Rotation distance between rooted binary trees measures the extent of similarity of
two trees with ordered leaves. There are no known polynomial-time algorithms for
computing rotation distance. If there are common edges or immediately changeable
edges between a pair of trees, the rotation distance problem breaks into smaller
subproblems. The number of crossings or conflicts of a tree pair also gives some
measure of the extent of similarity of two trees. Here we describe the distribution of
common edges and immediately changeable edges between randomly selected pairs of
trees via computer experiments, and examine the distribution of the amount of
conflicts between such pairs.