  We investigate the sensitivity of the next generation of flavor-based
low-energy experiments to probe the supersymmetric parameter space in the
context of the phenomenological MSSM (pMSSM), and examine the complementarity
with direct searches for Supersymmetry at the 13 TeV LHC in a quantitative
manner. To this end, we enlarge the previously studied pMSSM parameter space to
include all physical non-zero CP-violating phases, namely those associated with
the gaugino mass parameters, Higgsino mass parameter, and the tri-linear
couplings of the top quark, bottom quark and tau lepton. We find that future
electric dipole moment and flavor measurements can have a strong impact on the
viability of these models even if the sparticle spectrum is out of reach of the
13 TeV LHC. In particular, the lack of positive signals in future low-energy
probes would exclude values of the phases between ${\cal O}(10^{-2})$ and
${\cal O}(10^{-1})$. We also find regions of parameter space where large phases
remain allowed due to cancellations. Most interestingly, in some rare
processes, such as BR($B_s \to \mu^+ \mu^-$ ), we find that contributions
arising from CP-violating phases can bring the potentially large SUSY
contributions into better agreement with experiment and Standard Model
predictions.
