Assuming that the trees have a nonshared quartet with topology form ab|cd in T, and ad|bc in T', there are two internal nodes in each tree claiming the quartet: vab|c|d and vcd|a|b in T and v′ad|b|c MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG2bGDgaqbamaaBaaaleaacqWGHbqycqWGKbazcqGG8baFcqWGIbGycqGG8baFcqWGJbWyaeqaaaaa@3691@ and v′bc|a|d MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacuWG2bGDgaqbamaaBaaaleaacqWGIbGycqWGJbWycqGG8baFcqWGHbqycqGG8baFcqWGKbazaeqaaaaa@3691@ in T'. All of the four combinations of these will identify the quartet as nonshared. Therefore the total number of nonshared quartets between the two trees is: