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Rotation distance between rooted binary trees is the minimum number of simplerotations needed to transform one tree into the other. Computing the rotationdistance between a pair of rooted trees can be quickly reduced in cases wherethere is a common edge between the trees, or where a single rotation introducesa common edge. Tree pairs which do not have such a reduction are difficult treepairs, where there is no generally known first step. Here, we describe effortsto count and estimate the number of such difficult tree pairs, and find thatthe fraction decreases exponentially fast toward zero. We also describe howknowing the number of distinct instances of the rotation distance problem is ahelpful factor in making the computations more feasible.

Counting difficult tree pairs with respect to the rotation distance problem