ONE-RULE TRACE-REWRITING SYSTEMS AND CONFLUENCE

Confluence is an undecidable property even for finite noetherian trace-rewriting systems. Here we investigate this property for the special case of trace-rewriting systems with a single rule. For certain classes of one-rule trace-rewriting systems R we present syntactic characterizations that are necessary and sufficient for R to be confluent. Based on these characterizations confluence is easily decidable for these systems. In fact. each system satisfying one of these characterizations is strongly confluent. This raises the question of whether every confluent one-rule trace-rewriting system is strongly confluent. We close this paper with an example that answers this question in the negative.