I am not 100% sure what you are meaning, but I think you convey the notion of \( b^{\dots ^{b^c}} \) to \( u*\dots *u * p_b( c) \).
But thats probably not adequate.
When you do regular iteration the ordering is already contained.
It is about \( h \) time applying a function to an argument.
If the function is exponentiation (letting aside the fixed point shift) then this just means that the argument is on top of the tower and nowhere else.
The method only works for this case.
There is no freedom to rearrange the tower, say be rearring the \( u \)'s and \( p_b( c) \).
Was it that?
But thats probably not adequate.
When you do regular iteration the ordering is already contained.
It is about \( h \) time applying a function to an argument.
If the function is exponentiation (letting aside the fixed point shift) then this just means that the argument is on top of the tower and nowhere else.
The method only works for this case.
There is no freedom to rearrange the tower, say be rearring the \( u \)'s and \( p_b( c) \).
Was it that?