2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/76923It is shown how to use a small finite state automaton in two variables in order to carry out part of the Knuth--Bendix process for rewriting words in a group. The main objective is to provide a substitute for the most space-demanding module of the existing software which attempts to find a shortlex-automatic structure for a group. 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. In our context this operation is vital. We point out a small potential improvement in the subset algorithm for making a non-deterministic automaton deterministic.41 pages. In LaTeX2e using the packages amsmath, amssymb, xspace, epic. Submitted to Internat. J. Algebra ComputGroup Theory20F10, 20-04, 68Q42 (Primary) 03D40, 20F32 (Secondary)text