Grayson's balanced figure-eight convergence conjecture

A balanced figure-eight is a figure-eight curve whose lobes bound regions of equal area, and the curve-shortening flow is the evolution of a plane curve by curvature. Grayson's conjecture. Every balanced figure-eight converges to a point under the curve-shortening flow. Balanced figure-eights are known to evolve until their enclosed area converges to zero, but the supplied text states that it remains unknown whether all balanced figure-eights converge to a point or instead to a line segment.