We propose a new type of conditional term rewriting system: the membership-conditional term rewriting system, in which, each rewriting rule can have membership conditions which restrict the substitution values for the variables occurring in the rule. For example, the rule f(x, x, y) . g(x, y) if x ∈ T ′ yields the reduction f(M, M, N) → g(M, N) only when M is in the term set T ′. We study the c...

String rewriting can not only be applied on strings, but also on cycles and even on general graphs. In this paper we investigate termination of string rewriting applied on cycles, shortly denoted as cycle rewriting, which is a strictly stronger requirement than termination on strings. Most techniques for proving termination of string rewriting fail for proving termination of cycle rewriting, bu...

1. I n t r o d u c t i o n Many term rewriting systems and their modifications are considered in logic, automated theorem proving, and programming language [2,3,4,6,8,9]. A fundamental property of term rewriting systems is the confluence property. A few sufficient criteria for the confluence are well known [2,3,4,5,8,9]. However, if a term rewriting system is nonterminating and nonlinear, we kn...

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...

This work presents a constraint solver for the domain of rational trees. Since the problem is NP-hard the strategy used by the solver is to reduce as much as possible, in polynomial time, the size of the constraints using a rewriting system before applying a complete algorithm. This rewriting system works essentially by rewriting constraints using the information in a partial model. An efficien...

A property P of term rewriting system is persistent if for any many-sorted term rewriting system R, R has the property P i its underlying term rewriting system (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 sorts. This is the positi...

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 . Zantema showed that termination is persistent for term rewriting systems without collapsing or duplicating rules. In this paper, we show that the Zantema’s result can be extended to term rewriting ...

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that the direct sum of two term rewriting systems is not terminating, even if these systems are both terminating. Keyword: Term rewriting system, termination Introduction A term rewriting system R is a set of rewriting rules M → N , where M and N are terms [1, 3, 5]. The di...

We investigate properties of convergent and forward-closed string rewriting systems in the context of the syntactic criteria introduced in [8] by Christopher Lynch and Barbara Morawska (we call these LM-Systems). Since a string rewriting system can be viewed as a term-rewriting system over a signature of purely monadic function symbols, we adapt their definition to the string rewriting case. We...