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… (More)

The direct sum of two term rewriting systems is the union of systems having disjoint sets of function symbols. It is shown that if two term rewriting systems both have the Chruch-Rosser property,… (More)

A term rewriting system is called growing if each variable occurring on both the left-hand side and the right-hand side of a rewrite rule occurs at depth zero or one in the left-hand side. Jacquemard… (More)

We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature… (More)

A term rewriting system is called complete if it is both confluent and strongly normalising. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be… (More)

To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the… (More)

1. I n t r o d u c t i o n An important concern in building algebraic specifications is their hierarchical or modular structure. The same holds for term rewriting systems [1] which can be viewed as… (More)

A term rewriting system is called complete if it is confluent and terminating. We prove that completeness of TRSs is a “ modular” property (meaning that it stays preserved under direct sums),… (More)