  Well-known Nuclear Magnetic Resonance experiments show that the time
evolution according to (truncated) dipole-dipole interactions between n spins
can be inverted by simple pulse sequences. Independent of n, the reversed
evolution is only two times slower than the original one. Here we consider more
general spin-spin couplings with long range. We prove that some are
considerably more complex to invert since the number of required time steps and
the slow-down of the reversed evolutions are necessarily of the order n.
Furthermore, the spins have to be addressed separately. We show for which
values of the coupling parameters the phase transition between simple and
complex time-reversal schemes occurs.
