  In the presence of a scalar hair perturbation, the Cauchy horizon of a
Reissner-Nordstr\"om black hole disappears and is replaced by the rapid
collapse of the Einstein-Rosen bridge, which leads to a Kasner singularity
[1,2]. We study the time-dependence of holographic complexity, both for the
volume and for the action proposals, in a class of models with hairy black
holes. Volume complexity can only probe a portion of the black hole interior
that remains far away from the Kasner singularity. We provide numerical
evidence that the Lloyd bound is satisfied by the volume complexity rate in all
the parameter space that we explored. Action complexity can instead probe a
portion of the spacetime closer to the singularity. In particular, the
complexity rate diverges at the critical time $t_c$ for which the
Wheeler-DeWitt patch touches the singularity. After the critical time the
action complexity rate approaches a constant. We find that the Kasner exponent
does not directly affect the details of the divergence of the complexity rate
at $t=t_c$ and the late-time behaviour of the complexity. The Lloyd bound is
violated by action complexity at finite time, because the complexity rate
diverges at $t=t_c$. We find that the Lloyd bound is satisfied by the
asymptotic action complexity rate in all the parameter space that we
investigated.
