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In this paper we address the application properties of the decoupling multivariate polynomials problem algorithm proposed in [2]. By numerous examples we demonstrate that this algorithm, unfortunately, fails to provide a solution in some cases. Therefore we empirically determine the application scope of this algorithm and show that it is connected with the uniqueness conditions of the CP-decomposition (Canonical Polyadic Decomposition). We also investigate the approximation properties of this algorithm and show that it is capable of construction the best low-rank polynomial approximation provided that the CP-decomposition is unique.