User blog comment:P進大好きbot/Please Help me on study of Pair Sequence System (2-rowed Bashicu Matrix System)/@comment-35870936-20180813215517/@comment-35870936-20180814005732

The problem comes when you say that \(\alpha \leq \beta\) impies \(\psi_n(\alpha) \leq \psi_n(\beta)\). However, in UNOCF this is not the case.

We have psi(psi_1(psi_2(0))) = BHO, but psi(psi_1(psi_2(0)+psi_2(0))) = psi(e(W+2)) = psi(e(W+1)+1) = psi(W_2*2). So we have psi(e(W+2)) > psi(W_2), even though e(W+2) < W_2.

Normal OCFs do indeed have satisfy \(\alpha \leq \beta\) impies \(\psi_n(\alpha) \leq \psi_n(\beta)\), however UNOCF is different.