  To investigate the viability of the 4th root trick for the staggered fermion
determinant in a simpler setting, we consider a two taste (flavor) lattice
fermion formulation with no taste mixing but with exact taste-nonsinglet chiral
symmetries analogous to the taste-nonsinglet $U(1)_A$ symmetry of staggered
fermions. M. Creutz's objections to the rooting trick apply just as much in
this setting. To counter them we show that the formulation has robust would-be
zero-modes in topologically nontrivial gauge backgrounds, and that these
manifest themselves in a viable way in the rooted fermion determinant and also
in the disconnected piece of the pseudoscalar meson propagator as required to
solve the U(1) problem. Also, our rooted theory is heuristically seen to be in
the right universality class for QCD if the same is true for an unrooted mixed
fermion action theory.
