Before revision:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra , we prove that  the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.
After revision:  Morever , exploiting the connection between the PIC-NCP and max-plus algebra we prove that the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent d-periodic trajectory of the same period, for any value of d.