  We determine the effect on the computational complexity of a conformal
anomaly using the Complexity=Action prescription of the gauge/gravity
correspondence. To allow the involvement of said anomaly, we extend previous
studies to include arbitrary values for the anisotropic parameter and the
magnetic field respectively on the Mateos-Trancanelli and the D'Hoker-Kraus
holographic models. Our main result is that the rate of change of the
computational complexity is independent of the conformal anomaly in both cases.
In addition, this allows us to also show that, if so desired, the saturation of
Lloyd's bound at infinite time can be used as a renormalization condition.
