The computations in the second situation have the same fidelity and granularity as the first, and are morally equivalent. Your X is bigger (and therefore takes more to compute) than A(S), exactly because it contains both worlds. At any point in the physics simulation, you can subtract out Rt and get A(S)t.

OK, but this only moves the problem to a different place. Say I can find an operation that let's me transform the data irreversibly, in such a way that I can still get my computations and answers done, but no way of getting the original states back. What would you say then?