2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/118097We propose an algorithm for deciding whether a given braid is pseudo-Anosov, reducible, or periodic. The algorithm is based on Garside's weighted decomposition and is polynomial-time in the word-length of an input braid. Moreover, a reduction system of circles can be found completely if the input is a certain type of reducible braids.13 pages, 7 figuresGeometric TopologyGroup Theory20F36; 20F10text