In 2014, it was proved that a particular variant of the simplex method is NP-mighty, i.e., it can be used to solve, with polynomial overhead, any problem in NP implicitly during the algorithm's execution. Moreover, deciding whether a given variable ever enters the basis during the algorithm's execution on a given input, and determining the number of iterations needed for solving a given problem, are both NP-hard problems. At about the same time it was shown that there exists an artificial pivot rule for which computing its output is PSPACE-complete. In 2015, this was strengthened to show that computing the output of Dantzig's pivot rule is PSPACE-complete.