Termination of the point-to-edge matching uncrossing algorithm

Let $Q_1,\ldots,Q_n$ be points and let $B_1,\ldots,B_n$ be edges of a convex hull, with each point matched to one edge and the resulting triangles considered as in the preceding heuristic. Termination conjecture. The algorithm described above always terminates. This is presented as an observation relevant to the matching problem in the discussion, but no proof or resolution is given in the supplied text.