In addition, the new child state will be the suffix state of the child state.
the proof of Property F for GSt is achieved by considering the following formulae: given a substring w = xyz, where x, xy, xyz are the longest substrings in their respective classes: the above formulae can be computed in constant time, since each of the involved in the formula can be accessed from root by traversing one of the substrings: w, y, xy and yz.