YES After renaming modulo { 0->0, 2->1, 1->2, 3->3 }, it remains to prove termination of the 81-rule system { 0 0 0 0 1 1 0 2 3 2 1 3 2 0 1 0 3 3 -> 0 0 1 1 3 3 0 0 3 0 0 1 1 0 2 2 2 3 , 0 0 0 3 2 1 3 2 1 0 2 2 3 1 3 2 2 1 -> 0 3 0 2 3 2 2 2 0 0 1 1 2 2 3 1 1 3 , 0 0 2 2 1 1 3 0 2 3 2 3 3 2 3 3 0 3 -> 0 3 2 2 0 1 3 2 0 0 2 1 3 3 3 2 3 3 , 0 0 2 1 2 3 2 1 0 2 1 0 3 3 3 2 2 1 -> 1 3 1 3 2 2 2 2 3 0 1 2 0 3 2 0 0 1 , 0 0 2 1 3 1 2 1 2 1 2 3 0 1 2 2 1 1 -> 1 1 0 1 1 2 2 2 1 0 0 3 2 2 2 3 1 1 , 0 0 2 3 0 2 3 2 2 0 3 0 2 3 0 3 0 3 -> 0 0 0 0 3 2 3 0 2 2 3 3 3 0 2 2 3 0 , 0 0 2 3 2 3 1 3 3 2 1 0 2 3 3 0 2 2 -> 1 3 3 2 2 3 0 3 0 2 3 0 0 2 3 1 2 2 , 0 2 0 3 0 1 0 2 3 0 3 0 2 1 1 0 0 3 -> 0 3 0 0 0 1 1 2 0 0 3 0 1 3 3 2 2 0 , 0 2 2 3 3 2 3 3 2 1 2 2 3 0 1 0 2 1 -> 0 3 1 2 1 2 2 2 2 2 0 3 0 1 3 3 2 3 , 0 2 1 0 2 2 2 1 2 2 1 2 0 3 0 2 0 2 -> 2 1 0 0 0 1 2 0 1 2 2 2 2 3 2 2 0 2 , 0 2 1 2 1 0 3 3 2 1 2 3 2 1 2 3 2 0 -> 1 3 1 2 2 2 2 0 1 1 2 2 0 3 3 2 0 3 , 0 2 1 1 2 1 1 0 0 2 0 3 0 2 2 3 3 2 -> 0 2 0 3 2 0 1 2 3 1 3 0 1 1 2 2 0 2 , 0 2 1 3 2 0 2 0 1 2 3 1 2 1 0 2 0 2 -> 0 1 0 2 2 1 3 3 2 1 0 1 0 2 2 2 0 2 , 0 1 2 1 3 2 3 0 1 0 3 1 3 2 3 3 1 0 -> 1 3 3 0 1 3 3 1 0 0 3 1 2 2 2 3 1 0 , 0 1 2 3 2 1 3 0 2 3 1 1 3 2 2 2 0 2 -> 1 0 3 2 0 1 3 1 2 1 3 0 2 2 2 2 3 2 , 0 3 0 2 3 2 3 0 1 3 0 2 1 1 2 0 2 0 -> 0 3 3 2 1 3 0 0 3 0 0 2 2 2 2 1 1 0 , 0 3 0 1 2 1 2 3 3 0 0 0 3 2 1 3 0 2 -> 0 1 3 0 2 0 0 3 3 3 2 0 0 1 3 1 2 2 , 0 3 2 0 0 2 3 3 3 1 0 0 3 2 3 3 2 3 -> 0 3 3 3 3 1 3 0 2 3 0 2 2 0 2 0 3 3 , 0 3 1 2 3 2 1 1 0 0 0 3 1 0 2 0 2 3 -> 1 3 0 3 1 2 2 2 2 0 3 0 1 0 0 0 3 1 , 0 3 3 0 1 3 0 2 1 2 2 3 3 1 0 3 0 1 -> 0 3 1 3 3 0 3 1 3 3 2 2 0 0 1 2 0 1 , 0 3 3 3 1 2 3 2 2 1 1 1 0 1 0 2 2 2 -> 0 1 0 1 1 3 2 2 2 2 3 1 3 1 3 0 2 2 , 2 0 2 1 3 2 2 3 3 0 3 2 3 2 2 0 2 2 -> 2 2 2 2 0 1 3 0 0 2 2 3 3 2 3 3 2 2 , 2 0 1 2 0 3 1 3 2 3 0 2 2 0 1 3 0 1 -> 2 1 2 2 0 1 1 2 2 0 3 3 3 0 3 0 0 1 , 2 0 1 1 1 1 3 3 0 0 3 0 3 1 0 2 3 0 -> 2 2 3 1 0 1 3 3 0 1 0 0 1 3 1 3 0 0 , 2 0 3 1 1 3 1 0 2 3 3 2 2 3 2 0 2 0 -> 2 2 0 3 0 0 3 1 2 0 2 2 3 3 1 2 1 3 , 2 2 0 0 2 0 1 1 2 0 2 0 2 3 2 2 3 3 -> 2 2 2 3 0 2 3 0 1 2 2 1 2 2 0 0 3 0 , 2 2 0 3 3 3 2 1 2 1 3 2 0 2 0 0 2 1 -> 2 2 2 0 2 2 2 2 3 3 0 1 1 1 3 3 0 0 , 2 2 1 0 0 2 3 0 2 3 0 3 1 0 2 1 0 0 -> 2 2 0 0 3 1 0 2 3 0 1 3 1 0 2 2 0 0 , 2 2 3 2 1 0 0 1 2 0 0 0 2 3 3 2 1 3 -> 2 2 2 2 1 1 0 3 3 2 3 0 3 2 0 0 0 1 , 2 2 3 3 2 0 0 2 0 1 3 3 0 2 3 2 0 2 -> 2 3 0 0 3 0 3 3 2 1 3 0 2 2 2 2 0 2 , 2 1 0 0 2 1 0 2 2 1 2 3 2 2 0 3 2 1 -> 2 2 2 2 0 2 2 1 0 1 2 1 2 0 3 0 1 3 , 2 1 0 3 0 2 2 3 0 0 0 2 1 2 0 1 0 3 -> 2 3 1 1 2 0 0 0 0 3 3 1 2 0 2 2 0 0 , 2 1 2 3 2 0 3 1 1 1 3 3 1 2 1 2 3 3 -> 2 1 1 2 3 1 1 1 3 3 2 3 1 0 3 2 2 3 , 2 1 1 1 3 3 0 1 2 3 2 1 1 2 2 0 2 2 -> 2 1 1 1 3 0 2 3 2 1 1 0 3 1 2 2 2 2 , 2 1 3 1 0 2 3 3 2 1 0 2 3 1 1 3 3 3 -> 2 1 0 3 3 1 2 1 0 3 3 3 1 2 2 3 1 3 , 2 3 0 3 3 1 3 2 3 1 3 0 2 3 2 3 3 0 -> 2 3 0 2 2 3 0 1 1 3 3 3 2 3 3 3 3 0 , 2 3 2 1 2 2 0 2 0 1 1 3 2 0 3 2 1 2 -> 2 2 0 0 2 1 3 3 2 2 3 0 2 2 1 1 1 2 , 2 3 2 1 1 2 3 0 3 2 1 3 3 2 0 0 3 3 -> 2 3 0 1 2 0 2 1 3 0 3 3 3 2 2 1 3 3 , 2 3 1 2 3 1 0 2 2 2 3 2 2 1 2 3 1 1 -> 2 2 3 2 0 1 2 2 3 1 2 2 2 3 1 1 3 1 , 2 3 1 3 0 1 1 2 1 0 0 3 2 3 1 0 2 3 -> 2 3 0 0 1 2 1 3 3 2 2 0 3 1 0 1 1 3 , 2 3 3 0 2 0 0 1 0 0 2 3 2 3 2 0 2 3 -> 2 2 3 0 3 0 0 2 2 3 1 0 3 3 2 0 2 0 , 1 0 1 0 1 0 3 2 1 0 2 3 2 2 0 2 2 0 -> 1 2 2 2 0 0 1 3 0 0 2 2 2 3 1 1 0 0 , 1 2 0 2 1 2 2 0 1 3 2 2 1 2 0 2 2 1 -> 1 2 0 0 2 1 1 2 2 0 2 2 2 1 2 3 2 1 , 1 2 1 1 2 0 2 1 3 3 2 0 2 2 1 0 2 2 -> 1 2 3 0 0 2 3 0 1 1 2 1 2 2 2 1 2 2 , 1 2 3 2 1 2 2 0 0 2 0 1 2 1 1 2 2 1 -> 1 2 2 1 2 2 0 0 2 2 1 0 3 1 1 2 2 1 , 1 2 3 2 1 2 3 3 0 1 0 1 2 1 1 3 0 1 -> 1 2 1 1 2 2 1 3 3 1 0 1 1 0 2 3 0 3 , 1 1 0 1 1 1 2 1 2 3 0 0 2 0 3 3 0 0 -> 1 0 1 0 2 3 1 1 1 2 0 0 3 1 2 3 0 0 , 1 1 0 1 1 3 1 0 3 3 0 3 0 0 3 1 1 3 -> 1 3 1 3 1 0 3 3 1 0 3 0 0 1 0 1 1 3 , 1 1 2 1 3 2 2 2 0 1 3 3 3 0 2 0 1 3 -> 1 1 2 2 2 2 1 1 2 3 0 3 0 0 3 3 1 3 , 1 1 1 1 0 3 1 1 0 3 2 0 2 3 3 2 0 1 -> 1 1 1 1 2 0 1 1 2 0 3 2 0 3 0 3 3 1 , 1 1 3 2 3 0 0 3 2 3 1 0 2 2 3 3 3 0 -> 3 0 0 1 1 3 1 3 2 2 2 2 3 3 3 0 3 0 , 1 3 2 0 2 3 3 2 1 2 3 0 1 0 3 3 2 0 -> 3 2 2 2 0 3 1 2 3 0 3 2 0 1 0 1 3 3 , 1 3 2 1 0 0 3 1 1 1 1 0 0 0 2 0 2 3 -> 1 1 0 1 1 1 0 0 3 0 3 3 0 2 2 0 2 1 , 1 3 1 3 1 3 0 1 3 0 3 0 2 0 1 3 3 3 -> 1 3 0 3 3 1 3 1 2 0 0 3 1 0 3 1 3 3 , 1 3 3 2 1 2 3 0 0 3 2 3 0 3 2 0 2 1 -> 1 1 1 3 3 2 0 3 3 2 2 3 0 0 3 2 2 0 , 1 3 3 1 3 3 2 3 1 3 1 3 3 1 2 3 1 3 -> 1 3 1 3 1 1 2 3 1 2 3 3 3 3 3 3 1 3 , 3 0 0 0 2 0 1 1 2 1 3 1 3 0 2 0 0 1 -> 3 0 2 0 0 1 1 3 3 1 0 2 2 0 0 1 0 1 , 3 0 0 3 0 1 3 2 1 0 0 2 1 3 0 0 0 2 -> 3 0 2 0 0 0 0 1 2 0 1 1 0 3 3 0 3 2 , 3 0 2 0 0 2 2 3 2 2 3 0 0 2 3 2 3 3 -> 3 3 0 2 3 2 2 0 2 2 2 3 0 3 3 0 2 0 , 3 0 2 1 0 0 1 0 0 2 3 0 2 2 2 0 2 2 -> 0 1 2 2 2 2 0 0 2 0 3 0 3 0 1 0 2 2 , 3 0 2 3 3 2 2 3 2 1 2 2 3 1 3 2 0 2 -> 3 2 2 3 3 2 3 3 0 2 1 2 2 3 1 2 0 2 , 3 0 1 3 1 0 3 2 0 3 3 2 2 1 3 2 3 2 -> 3 1 3 1 3 3 2 2 2 3 0 0 3 0 1 2 3 2 , 3 0 3 0 2 2 1 2 1 3 3 2 0 1 1 3 2 1 -> 1 0 2 3 3 3 1 3 1 0 2 2 2 1 0 1 2 3 , 3 2 0 0 1 0 2 2 1 2 3 1 1 1 1 0 0 0 -> 1 3 1 2 0 1 3 2 0 0 2 2 1 1 1 0 0 0 , 3 2 0 1 0 3 2 0 1 1 1 3 2 1 1 3 2 3 -> 1 1 3 2 1 3 0 1 3 1 3 0 0 3 2 2 2 1 , 3 2 0 3 2 1 1 3 2 3 3 3 1 2 2 3 0 2 -> 1 3 1 2 1 3 3 2 2 3 3 2 2 0 3 3 0 2 , 3 2 1 2 3 0 0 1 2 1 3 1 0 2 3 2 3 3 -> 3 2 2 3 0 3 2 3 1 3 0 1 2 3 1 1 2 0 , 3 2 1 3 1 1 1 1 1 2 0 2 0 1 0 0 0 3 -> 3 1 3 1 0 2 0 1 2 0 1 1 2 1 1 0 0 3 , 3 2 3 2 1 2 0 2 0 3 3 2 1 3 3 3 0 3 -> 3 3 3 2 2 0 3 0 1 2 2 3 2 3 3 1 0 3 , 3 2 3 2 1 3 0 1 3 3 2 3 2 2 1 2 0 0 -> 1 0 3 2 3 2 1 2 3 3 3 2 2 3 1 2 0 0 , 3 2 3 1 2 3 2 0 2 1 