Adler function, Bjorken polarized sum rule: confirmation of elements of the $\{\beta \}$-expansion and the diagrams

Different ways exist to obtain the elements of the $\{\beta \}$-expansion for renormgroup invariant quantities. Here we consider independent confirmation within the standard QCD of a number of our results [1] for the values of elements of this expansion for the nonsinglet Adler $D_A$-function, Bjorken polarized sum rules $S^{Bjp}$ up to the order N${}^4$LO. We suggest an approach to estimate the results of high order QCD calculations using a smaller number of diagrams of the specific type. This type is based on a proposed generalization of Naive NonAbelianization.