Bummer!

[Kouznetsov]

If \( f \) is a function holomorphic and single valued on the complement of a closed countable set in the extended complex plane. Let \( s_1\neq s_2 \) two fixed points of \( f \) such that \( |f'(s_0)|,|f'(s_1)|\neq 0,1 \) and \( f([s_1,s_2])\subseteq [s_1,s_2] \). Then the regular iterations at \( s_1 \) and \( s_2 \) are equal if and only if \( f \) is a fractional linear function. ...

Example: for positive b, let f(z)=z^b.
It has fixed points 0 and 1.
The superfunction for such f is F(z)=exp(b^z)
Does it correspond to some fractional linear Schroeder?