1 3 3 0 3 3 2 2 -> 3 3 3 2 1 0 1 2 3 1 3 3 3 0 2 2 2 2 , 3 2 3 1 1 1 1 3 1 0 3 0 0 3 1 1 1 1 -> 1 1 2 0 3 1 1 1 3 0 0 1 3 3 3 1 1 1 , 3 1 1 1 2 0 2 3 2 2 1 3 2 0 2 2 3 3 -> 3 2 1 3 2 2 2 3 0 1 1 1 3 2 2 2 0 3 , 3 3 0 1 2 1 1 3 2 1 0 1 0 2 3 0 0 2 -> 1 2 3 1 3 3 1 3 0 0 0 1 0 0 1 2 2 2 , 3 3 2 0 1 2 1 2 3 3 2 3 2 1 3 1 2 0 -> 3 3 1 2 2 2 2 2 3 3 3 1 0 3 2 1 0 1 , 3 3 2 0 3 0 3 1 1 1 3 2 2 1 3 1 2 3 -> 1 2 2 2 3 0 3 1 0 1 3 3 3 1 2 1 3 3 , 3 3 2 2 1 3 1 2 1 2 1 3 0 0 1 1 2 2 -> 3 1 2 1 2 1 3 0 1 3 3 1 0 1 2 2 2 2 , 3 3 1 2 0 1 3 2 1 1 1 1 2 3 3 0 3 1 -> 3 1 3 0 1 1 2 2 3 3 1 2 0 3 1 1 3 1 , 3 3 1 1 3 0 3 2 1 3 3 0 2 1 2 1 0 1 -> 3 1 2 2 1 3 1 1 2 3 3 3 0 0 3 0 1 1 , 3 3 3 2 0 1 2 0 2 3 3 2 3 3 3 0 2 1 -> 3 3 0 3 3 1 2 0 1 3 3 3 2 0 2 2 2 3 , 0 2 1 3 ->= 0 2 1 3 } The system was reversed. After renaming modulo { 3->0, 0->1, 1->2, 2->3 }, it remains to prove termination of the 81-rule system { 0 0 1 2 1 3 0 2 3 0 3 1 2 2 1 1 1 1 -> 0 3 3 3 1 2 2 1 1 0 1 1 0 0 2 2 1 1 , 2 3 3 0 2 0 3 3 1 2 3 0 2 3 0 1 1 1 -> 0 2 2 0 3 3 2 2 1 1 3 3 3 0 3 1 0 1 , 0 1 0 0 3 0 0 3 0 3 1 0 2 2 3 3 1 1 -> 0 0 3 0 0 0 2 3 1 1 3 0 2 1 3 3 0 1 , 2 3 3 0 0 0 1 2 3 1 2 3 0 3 2 3 1 1 -> 2 1 1 3 0 1 3 2 1 0 3 3 3 3 0 2 0 2 , 2 2 3 3 2 1 0 3 2 3 2 3 2 0 2 3 1 1 -> 2 2 0 3 3 3 0 1 1 2 3 3 3 2 2 1 2 2 , 0 1 0 1 0 3 1 0 1 3 3 0 3 1 0 3 1 1 -> 1 0 3 3 1 0 0 0 3 3 1 0 3 0 1 1 1 1 , 3 3 1 0 0 3 1 2 3 0 0 2 0 3 0 3 1 1 -> 3 3 2 0 3 1 1 0 3 1 0 1 0 3 3 0 0 2 , 0 1 1 2 2 3 1 0 1 0 3 1 2 1 0 1 3 1 -> 1 3 3 0 0 2 1 0 1 1 3 2 2 1 1 1 0 1 , 2 3 1 2 1 0 3 3 2 3 0 0 3 0 0 3 3 1 -> 0 3 0 0 2 1 0 1 3 3 3 3 3 2 3 2 0 1 , 3 1 3 1 0 1 3 2 3 3 2 3 3 3 1 2 3 1 -> 3 1 3 3 0 3 3 3 3 2 1 3 2 1 1 1 2 3 , 1 3 0 3 2 3 0 3 2 3 0 0 1 2 3 2 3 1 -> 0 1 3 0 0 1 3 3 2 2 1 3 3 3 3 2 0 2 , 3 0 0 3 3 1 0 1 3 1 1 2 2 3 2 2 3 1 -> 3 1 3 3 2 2 1 0 2 0 3 2 1 3 0 1 3 1 , 3 1 3 1 2 3 2 0 3 2 1 3 1 3 0 2 3 1 -> 3 1 3 3 3 1 2 1 2 3 0 0 2 3 3 1 2 1 , 1 2 0 0 3 0 2 0 1 2 1 0 3 0 2 3 2 1 -> 1 2 0 3 3 3 2 0 1 1 2 0 0 2 1 0 0 2 , 3 1 3 3 3 0 2 2 0 3 1 0 2 3 0 3 2 1 -> 3 0 3 3 3 3 1 0 2 3 2 0 2 1 3 0 1 2 , 1 3 1 3 2 2 3 1 0 2 1 0 3 0 3 1 0 1 -> 1 2 2 3 3 3 3 1 1 0 1 1 0 2 3 0 0 1 , 3 1 0 2 3 0 1 1 1 0 0 3 2 3 2 1 0 1 -> 3 3 2 0 2 1 1 3 0 0 0 1 1 3 1 0 2 1 , 0 3 0 0 3 0 1 1 2 0 0 0 3 1 1 3 0 1 -> 0 0 1 3 1 3 3 1 0 3 1 0 2 0 0 0 0 1 , 0 3 1 3 1 2 0 1 1 1 2 2 3 0 3 2 0 1 -> 2 0 1 1 1 2 1 0 1 3 3 3 3 2 0 1 0 2 , 2 1 0 1 2 0 0 3 3 2 3 1 0 2 1 0 0 1 -> 2 1 3 2 1 1 3 3 0 0 2 0 1 0 0 2 0 1 , 3 3 3 1 2 1 2 2 2 3 3 0 3 2 0 0 0 1 -> 3 3 1 0 2 0 2 0 3 3 3 3 0 2 2 1 2 1 , 3 3 1 3 3 0 3 0 1 0 0 3 3 0 2 3 1 3 -> 3 3 0 0 3 0 0 3 3 1 1 0 2 1 3 3 3 3 , 2 1 0 2 1 3 3 1 0 3 0 2 0 1 3 2 1 3 -> 2 1 1 0 1 0 0 0 1 3 3 2 2 1 3 3 2 3 , 1 0 3 1 2 0 1 0 1 1 0 0 2 2 2 2 1 3 -> 1 1 0 2 0 2 1 1 2 1 0 0 2 1 2 0 3 3 , 1 3 1 3 0 3 3 0 0 3 1 2 0 2 2 0 1 3 -> 0 2 3 2 0 0 3 3 1 3 2 0 1 1 0 1 3 3 , 0 0 3 3 0 3 1 3 1 3 2 2 1 3 1 1 3 3 -> 1 0 1 1 3 3 2 3 3 2 1 0 3 1 0 3 3 3 , 2 3 1 1 3 1 3 0 2 3 2 3 0 0 0 1 3 3 -> 1 1 0 0 2 2 2 1 0 0 3 3 3 3 1 3 3 3 , 1 1 2 3 1 2 0 1 0 3 1 0 3 1 1 2 3 3 -> 1 1 3 3 1 2 0 2 1 0 3 1 2 0 1 1 3 3 , 0 2 3 0 0 3 1 1 1 3 2 1 1 2 3 0 3 3 -> 2 1 1 1 3 0 1 0 3 0 0 1 2 2 3 3 3 3 , 3 1 3 0 3 1 0 0 2 1 3 1 1 3 0 0 3 3 -> 3 1 3 3 3 3 1 0 2 3 0 0 1 0 1 1 0 3 , 2 3 0 1 3 3 0 3 2 3 3 1 2 3 1 1 2 3 -> 0 2 1 0 1 3 2 3 2 1 2 3 3 1 3 3 3 3 , 0 1 2 1 3 2 3 1 1 1 0 3 3 1 0 1 2 3 -> 1 1 3 3 1 3 2 0 0 1 1 1 1 3 2 2 0 3 , 0 0 3 2 3 2 0 0 2 2 2 0 1 3 0 3 2 3 -> 0 3 3 0 1 2 0 3 0 0 2 2 2 0 3 2 2 3 , 3 3 1 3 3 2 2 3 0 3 2 1 0 0 2 2 2 3 -> 3 3 3 3 2 0 1 2 2 3 0 3 1 0 2 2 2 3 , 0 0 0 2 2 0 3 1 2 3 0 0 3 1 2 0 2 3 -> 0 2 0 3 3 2 0 0 0 1 2 3 2 0 0 1 2 3 , 1 0 0 3 0 3 1 0 2 0 3 0 2 0 0 1 0 3 -> 1 0 0 0 0 3 0 0 0 2 2 1 0 3 3 1 0 3 , 3 2 3 0 1 3 0 2 2 1 3 1 3 3 2 3 0 3 -> 3 2 2 2 3 3 1 0 3 3 0 0 2 3 1 1 3 3 , 0 0 1 1 3 0 0 2 3 0 1 0 3 2 2 3 0 3 -> 0 0 2 3 3 0 0 0 1 0 2 3 1 3 2 1 0 3 , 2 2 0 3 2 3 3 0 3 3 3 1 2 0 3 2 0 3 -> 2 0 2 2 0 3 3 3 2 0 3 3 2 1 3 0 3 3 , 0 3 1 2 0 3 0 1 1 2 3 2 2 1 0 2 0 3 -> 0 2 2 1 2 0 1 3 3 0 0 2 3 2 1 1 0 3 , 0 3 1 3 0 3 0 3 1 1 2 1 1 3 1 0 0 3 -> 1 3 1 3 0 0 1 2 0 3 3 1 1 0 1 0 3 3 , 1 3 3 1 3 3 0 3 1 2 3 0 1 2 1 2 1 2 -> 1 1 2 2 0 3 3 3 1 1 0 2 1 1 3 3 3 2 , 2 3 3 1 3 2 3 3 0 2 1 3 3 2 3 1 3 2 -> 2 3 0 3 2 3 3 3 1 3 3 2 2 3 1 1 3 2 , 3 3 1 2 3 3 1 3 0 0 2 3 1 3 2 2 3 2 -> 3 3 2 3 3 3 2 3 2 2 1 0 3 1 1 0 3 2 , 2 3 3 2 2 3 2 1 3 1 1 3 3 2 3 0 3 2 -> 2 3 3 2 2 0 1 2 3 3 1 1 3 3 2 3 3 2 , 2 1 0 2 2 3 2 1 2 1 0 0 3 2 3 0 3 2 -> 0 1 0 3 1 2 2 1 2 0 0 2 3 3 2 2 3 2 , 1 1 0 0 1 3 1 1 0 3 2 3 2 2 2 1 2 2 -> 1 1 0 3 2 0 1 1 3 2 2 2 0 3 1 2 1 2 , 0 2 2 0 1 1 0 1 0 0 1 2 0 2 2 1 2 2 -> 0 2 2 1 2 1 1 0 1 2 0 0 1 2 0 2 0 2 , 0 2 1 3 1 0 0 0 2 1 3 3 3 0 2 3 2 2 -> 0 2 0 0 1 1 0 1 0 3 2 2 3 3 3 3 2 2 , 2 1 3 0 0 3 1 3 0 1 2 2 0 1 2 2 2 2 -> 2 0 0 1 0 1 3 0 1 3 2 2 1 3 2 2 2 2 , 1 0 0 0 3 3 1 2 0 3 0 1 1 0 3 0 2 2 -> 1 0 1 0 0 0 3 3 3 3 0 2 0 2 2 1 1 0 , 1 3 0 0 1 2 1 0 3 2 3 0 0 3 1 3 0 2 -> 0 0 2 1 2 1 3 0 1 0 3 2 0 1 3 3 3 0 , 0 3 1 3 1 1 1 2 2 2 2 0 1 1 2 3 0 2 -> 2 3 1 3 3 1 0 0 1 0 1 1 2 2 2 1 2 2 , 0 0 0 2 1 3 1 0 1 0 2 1 0 2 0 2 0 2 -> 0 0 2 0 1 2 0 1 1 3 2 0 2 0 0 1 0 2 , 2 3 1 3 0 1 0 3 0 1 1 0 3 2 3 0 0 2 -> 1 3 3 0 1 1 0 3 3 0 0 1 3 0 0 2 2 2 , 0 2 0 3 2 0 0 2 0 2 0 3 0 0 2 0 0 2 -> 0 2 0 0 0 0 0 0 3 2 0 3 2 2 0 2 0 2 , 2 1 1 3 1 0 2 0 2 3 2 2 1 3 1 1 1 0 -> 2 1 2 1 1 3 3 1 2 0 0 2 2 1 1 3 1 0 , 3 1 1 1 0 2 3 1 1 2 3 0 2 1 0 1 1 0 -> 3 0 1 0 0 1 2 2 1 3 2 1 1 1 1 3 1 0 , 0 0 3 0 3 1 1 0 3 3 0 3 3 1 1 3 1 0 -> 1 3 1 0 0 1 0 3 3 3 1 3 3 0 3 1 0 0 , 3 3 1 3 3 3 1 0 3 1 1 2 1 1 2 3 1 0 -> 3 3 1 2 1 0 1 0 1 3 1 1 3 3 3 3 2 1 , 3 1 3 0 2 0 3 3 2 3 0 3 3 0 0 3 1 0 -> 3 1 3 2 0 3 3 2 3 1 0 0 3 0 0 3 3 0 , 3 0 3 0 2 3 3 0 0 1 3 0 1 2 0 2 1 0 -> 3 0 3 2 1 0 1 1 0 3 3 3 0 0 2 0 2 0 , 2 3 0 2 2 1 3 0 0 2 3 2 3 3 1 0 1 0 -> 0 3 2 1 2 3 3 3 1 2 0 2 0 0 0 3 1 2 , 1 1 1 2 2 2 2 0 3 2 3 3 1 2 1 1 3 0 -> 1 1 1 2 2 2 3 3 1 1 3 0 2 1 3 2 0 2 , 0 3 0 2 2 3 0 2 2 2 1 3 0 1 2 1 3 0 -> 2 3 3 3 0 1 1 0 2 0 2 1 0 2 3 0 2 2 , 3 1 0 3 3 2 0 0 0 3 0 2 2 3 0 1 3 0 -> 3 1 0 0 1 3 3 0 0 3 3 0 0 2 3 2 0 2 , 0 0 3 0 3 1 2 0 2 3 2 1 1 0 3 2 3 0 -> 1 3 2 2 0 3 2 1 0 2 0 3 0 1 0 3 3 0 , 0 1 1 1 2 1 3 1 3 2 2 2 2 2 0 2 3 0 -> 0 1 1 2 2 3 2 2 1 3 2 1 3 1 2 0 2 0 , 0 1 0 0 0 2 3 0 0 1 3 1 3 2 3 0 3 0 -> 0 1 2 0 0 3 0 3 3 2 1 0 1 3 3 0 0 0 , 1 1 3 2 3 3 0 3 0 0 2 1 0 2 3 0 3 0 -> 1 1 3 2 0 3 3 0 0 0 3 2 3 0 3 0 1 2 , 3 3 0 0 1 0 0 2 2 3 1 3 0 3 2 0 3 0 -> 3 3 3 3 1 0 0 0 2 0 3 2 1 2 3 0 0 0 , 2 2 2 2 0 1 1 0 1 2 0 2 2 2 2 0 3 0 -> 2 2 2 0 0 0 2 1 1 0 2 2 2 0 1 3 2 2 , 0 0 3 3 1 3 0 2 3 3 0 3 1 3 2 2 2 0 -> 0 1 3 3 3 0 2 2 2 1 0 3 3 3 0 2 3 0 , 3 1 1 0 3 1 2 1 2 3 0 2 2 3 2 1 0 0 -> 3 3 3 2 1 1 2 1 1 1 0 2 0 0 2 0 3 2 , 1 3 2 0 2 3 0 3 0 0 3 2 3 2 1 3 0 0 -> 2 1 2 3 0 1 2 0 0 0 3 3 3 3 3 2 0 0 , 0 3 2 0 2 3 3 0 2 2 2 0 1 0 1 3 0 0 -> 0 0 2 3 2 0 0 0 2 1 2 0 1 0 3 3 3 2 , 3 3 2 2 1 1 0 2 3 2 3 2 0 2 3 3 0 0 -> 3 3 3 3 2 1 2 0 0 2 1 0 2 3 2 3 2 0 , 2 0 1 0 0 3 2 2 2 2 3 0 2 1 3 2 0 0 -> 2 0 2 2 0 1 3 2 0 0 3 3 2 2 1 0 2 0 , 2 1 2 3 2 3 1 0 0 2 3 0 1 0 2 2 0 0 -> 2 2 1 0 1 1 0 0 0 3 2 2 0 2 3 3 2 0 , 2 3 1 0 0 0 3 0 0 3 1 3 2 1 3 0 0 0 -> 0 3 3 3 1 3 0 0 0 2 1 3 2 0 0 1 0 0 , 0 2 3 1 ->= 0 2 3 1 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 2]->2, [2, 1]->3, [1, 3]->4, [3, 0]->5, [0, 2]->6, [2, 3]->7, [0, 3]->8, [3, 1]->9, [2, 2]->10, [1, 1]->11, [1, 0]->12, [3, 3]->13, [2, 0]->14, [3, 2]->15 }, it remains to prove termination of the 1296-rule system { 0 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 12 -> 0 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 12 , 6 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 12 -> 0 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 12 , 0 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 12 -> 0 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 12 , 6 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 12 -> 6 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 14 , 6 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 12 -> 6 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 14 , 0 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 12 -> 1 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 12 , 8 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 12 -> 8 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 14 , 0 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 12 -> 1 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 12 , 6 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 12 -> 0 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 12 , 8 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 12 -> 8 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 5 , 1 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 12 -> 0 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 14 , 8 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 12 -> 8 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 12 , 8 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 12 -> 8 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 12 , 1 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 12 -> 1 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 14 , 8 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 12 -> 8 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 14 , 1 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 12 -> 1 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 12 , 8 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 12 -> 8 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 12 , 0 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 12 -> 0 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 12 , 0 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 12 -> 6 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 14 , 6 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 12 -> 6 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 12 , 8 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 12 -> 8 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 12 , 8 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 5 -> 8 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 5 , 6 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 5 -> 6 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 5 , 1 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 5 -> 1 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 5 , 1 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 5 -> 0 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 5 , 0 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 5 -> 1 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 5 , 6 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 5 -> 1 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 5 , 1 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 5 -> 1 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 5 , 0 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 5 -> 6 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 5 , 8 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 5 -> 8 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 5 , 6 