  We present a pseudoclassical mechanics model which exhibits gauge symmetry
and time-reparametrization invariance. As such, first- and second-class
constraints restrict the phase space, and the Hamiltonian weakly vanishes. We
show that the Dirac conjecture does not hold -- the secondary first-class
constraint is not a symmetry generator -- and only the gauge fixing condition
associated with the primary first-class constraint is needed to remove the
gauge ambiguities. The gauge fixed theory is equivalent to the Fermi harmonic
oscillator extended by a boundary term. We quantize in the deformation
quantization and in the Schrodinger representation approaches and observe that
the boundary term prepares the system in the state of positive energy.
