Decomposition of functions of finite analytical complexity

Functions of two variables can be obtained from functions of one variable by substitutions and additions. Each composition scheme corresponds to a class of functions of two variables, such that they can be represented as a composition with this scheme. It was shown that each class consists of analytical solutions of a certain system of differential polynomials (equations of the class). The paper describes an algorithm for constructing a system of equations of the scheme and for obtaining function representation in the form of a composition with this scheme.