  The main objective of this paper is to present an answer to Bressoud's
conjecture for the case $j=0$, resulting in a complete solution to the
conjecture. The case for $j=1$ has been recently resolved by Kim. Using the
connection established in our previous paper between the ordinary partition
function $B_0$ and the overpartition function $\overline{B}_1$, we found that
the proof of Bressoud's conjecture for the case $j=0$ is equivalent to
establishing an overpartition analogue of the conjecture for $j=1$. By
generalizing Kim's method, we obtain the desired overpartition analogue of
Bressoud's conjecture for $j=1$, which eventually enables us to confirm
Bressoud's conjecture for the case $j=0$.
