I don't actually understand OCFs, which will make this attempt at one that is intentionally weak funnier.
a and b are assumed to be natural numbers.
#1 the weak rule: badocf(a,b)=badocf(w^a,b-1) if b>0, else w^a
this... goes to just e0. now let's do what a lot of array notations do and add like 5 more rules to make this be able to be compared to 2 entry veblen notation.
n is assumed to also be a natural number.
#3 the transfinite a rule: badocf(Ωn,b)=badocf(Ωn-1,Ωn-1) if n>0, else badocf(badocf(b,b),badocf(b,b))
x and y are assumed to be natural numbers
#4 the doubly transfinite rule: badocf(Ωx,Ωy)=badocf(Ωbadocf(Ωx,x),y)
#2 the omega fixed point rule: if there is an omega fixed point, replace it with Ω_Ω_Ω... with a y long chain of Ω if the omega fixed point is in x, an x long chain of Ω if the omega fixed point is in y, and make them both 1000 long if they are both.
this should go to 2 entry veblen if I'm not wrong, which... is really weak for an OCF. This was just made as a joke, so yeah, I probably did everything wrong, but it was fun to make
updated so omega fixed points would work