Scheme inclusion verification algorithm in algebraic model of programs with constants

An algorithm is described to check the inclusion relation in the algebraic model of programs and constants, and for the estimation of its complexity. The algorithm is constructed without using questionable tricks, and is aimed at improving asymptotic complexity, which is often not applicable to program implementations. The equivalence problem in the algebraic model of programs, which is the problem of existence of an algorithm that recognizes the equivalence is PSPACE-complete with respect to the number of occurrences. Estimating complexity of the algorithm under elementary operations on objects such as graphs, automata, methods of working with these objects is not described. Primarily the algebraic model of programs with constants is defined, followed by algorithm main for checking scheme inclusion description. The next step is for checking diagram inclusion algorithm description for checking relations on schemes of programs concluded by the complexity estimation of the algorithm.