User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-35392788-20180813124110/@comment-28606698-20180813152411

Normal form condition \alpha=_{NF}\psi_\nu(\beta) iff \alpha=\psi_\nu(\beta)\wedge\beta\in C_\nu(\beta)

\psi_0(\psi_1(\psi_2(0))) is not written in the normal form since \psi_2(0)>\psi_1(\psi_2(0)) and that is why \psi_1(\psi_2(0)) cannot appear in the set C_0(\psi_1(\psi_2(0)))

So Buchholz function doesn't grow between \psi_0(\psi_1(\psi_2(0))) and \psi_0(\psi_2(0)). Hence \psi_0(\psi_1(\psi_2(0)))=\psi_0(\psi_2(0))