the ranks of the nodes in a wavl tree can be converted to a system of ranks of nodes, obeying the requirements for red–black trees, by dividing each rank by two and rounding up to the nearest integer. because of this conversion, for every wavl tree there exists a valid red–black tree with the same structure. because red–black trees have maximum height formula_3, the same is true for wavl trees. however, there exist red–black trees that cannot be given a valid wavl tree rank function.