In the other direction, if the last tree of an n + 1 tree derivation in G A is of the shape in Figure 3(d), then this implies the 4 It is easy to verify by inspection of Figure 3 that whenever one rule from G can be applied to the output of another rule, then the tree pairs in GXA which correspond to these rules can compose with one another.
we can add the new tree to the existing derivation and be assured that it will compose with one of the trees that is already present.