On Heegaard splittings with finite many pairs of disjoint compression disks

Suppose $V{\cup }_{S}W$ is a weakly reducible Heegaard splitting of a closed 3-manifold which admits only $n$ pairs of disjoint compression disks on distinct sides and $g>2$. We show $V{\cup }_{S}W$ admits an untelescoping: $(V_1{\cup }_{S_1}{W}_1){\cup }_F(W_2{\cup }_{S_2}{V}_2)$ such that $W_i$ has only one separating compressing disk and $d(S_i)\ge 2$, for $i=1,2$. If $n>1$, at least one of $d(S_i)$ is 2 and $S$ is a critical Heegaard surface.