User blog comment:Boboris02/Analysis of Taranovsky's Ordinal Notation with "standard OCFs."/@comment-11227630-20180114002919

You have got the definition wrong. C(a,b) is in standard form if all the followings are true: You have got wrong order of a and b in 2 and 3.
 * 1) Both a and b are in standard form
 * 2) If b = C(c,d), then $$a\le c$$
 * 3) a is n-built from below from <C(a,b)