In the end, the GI index of the VP is better than that of the ill-formed NP: For the same reasons, the higher level construction S also compensates the bad score of the NP.
in the end, the final GI of the sentence is much lower than that of the corresponding wellformed sentence (see above The different figures of the sentence (2b) show that the violation of a unique constraint (in this case the Oblig(Adj) indicating the absence of the head in the AP) can lead to a global lower GI than the violation of two heavy constraints as for (2a).