The problem of coincidence in a theory of temporal multiple recurrence

The coincidence problem is described as: if two complex eventualities (or eventuality sequences) consisting respectively of component eventualities x0,x1,…,xr and y0,y1,…,ys both recur over an interval k and all eventualities are of fixed durations, is there a subinterval of k over which the incidence xt and yu for 0≤t≤r and 0≤u≤s coincide? The solution presented here formalizes the intuition that a solution can be found by temporal projection over a cycle of the multiple recurrence of both sequences.