for left-linear rst-order term rewriting systems (TRSs) the orthogonality restriction can be relaxed somewhat by allowing critical pairs (arising fro...

We study Higher-Order Rewrite Systems (HRSs) which extend term rewriting to-terms. HRSs can describe computations over terms with bound variables. We show that rewriting with HRSs is closely related to undirected equational reasoning. We deene Pattern Rewrite Systems (PRSs) as a special case of HRSs and extend three connuence results from term rewriting to PRSs: the critical pair lemma by Knuth...