Trying to find A and B I got the following:
A and B = {
(134)(2)()(), (134)()(2)(), (134)()()(2),
(2)(134)()(), ()(134)(2)(), ()(134)()(2),
(2)()(134)(), ()(2)(134)(), ()()(134)(2),
(2)()()(134), ()(2)()(134), ()()(2)(134)
}
Where () is a cell and 1,2,3,4 are the balls labeled...