In the binary tree representation, a successful search can be represented by a path from the root to the target node, called an "internal path". The length of a path is the number of edges (connections between nodes) that the path passes through. The number of iterations performed by a search, given that the corresponding path has length formula_113, is formula_114 counting the initial iteration. The "internal path length" is the sum of the lengths of all unique internal paths. Since there is only one path from the root to any single node, each internal path represents a search for a specific element. If there are formula_2 elements, which is a positive integer, and the internal path length is formula_116, then the average number of iterations for a successful search formula_117, with the one iteration added to count the initial iteration.