What about this example?

    f0 x = (x,x)
    f1 x = f0 (f0 x)
    f2 x = f1 (f1 x)
    f3 x = f2 (f2 x)
    f4 x = f3 (f3 x)

This is worse than O(c^n): the size of the last function's type is O(2^2^n).

(In spacemanaki's blog example, each new expression doubles the size of the previous one. Here, each new expression squares the size. f4 builds 2^2^4 = 65,536 copies of 'x', and f5 will crash your compiler if you define it).