The last point to mention is that the goal of the AR method is to generate a quasioptimal 'converged order' to reduce the scalar part in X rather than to optimize the energy functional. Owing to this imperfect starting point, 'converged order' is not guaranteed to give a lower energy than the input one or the other orders generated in the intermediate steps of AR. The mechanism of the AR method is to generate an 'converged order' which is close to an order-independent Ansätze and the energy of 'converged order' Ansätze is regarded as an upper bound of the solution. Therefore, all the sequences generated by each step of AR and their corresponding optimized energy should be stored, and the final output sequence is the one which has the lowest energy.