Finally, if p has a head k in G x , then k must be in λ c q and any j such that j ∈ λ c q and k < j must either be a dependent of p in G x or must have a head to the left in both G x and G x (anything else would again be inconsistent with the assumption that G x is projective).
we can construct a transition sequence C 0,m such that G c m = G x , by starting in c 0 = c s (x) and applying exactly the same q transitions as in C 0,q , followed by as many LEFT-ARC p l transitions as there are left dependents of p in G x , interleaving NO-ARC p transitions whenever the node at the head of λ 1 already has a head, followed by a RIGHT-ARC p l transition if p has a head in G x .