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 5 -> 0 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 5 , 0 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 5 -> 1 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 5 , 0 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 5 -> 0 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 5 , 8 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 5 -> 8 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 5 , 0 0 0 6 10 14 8 9 2 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11 , 12 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 11 -> 12 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 11 , 2 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 11 -> 2 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 3 , 2 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 11 -> 2 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 3 , 12 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 11 -> 11 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 11 , 4 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 11 -> 4 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 3 , 12 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 11 -> 11 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 11 , 2 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 11 -> 12 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 11 , 4 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 11 -> 4 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 9 , 11 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 11 -> 12 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 3 , 4 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 11 -> 4 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 11 , 4 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 11 -> 4 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 11 , 11 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 11 -> 11 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 3 , 4 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 11 -> 4 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 3 , 11 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 11 -> 11 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 11 , 4 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 11 -> 4 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 11 , 12 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 11 -> 12 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 11 , 12 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 11 -> 2 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 3 , 2 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 11 -> 2 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 11 , 4 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 11 -> 4 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 11 , 4 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 9 -> 4 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 9 , 2 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 9 -> 2 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 9 , 11 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 9 -> 11 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 9 , 11 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 9 -> 12 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 9 , 12 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 9 -> 11 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 9 , 2 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 9 -> 11 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 9 , 11 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 9 -> 11 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 9 , 12 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 9 -> 2 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 9 , 4 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 9 -> 4 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 9 , 2 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 9 -> 12 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 9 , 12 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 9 -> 11 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 9 , 12 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 9 -> 12 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 9 , 4 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 9 -> 4 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 9 , 12 0 0 6 10 14 8 9 2 7 5 0 8 9 2 14 6 7 9 -> 12 6 14 8 13 15 14 0 0 1 2 7 15 14 0 1 2 7 9 , 11 12 0 8 5 8 9 12 6 14 8 5 6 14 0 1 12 8 9 -> 11 12 0 0 0 8 5 0 0 6 10 3 12 8 13 9 12 8 9 , 4 15 7 5 1 4 5 6 10 3 4 9 4 13 15 7 5 8 9 -> 4 15 10 10 7 13 9 12 8 13 5 0 6 7 9 11 4 13 9 , 12 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 9 -> 12 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 9 , 2 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 9 -> 2 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 9 , 12 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 9 -> 12 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 9 , 12 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 9 -> 11 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 9 , 11 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 3 -> 11 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 3 , 2 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 3 -> 2 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 3 , 4 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 