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