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This paper is a contribution to the long standing open problem of uniform termination of Semi-Thue Systems that consist of one rule s→ t. McNaughton previously showed that rules incapable of (1) deleting t completely from both sides, (2) deleting t completely from the left, and (3) deleting t completely from the right, have a decidable uniform termination problem. We use a novel approach to show that Premise (2) or, symmetrically, Premise (3), is inessential. Our approach is based on derivations in which every pair of successive steps has an overlap. We call such derivations single-threaded.

Termination of Single-Threaded One-Rule Semi-Thue Systems