Restricted Proof - Upper Bound of the Sum Over All 2^(-|A|), where A is an Edge Cover of a given Graph is in P

We consider the sum of all 2^(-|A|), where A is an edge cover of a graph G=(V, E), restricted to cases where |E| < 2|V| - 2. We show that this expression, under the given assumptions, is in P. This means that it is in O(Poly(G)) = O(Poly(V, E))