For eeciency reasons, term rewriting is usually implemented by graph rewriting. It is known that graph rewriting is a sound and complete implementation of (almost) orthogonal term rewriting systems; see BEG + 87]. In this paper, we extend the result to properly oriented orthogonal conditional systems with strict equality. In these systems extra variables are allowed in conditions and right-hand...

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...

Properties of Term Rewriting Systems are called modular iff they are preserved under (and reflected by) disjoint union, i.e. when combining two Term Rewriting Systems with disjoint signatures. Convergence is the property of Infinitary Term Rewriting Systems that all reduction sequences converge to a limit. Strong Convergence requires in addition that redex positions in a reduction sequence move...

Nominal rewriting has been introduced as an extension of first-order term rewriting by a binding mechanism based on the nominal approach. In this paper, we extend Huet’s parallel closure theorem and its generalisation on confluence of left-linear term rewriting systems to the case of nominal rewriting. The proof of the theorem follows a previous inductive confluence proof for orthogonal uniform...

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...

In this paper we examine a number of term rewriting system for integer number representations, building further upon the datatype defining systems described in [2]. In particular, we look at automated methods for proving confluence and termination in binary and decimal term rewriting systems for both append and tree constructor functions. We find that some of these term rewriting systems are no...

A property is persistent if for any many-sorted 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 weak normalization is persistent for term rewriting systems. Furthermore we obtain that semi-completeness is persistent for term rewriting systems and we give the exampl...

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 non-overlapping term rewriting systems and we give the example as application of this result. Furthermore we obtain that completeness...

A property P of term rewriting systems is persistent if for any many-sorted term rewriting system R, R has the property P if and only if its underlying term rewriting system Θ(R), which results from R by omitting its sort information, has the property P . It is shown that termination is a persistent property of many-sorted term rewriting systems that contain only variables of the same sort.