It is not known whether the termination problem is decidable for one-rule string-rewriting systems, though the con uence of such systems is decidable by Wrathall (in: Word Equations and In this paper we develop techniques to attack the termination and complexity problems of con uent one-rule string-rewriting systems. With given such a system we associate another rewriting system over another alphabet. The behaviour of the two systems is closely related and the termination problem for the new

more »

... tem is sometimes easier than for the original system. We apply our method to systems of the special type {a p b q → t}, where t is an arbitrary word over {a; b}, and give a complete characterization for termination. We also give a complete analysis of the derivational complexity for the system {a p b q → b n a m }.