User blog comment:Alemagno12/I made a Pi w-reflection OCF, how horribly wrong am I?/@comment-35470197-20180812220655/@comment-25601061-20180813020429

Not yet, sorry.

However, we can easily define an FS system for the OCF by defining the complexity of expressions expressible using the OCF:

\(\mathcal{C}(0) = 0\)

\(\mathcal{C}(\omega^{\alpha}) = \mathcal{C}(\alpha^{+}) = \mathcal{C}(\alpha)+1\)

\(\mathcal{C}(\alpha+\beta) = \mathcal{C}(\alpha)+\mathcal{C}(\beta)+1\)

\(\mathcal{C}(\Psi^{P_m,A}_{\alpha}(\beta)) = \mathcal{C}(M^{P_m,A}_{\alpha}(\beta)) = \mathcal{C}(\alpha)+\mathcal{C}(\beta)+\mathcal{C}(A)+1\)

\(\alpha[n]=\max\{\beta|\beta < \alpha\wedge\mathcal{C}(\beta)\leq\mathcal{C}(\alpha)n\}\)