3 -> 4 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 3 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5 0 6 3 -> 11 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 3 , 12 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 3 -> 12 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 3 , 2 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 1 -> 2 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 1 , 4 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 1 -> 4 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 1 , 12 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 1 -> 11 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 1 , 4 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 1 -> 4 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 11 , 4 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 1 -> 4 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 1 , 4 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 1 -> 4 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 1 , 2 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 1 -> 12 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 3 , 11 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 1 -> 11 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 3 , 12 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 1 -> 2 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 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0 0 8 13 9 12 8 5 1 11 11 11 2 , 4 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 2 -> 4 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 10 , 12 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 2 -> 11 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 2 , 2 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 2 -> 12 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 2 , 4 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 2 -> 4 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 15 , 11 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 2 -> 12 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 10 , 4 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 2 -> 4 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 2 , 4 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 2 -> 4 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 2 , 11 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 2 -> 11 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 10 , 4 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 2 -> 4 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 10 , 11 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 2 -> 11 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 2 , 4 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 2 -> 4 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 2 , 12 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 2 -> 12 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 2 , 12 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 2 -> 2 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 10 , 2 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 2 -> 2 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 2 , 4 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 2 -> 4 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 2 , 4 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 15 -> 4 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 15 , 2 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 15 -> 2 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 15 , 11 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 15 -> 11 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 15 , 11 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 15 -> 12 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 15 , 12 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 15 -> 11 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 15 , 2 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 15 -> 11 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 15 , 11 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 15 -> 11 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 15 , 12 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 15 -> 2 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 15 , 4 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 15 -> 4 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 15 , 2 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 15 -> 12 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 15 , 12 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 15 -> 11 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 15 , 12 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 15 -> 12 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 15 , 4 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 15 -> 4 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 15 , 12 0 0 6 10 14 8 9 2 7 5 0 8 9 2 14 6 7 15 -> 12 6 14 8 13 15 14 0 0 1 2 7 15 14 0 1 2 7 15 , 11 12 0 8 5 8 9 12 6 14 8 5 6 14 0 1 12 8 15 -> 11 12 0 0 0 8 5 0 0 6 10 3 12 8 13 9 12 8 15 , 4 15 7 5 1 4 5 6 10 3 4 9 4 13 15 7 5 8 15 -> 4 15 10 10 7 13 9 12 8 13 5 0 6 7 9 11 4 13 15 , 12 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 15 -> 12 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 15 , 2 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 15 -> 2 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 15 , 12 