 It is an open question if there is a variation with polynomial time, although sub-exponential pivot rules are known.In 2018, 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.