The lattice description of the affine Grassmannian in type $A$ implies equations for MV cycles (up to translation) are completely determined by equations for orbital varieties, which can be obtained systematically by a Spaltenstein algorithm. Recently, Calder Morton-Ferguson and I used this result to show that the MV basis and the dual semicanonical basis, which agree as crystal bases, are not equal. I will explain the Spaltenstein algorithm, why it works, and how we used it to obtain a counterexample.