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 15 -> 12 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 15 , 12 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 15 -> 11 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 15 , 11 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 10 -> 11 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 10 , 2 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 10 -> 2 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 10 , 4 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 10 -> 4 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 10 , 2 7 13 15 10 7 15 3 4 9 11 4 13 15 7 5 8 15 10 -> 2 7 13 15 10 14 1 2 7 13 9 11 4 13 15 7 13 15 10 , 2 3 12 6 10 7 15 3 2 3 12 0 8 15 7 5 8 15 10 -> 12 1 12 8 9 2 10 3 2 14 0 6 7 13 15 10 7 15 10 , 11 11 12 0 1 4 9 11 12 8 15 7 15 10 10 3 2 10 10 -> 11 11 12 8 15 14 1 11 4 15 10 10 14 8 9 2 3 2 10 , 12 6 10 14 1 11 12 1 12 0 1 2 14 6 10 3 2 10 10 -> 12 6 10 3 2 3 11 12 1 2 14 0 1 2 14 6 14 6 10 , 12 6 3 4 9 12 0 0 6 3 4 13 13 5 6 7 15 10 10 -> 12 6 14 0 1 11 12 1 12 8 15 10 7 13 13 13 15 10 10 , 2 3 4 5 0 8 9 4 5 1 2 10 14 1 2 10 10 10 10 -> 2 14 0 1 12 1 4 5 1 4 15 10 3 4 15 10 10 10 10 , 11 12 0 0 8 13 9 2 14 8 5 1 11 12 8 5 6 10 10 -> 11 12 1 12 0 0 8 13 13 13 5 6 14 6 10 3 11 12 6 , 11 4 5 0 1 2 3 12 8 15 7 5 0 8 9 4 5 6 10 -> 12 0 6 3 2 3 4 5 1 12 8 15 14 1 4 13 13 5 6 , 12 8 9 4 9 11 11 2 10 10 10 14 1 11 2 7 5 6 10 -> 2 7 9 4 13 9 12 0 1 12 1 11 2 10 10 3 2 10 10 , 12 0 0 6 3 4 9 12 1 12 6 3 12 6 14 6 14 6 10 -> 12 0 6 14 1 2 14 1 11 4 15 14 6 14 0 1 12 6 10 , 2 7 9 4 5 1 12 8 5 1 11 12 8 15 7 5 0 6 10 -> 11 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 10 , 12 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 10 -> 12 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 10 , 2 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 6 -> 2 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 6 , 4 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 6 -> 4 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 6 , 12 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 6 -> 11 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 6 , 4 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 6 -> 4 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 2 , 4 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 6 -> 4 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 6 , 4 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 6 -> 4 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 6 , 2 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 6 -> 12 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 10 , 11 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 6 -> 11 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 10 , 12 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 6 -> 2 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 10 , 4 9 12 8 13 15 14 0 0 8 5 6 10 7 5 1 4 5 6 -> 4 9 12 0 1 4 13 5 0 8 13 5 0 6 7 15 14 6 10 , 12 0 8 5 8 9 2 14 6 7 15 3 11 12 8 15 7 5 6 -> 11 4 15 10 14 8 15 3 12 6 14 8 5 1 12 8 13 5 6 , 12 1 11 11 2 3 4 9 4 15 10 10 10 10 14 6 7 5 6 -> 12 1 11 2 10 7 15 10 3 4 15 3 4 9 2 14 6 14 6 , 12 1 12 0 0 6 7 5 0 1 4 9 4 15 7 5 8 5 6 -> 12 1 2 14 0 8 5 8 13 15 3 12 1 4 13 5 0 0 6 , 11 11 4 15 7 13 5 8 5 0 6 3 12 6 7 5 8 5 6 -> 11 11 4 15 14 8 13 5 0 0 8 15 7 5 8 5 1 2 10 , 4 13 5 0 1 12 0 6 10 7 9 4 5 8 15 14 8 5 6 -> 4 13 13 13 9 12 0 0 6 14 8 15 3 2 7 5 0 0 6 , 2 10 10 10 14 1 11 12 1 2 14 6 10 10 10 14 8 5 6 -> 2 10 10 14 0 0 6 3 11 12 6 10 10 14 1 4 15 10 10 , 12 0 8 13 9 4 5 6 7 13 5 8 9 4 15 10 10 14 6 -> 12 1 4 13 13 5 6 10 10 3 12 8 13 13 5 6 7 5 6 , 4 9 11 12 8 9 2 3 2 7 5 6 10 7 15 3 12 0 6 -> 4 13 13 15 3 11 2 3 11 11 12 6 14 0 6 14 8 15 10 , 11 4 15 14 6 7 5 8 5 0 8 15 7 15 3 4 5 0 6 -> 2 3 2 7 5 1 2 14 0 0 8 13 13 13 13 15 14 0 6 , 12 8 15 14 6 7 13 5 6 10 10 14 1 12 1 4 5 0 6 -> 12 0 6 7 15 14 0 0 6 3 2 14 1 12 8 13 13 15 10 , 4 13 15 10 3 11 12 6 7 15 7 15 14 6 7 13 5 0 6 -> 4 13 13 13 15 3 2 14 0 6 3 12 6 7 15 7 15 14 6 , 2 14 1 12 0 8 15 10 10 10 7 5 6 3 4 15 14 0 6 -> 2 14 6 10 14 1 4 15 14 0 8 13 15 10 3 12 6 14 6 , 2 3 2 7 15 7 9 12 0 6 7 5 1 12 6 10 14 0 6 -> 2 10 3 12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 6 , 2 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 6 -> 12 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 6 , 12 6 7 9 2 ->= 12 6 7 9 2 , 12 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 4 -> 12 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 4 , 2 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 4 -> 12 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 4 , 12 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 4 -> 12 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 4 , 2 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 4 -> 2 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 7 , 2 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 4 -> 2 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 7 , 12 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 4 -> 11 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 4 , 4 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 4 -> 4 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 7 , 12 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 4 -> 11 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 4 , 2 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 4 -> 12 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 4 , 4 