Fringes capture the fact that in an incremental derivation, a prefix tree can only be combined with an elementary tree at a limited set of nodes.
for instance, the prefix tree in figure 1 has two substitution nodes, for B and C. only substitution into B leads to a valid new prefix tree; if we substitute into C, we obtain the tree in figure 1b, which is not a valid prefix tree (i.e., it represents a non-incremental derivation).