User blog comment:Boboris02/Analysis of Taranovsky's Ordinal Notation with "standard OCFs."/@comment-25601061-20180113214110/@comment-11227630-20180115000208

C(Ω,Ω) is valid because Ω is not in the form C(a,b) (Ω is an "atom expression").

However, the standard representation of 1 is C(0,0) (1 is not "atom expression"), so C(1,1) = C(C(0,0),C(0,0)), in which C(0,0) > 0, and thus C(1,1) is not valid.

By the way, $$C(\varepsilon_0,\varepsilon_0)=C(C(\Omega_1,0),C(\Omega_1,0))$$ is valid since $$C(\Omega_1,0)\le\Omega_1$$.