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-35392788-20180813134216

> \(\psi_0(\psi_1(\psi_2(\psi_3(0)))) = \psi_0(\psi_2(0))\)

That doesn't make any sense. Did you rather mean \(\psi_0(\psi_3(0))\) ?

Otherwise, I'd suggest not looking at expressions that get directly translated to non-standard expressions, as weird stuff happens if we try to derive conclusions from nonstandard expressions.

For example, \(\psi_0(\psi_3(0))\) gets translated to (0,0)(1,3), which is not standard. As a result, it expands exactly like (0,0)(1,1). That would lead to the nonsensical statement that \(\psi_0(\psi_1(0)) = \psi_0(\psi_3(0))\).