We now define the input to the 2 nd stage for 2-Hard more precisely, Let T be the complete tree that should be output by the 2 nd stage parser and let G be the subgraph of T that is input to the second stage.
then G should satisfy the following constraint: if the arc x → y is in G, then, for every z such that y → z is in t, y → z is also in G. if an arc is included in the 1 st stage partial parse, the complete subtree under the dependent must also be included.