Effective algorithm for construction of terms of minimum computational complexity

The problem of construction of terms of the minimum computational complexity by the program which contains only assignments and a finite number of variables, and operating on the free one-generated gruppoide with the signature consisting of a binary operation symbol and one generating element is considered. Such terms are considered that leaves of the corresponding full binary trees are labeled by pairwise different subterms. The effective algorithm of such construction is given and it is proved that for any natural $m$ it is possible to construct a term of height $h$ with $h-m$ variables.