  It is usually assumed that any consistent interaction either deforms or
retains the gauge symmetries of the corresponding free theory. We propose a
simple model where an obvious irreducible gauge symmetry does not survive an
interaction, while the interaction is consistent as it preserves the number of
physical degrees of freedom. The model turns out admitting a less obvious
reducible set of gauge generators which is compatible with the interaction and
smooth in coupling constant. Possible application to gravity models is
discussed.
