2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/142184We present a sequence of diagrams of the unknot for which the minimum number of Reidemeister moves required to pass to the trivial diagram is quadratic with respect to the number of crossings. These bounds apply both in $S^2$ and in $\R^2$.Geometric Topology57M25text