User blog comment:Mh314159/YIP notation/@comment-35470197-20190704230823/@comment-35470197-20190705025656

Good. Then the resulting functions can be analysed in the following way: \begin{eqnarray*} X_0(a,3) & = & [a,2] \sim F_{2 \omega + 2}(F_{2 \omega + 1}(F_{2 \omega}(a))) \\ X_n(a,3) & = & (F_{2 \omega + 2} \circ F_{2 \omega + 1} \circ F_{2 \omega})^n(a) \\ & \leq & F_{2 \omega + 2}^{2n}(a) \\ [a,3] & = & X_{[a,2]}(a,3) \leq F_{2 \omega + 3}(F_{2 \omega + 2}^2(a)) \\ [a,n] & \leq & F_{2 \omega + n}(F_{2 \omega + n - 1}^2(a)) \\ [n,n] & \leq & F_{2 \omega + 1 + \omega}(n) \end{eqnarray*} Therefore this system is approaximately bounded by \(\omega \times 2\) in FGH. It is natural that this kind of array notations corresponds to \(\omega^{\ell}\), where \(\ell\) is the length of the array.