Preconditions related to rootedness, singleheadedness, and acyclicity follow the arc-eager system straightforwardly: each transition that adds an arc (h, m) checks that m is not the root, m does not already have a head, and that h is not a descendant of m. Preconditions used to guarantee that trees output by the system are within the desired class are listed in Table 4.
they ensure that all crossed arcs are incident to registers, and that each pair of registers entails an interval corresponding to a selfcontained set of crossed edges.