A Solution to Zantema's Problem

Hans Zantema raised the question: Does the one-rule string rewriting system OOII ! IIIOOO terminate? Two successful termination proofs have been given by Nachum Der-showitz: One by minimal counterexample, and the other, by a forward closure argument. We give a diierent, more constructive, termination proof, following Zantema's original proof attempt, and using Bellegarde/Lescanne's transformation order method to verify a subtle transformation step.