For the whole class of linear term rewriting systems and for each integer k, we define k-bounded rewriting as a restriction of the usual notion of rewriting. We show that the k-bounded uniform termination, the k-bounded termination, the inverse k-bounded uniform, and the inverse kbounded problems are decidable. The k-bounded class (BO(k)) is, by definition, the set of linear systems for which e...

An automatic and easy to implement transformation of conditional term rewrite systems into computationally equivalent unconditional term rewrite systems is presented. No special support is needed from the underlying unconditional rewrite engine. Since unconditional rewriting is more amenable to parallelization, our transformation is expected to lead to efficient concurrent implementations of re...

We prove modularity of constructive confluence for term rewriting systems using a novel decomposition of terms into tall aliens and bases. The proof is modular itself in that it factors through the decreasing diagrams theorem for abstract rewriting systems.

The rewriting calculus has been introduced as a general formalism that uniformly integrates rewriting and λ-calculus. In this calculus all the basic ingredients of rewriting such as rewrite rules, rule applications and results are rst-class objects. The rewriting calculus has been originally designed and used for expressing the semantics of rule based as well as object oriented paradigms. We ha...

We investigate the rewrite relation over graphs induced by constructor-based weakly orthogonal graph rewriting systems. It is well known that this relation is not confluent in general whereas it is confluent in the case of weakly orthogonal term rewriting systems. We show, however, that the considered relation is always confluent, as well as confluent modulo bisimilarity, for a large class of g...

Innnite terms in universal algebras are a well-known topic since the seminal work of the ADJ group 1]. The recent interest in the eld of term rewriting (tr) for innnite terms is due to the use of term graph rewriting to implement tr, where terms are represented by graphs: so, a cyclic graph is a nitary description of a possibly innnite term. In this paper we introduce innnite rewriting logic, w...

p. 1 Redundancy Criteria for Constrained Completion p. 2 Bi-rewriting, a Term Rewriting Technique for Monotonic Order Relations p. 17 A Case Study of Completion Modulo Distributivity and Abelian Groups p. 32 A Semantic Approach to Order-Sorted Rewriting p. 47 Distributing Equational Theorem Proving p. 62 On the Correctness of a Distributed Memory Grobner Basis Algorithm p. 77 Improving Transfor...

For nite convergent term-rewriting systems it is shown that the equational unii-cation problem is recursively independent of the equational matching problem, the word matching problem, and the 2 nd-order equational matching problem. Apart from the latter these results are derived by considering term-rewriting systems on signatures that contain unary function symbols only (that is, string-rewrit...

This paper describes an extension of head-needed rewriting on term rewriting systems to higher-order rewrite systems. The main di culty of this extension is caused by the -reductions induced from the higher-order reductions. In order to overcome this di culty, we de ne a new descendant of higher-order rewrite systems. This paper shows the new de nition of descendant, its properties and head nor...

The rewriting calculus has been introduced as a general formalism that uniformlyintegrates rewriting and λ-calculus. In this calculus all the basic ingredients ofrewriting such as rewrite rules, rule applications and results are rst-class objects.The rewriting calculus has been originally designed and used for expressing thesemantics of rule based as well as object oriented ...