2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58497It is shown how to use a small finite state automaton in two variables in order to carry out the Knuth-Bendix process for rewriting words in a group in shortlex order. The two-variable automaton can be used to store an infinite set of rules and to carry out fast reduction of arbitrary words using this infinite set. We introduce a new operation, which we call welding, which applies to an arbitrary finite state automaton. We show how to improve on the standard subset construction to determinize a non-deterministic automaton under special conditions which hold in our situation.63 pages, 6 figures. A completely rewritten version of math/9805057. A slightly shortened version of this paper has been accepted by IJACGroup Theory20F10,20-04,68Q42 (Primary); 03D40,20F32 (Secondary)text