  The state space of a machine admits the structure of time. For example, the
geometric realization of a precubical set, a generalization of an unlabeled
asynchronous transition system, admits a "local preorder" encoding control
flow. In the case where time does not loop, the "locally preordered" state
space splits into causally distinct components. The set of such components
often gives a computable invariant of machine behavior. In the general case, no
such meaningful partition could exist. However, as we show in this note, the
locally preordered geometric realization of a precubical set admits a "locally
monotone" covering from a state space in which time does not loop. Thus we hope
to extend geometric techniques in static program analysis to looping processes.
