The decomposition can continue as long as there exists a real number $c$, such that the Lagrangian components can be partitioned into two types, with Lagrangian potential strictly smaller than $c$ (resp. greater than $c$). As long as $\inf_{L_{i}}f_{L_{i}}>\sup_{L_{j}}f_{L_{j}}$ whenever $i>j$, the Novikov positivity condition on the Lagrangian intersection points would imply that the entries $b_{ij}\in CF^{1}(L_{i},L_{j})$ of $b$ can only go in the direction $i>j$ and not vice versa, so the immersed Lagrangian $L$ is necessarily of the twisted complex form. This algorithm stops in finitely many steps since there are only finitely many components involved. ∎