Before revision:  consequently, we prove that the same algorithm can be used to find d-periodic trajectories in P-TEGs faster than with previous approaches .
After revision:  consequently, we prove that the same algorithm can be used to find d-periodic trajectories in P-TEGs . 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 .