Two possible minimal uncrossing transformations.

<p>Two possible untangling transformations. The top transformation involves twisting of the loop. The lower transformation involves a snake like movement of the vertical leg. A third one would involve moving the horizontal leg, in a similar snake-like fashion. Note that the moves represented here are not necessarily the most efficient ones in their topological class, but rather the most intuitive ones. There are transformations that are topologically equivalent but generally involve less total motion of the chain (see for example <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0053642#pone-0053642-g011" target="_blank">Figures 11(a), 11(b</a>)).