  Gauge symmetries lead to first-class constraints. This assertion is of course
true only for non trivial gauge symmetries, i.e., gauge symmetries that act non
trivially on-shell on the dynamical variables. We illustrate this
well-appreciated fact for time reparametrization invariance in the context of
modifications of gravity -suggested in a recent proposal by Horava-in which the
Hamiltonian constraint is deformed by arbitrary spatial diffeomorphism
invariant terms, where some subtleties are found to arise.
