$$W(i,j) = \min \left[ \begin{array}{l} W(i-1,j) \\ W(i,j+1) \\ V(i,j) \\ \min_{i\le k<j} \{W(i,k) + W(k+1,j)\} \end{array} \right.\\ V(i,j) = \min \left[ \begin{array}{l} F_1(i,j) \\ \min_{i<h<\ell<j} F_2(i,j,h,\ell) + V(h,\ell)\\ \min_{i+1<k<j-1} W(i+1,k) + W(k+1,j-1) \end{array} \right.$$