The key insight of this algorithm is the inner-to-outer dynamic-programming structure: inner modifiers (r) of a head (s) and their "best" labels (l * (s,r) ) are generated before outer ones (t).
using already computed "best" labels of inner dependency edges makes us get rid of maximizing over two labels, l and l. Moreover, we do not have to extend each incomplete span by the augmentation with a "label" index.