X &$r^{\ast}(\epsilon_{0}) - \mu^-$ & $r^{\ast}(\epsilon_{0})$ &-\
W &$-r^{\ast}(\epsilon_{0}) +\mu^-$ &$r^{\ast}(\epsilon_{0})$ &-\
Y &$r^{\ast}(\epsilon_{0}) + \mu^+$ & $r^{\ast}(\epsilon_{0})$ &-\
Z &$-r^{\ast}(\epsilon_{0}) - \mu^+$ &$r^{\ast}(\epsilon_{0})$ &-\
P &$\frac{-1}{2}( \mu^+ + \mu^-)$ &$\frac{1}{2}( \mu^- - \mu^+)$ &+\
Q &$\frac{1}{2}(\mu^+ + \mu^-)$ &$\frac{1}{2}( \mu^- - \mu^{+})$ &+\

In the calculation of [@Carmi:2017jqz] for the asymptotically AdS black holes the complexity growth is evaluated in the time that is given by adding left and right times. For the asymptotically flat cases, besides left and right development, the lower and upper sides of the WDW path can develop independently. The origin of this difference is that the times of past and future null infinities are given by advanced and retarded times. In order to reproduce the results that are given by taking the flat space limit, we have to consider symmetric evolution on the future and past null infinities. Precisely, we need to calculate the rate of complexity growth with respect to $\mu$ where $$\label{symmetricquantity}
  \mu^+ = \mu^- + \chi,  \qquad \mu^+ +\mu^- =\mu,$$ where $\chi$ is a constant. In Appendix A we calculate the nonsymmetric evolution by considering the $\mu^+ = \gamma \mu^-+\chi$ case. The results of taking the flat space limit are given 