Oh, I am sorry, I actually made a mistake and the time complexity is actually more like $$$O(f\cdot2^f)$$$.

When I saw your code, I deduced that your recursive method is actually just recursing over all subsets(which is equal to $$$2^f$$$) and each recursive call also iterates from $$$i..f$$$ branching more recursive calls. Therefore, $$$2^f$$$ recursive calls, and for each call, we iterate at most $$$f$$$ times making our time complexity $$$O(f\cdot2^f)$$$

If you want a bit more concrete explanation, I can try :), let's denote $$$T(f)$$$ to be the number of operations your recursive method performs for a size $$$f$$$ array. Note that, the $$$T(f)$$$ could be written as $$$T(f)=f+T(f-1)+T(f-2).......$$$.

Now, working some math out $$$T(f)=f+T(f-1)+T(f-2).......\leq f\cdot 2^f$$$ which I will convinentiely skip ;). Hence, our time complexity is $$$O(f\cdot2^f)$$$