Thank for this reading.
In abstract it was noted that the method "to solve the DLP in an interval of size N with heuristic average case expected running time of close to 1.36√N group operations for groups with fast inversion".

We do not have fast inversions. They also showed in practice that the total number of operations was not 1.36sqrt(N), but 1.46-1.49sqrt(N).

Here fast inversion means that computing u^−1 for any u in the group is much faster  than  a  general  group  operation.