Before revision:  When the input is generic, involves s polynomials of degree bounded by D with n quantified variables and t unquantified ones, we prove that this algorithm outputs semi-algebraic formulas of degree bounded by D using O\ {~}\left ( n \ 8^{t}\ D^{3t+2} \ \binom{t+\mathcal{D}}{t} \right ) arithmetic operations in the ground field where \mathcal{D} = n \ D^s(D-1)^{n-s+1}\ \binom{n}{s}.
After revision:  When the input is generic, involves s polynomials of degree bounded by D with n quantified variables and t unquantified ones, we prove that this algorithm outputs semi-algebraic formulas of degree bounded by D using O\ {~}\left ( (n-s+1) \ 8^{t}\ D^{3t+2} \ \binom{t+\mathcal{D}}{t} \right ) arithmetic operations in the ground field where \mathcal{D} = n \ D^s(D-1)^{n-s+1}\ \binom{n}{s}.