How to solve multiple minimal covers for functional dependencies?

I have the schema: a,b,c,d,e,g and the following functional dependencies: b->c, dg->ce, bc->dg, e->a, g->bd for which I want to find the minimal cover. It seems that more than one scenario is possible. First I represent the dependencies by splitting the right-hand side: b->c, dg->c, dg->e, bd->d, bc->g, e->a, g->b, g->d For dg->c there's one extraneous attributed. Same goes for dg->e. For bc->d the attribute c is extraneous as well as for bc->g. For g->bd the attribute d is extraneous because if we have g->b then g+ = {gbcd} which contains d. So we have 4 possible minimal covers: b->c, g->c OR g->e, b->d OR b->g, g->b, e->a. The correct answer is g-->c; g-->e; b-->g; e-->a; g-->b; g-->d according to this tool . I cannot get the same answer from simplifying my minimal cover. What am I doing wrong?