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 4 -> 4 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 13 , 11 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 4 -> 12 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 7 , 4 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 4 -> 4 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 4 , 4 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 4 -> 4 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 4 , 11 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 4 -> 11 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 7 , 4 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 4 -> 4 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 7 , 11 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 4 -> 11 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 4 , 4 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 4 -> 4 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 4 , 12 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 4 -> 12 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 4 , 12 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 4 -> 2 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 7 , 2 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 4 -> 2 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 4 , 4 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 4 -> 4 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 4 , 4 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 13 -> 4 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 13 , 2 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 13 -> 2 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 13 , 11 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 13 -> 11 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 13 , 11 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 13 -> 12 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 13 , 12 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 13 -> 11 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 13 , 2 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 13 -> 11 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 13 , 11 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 13 -> 11 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 13 , 12 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 13 -> 2 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 13 , 4 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 13 -> 4 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 13 , 2 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 13 -> 12 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 13 , 12 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 13 -> 11 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 13 , 12 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 13 -> 12 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 13 , 4 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 13 -> 4 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 13 , 12 0 0 6 10 14 8 9 2 7 5 0 8 9 2 14 6 7 13 -> 12 6 14 8 13 15 14 0 0 1 2 7 15 14 0 1 2 7 13 , 11 12 0 8 5 8 9 12 6 14 8 5 6 14 0 1 12 8 13 -> 11 12 0 0 0 8 5 0 0 6 10 3 12 8 13 9 12 8 13 , 4 15 7 5 1 4 5 6 10 3 4 9 4 13 15 7 5 8 13 -> 4 15 10 10 7 13 9 12 8 13 5 0 6 7 9 11 4 13 13 , 12 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 13 -> 12 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 13 , 2 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 13 -> 2 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 13 , 12 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 13 -> 12 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 13 , 12 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 13 -> 11 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 13 , 11 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 7 -> 11 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 7 , 2 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 7 -> 2 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 7 , 4 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 7 -> 4 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 7 , 2 7 13 15 10 7 15 3 4 9 11 4 13 15 7 5 8 15 7 -> 2 7 13 15 10 14 1 2 7 13 9 11 4 13 15 7 13 15 7 , 2 3 12 6 10 7 15 3 2 3 12 0 8 15 7 5 8 15 7 -> 12 1 12 8 9 2 10 3 2 14 0 6 7 13 15 10 7 15 7 , 11 11 12 0 1 4 9 11 12 8 15 7 15 10 10 3 2 10 7 -> 11 11 12 8 15 14 1 11 4 15 10 10 14 8 9 2 3 2 7 , 12 6 10 14 1 11 12 1 12 0 1 2 14 6 10 3 2 10 7 -> 12 6 10 3 2 3 11 12 1 2 14 0 1 2 14 6 14 6 7 , 12 6 3 4 9 12 0 0 6 3 4 13 13 5 6 7 15 10 7 -> 12 6 14 0 1 11 12 1 12 8 15 10 7 13 13 13 15 10 7 , 2 3 4 5 0 8 9 4 5 1 2 10 14 1 2 10 10 10 7 -> 2 14 0 1 12 1 4 5 1 4 15 10 3 4 15 10 10 10 7 , 11 12 0 0 8 13 9 2 14 8 5 1 11 12 8 5 6 10 7 -> 11 12 1 12 0 0 8 13 13 13 5 6 14 6 10 3 11 12 8 , 11 4 5 0 1 2 3 12 8 15 7 5 0 8 9 4 5 6 7 -> 12 0 6 3 2 3 4 5 1 12 8 15 14 1 4 13 13 5 8 , 12 8 9 4 9 11 11 2 10 10 10 14 1 11 2 7 5 6 7 -> 2 7 9 4 13 9 12 0 1 12 1 11 2 10 10 3 2 10 7 , 12 0 0 6 3 4 9 12 1 12 6 3 12 6 14 6 14 6 7 -> 12 0 6 14 1 2 14 1 11 4 15 14 6 14 0 1 12 6 7 , 2 7 9 4 5 1 12 8 5 1 11 12 8 15 7 5 0 6 7 -> 11 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 7 , 12 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 7 -> 12 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 7 , 2 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 8 -> 2 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 