I'll make an educated guess... the advancement is knowing that if you make a machine that can bruteforce 6 sides x 2 turn directions, you can stop searching onc

I'll make an educated guess... the advancement is knowing that if you make a machine that can bruteforce 6 sides x 2 turn directions, you can stop searching once a 20th movement is not enough to get the cube solved, and in the worst scenario, you will check ( 6 x 2 )^20 movements in total. I think that scores as test cases :P