Complexity of recursive algorithm
The obvious algorithm tries all subsets, i.e., is $O(2^n)$ if you have $n$ elements to select. And your algorithm does that (try with first element, try without first element).

Complexity is given by the recurrence:

$$T(n) = 2 T(n - 1), T(0) \text{ given}$$

(try two posibilities for first one, recurse on the $n - 1$ others for each).