8 , 4 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 8 -> 4 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 8 , 12 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 8 -> 11 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 8 , 4 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 8 -> 4 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 4 , 4 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 8 -> 4 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 8 , 4 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 8 -> 4 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 8 , 2 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 8 -> 12 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 7 , 11 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 8 -> 11 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 7 , 12 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 8 -> 2 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 7 , 4 9 12 8 13 15 14 0 0 8 5 6 10 7 5 1 4 5 8 -> 4 9 12 0 1 4 13 5 0 8 13 5 0 6 7 15 14 6 7 , 12 0 8 5 8 9 2 14 6 7 15 3 11 12 8 15 7 5 8 -> 11 4 15 10 14 8 15 3 12 6 14 8 5 1 12 8 13 5 8 , 12 1 11 11 2 3 4 9 4 15 10 10 10 10 14 6 7 5 8 -> 12 1 11 2 10 7 15 10 3 4 15 3 4 9 2 14 6 14 8 , 12 1 12 0 0 6 7 5 0 1 4 9 4 15 7 5 8 5 8 -> 12 1 2 14 0 8 5 8 13 15 3 12 1 4 13 5 0 0 8 , 11 11 4 15 7 13 5 8 5 0 6 3 12 6 7 5 8 5 8 -> 11 11 4 15 14 8 13 5 0 0 8 15 7 5 8 5 1 2 7 , 4 13 5 0 1 12 0 6 10 7 9 4 5 8 15 14 8 5 8 -> 4 13 13 13 9 12 0 0 6 14 8 15 3 2 7 5 0 0 8 , 2 10 10 10 14 1 11 12 1 2 14 6 10 10 10 14 8 5 8 -> 2 10 10 14 0 0 6 3 11 12 6 10 10 14 1 4 15 10 7 , 12 0 8 13 9 4 5 6 7 13 5 8 9 4 15 10 10 14 8 -> 12 1 4 13 13 5 6 10 10 3 12 8 13 13 5 6 7 5 8 , 4 9 11 12 8 9 2 3 2 7 5 6 10 7 15 3 12 0 8 -> 4 13 13 15 3 11 2 3 11 11 12 6 14 0 6 14 8 15 7 , 11 4 15 14 6 7 5 8 5 0 8 15 7 15 3 4 5 0 8 -> 2 3 2 7 5 1 2 14 0 0 8 13 13 13 13 15 14 0 8 , 12 8 15 14 6 7 13 5 6 10 10 14 1 12 1 4 5 0 8 -> 12 0 6 7 15 14 0 0 6 3 2 14 1 12 8 13 13 15 7 , 4 13 15 10 3 11 12 6 7 15 7 15 14 6 7 13 5 0 8 -> 4 13 13 13 15 3 2 14 0 6 3 12 6 7 15 7 15 14 8 , 2 14 1 12 0 8 15 10 10 10 7 5 6 3 4 15 14 0 8 -> 2 14 6 10 14 1 4 15 14 0 8 13 15 10 3 12 6 14 8 , 2 3 2 7 15 7 9 12 0 6 7 5 1 12 6 10 14 0 8 -> 2 10 3 12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 8 , 2 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 8 -> 12 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 8 , 12 6 7 9 4 ->= 12 6 7 9 4 , 14 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 12 -> 14 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 12 , 10 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 12 -> 14 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 12 , 14 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 12 -> 14 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 12 , 10 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 12 -> 10 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 14 , 10 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 12 -> 10 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 14 , 14 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 12 -> 3 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 12 , 7 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 12 -> 7 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 14 , 14 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 12 -> 3 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 12 , 10 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 12 -> 14 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 12 , 7 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 12 -> 7 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 5 , 3 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 12 -> 14 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 14 , 7 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 12 -> 7 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 12 , 7 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 12 -> 7 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 12 , 3 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 12 -> 3 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 14 , 7 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 12 -> 7 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 14 , 3 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 12 -> 3 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 12 , 7 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 12 -> 7 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 12 , 14 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 12 -> 14 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 12 , 14 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 12 -> 10 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 14 , 10 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 12 -> 10 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 12 , 7 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 12 -> 7 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 12 , 7 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 5 -> 7 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 5 , 10 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 5 -> 10 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 5 , 3 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 5 -> 3 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 5 , 3 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 5 -> 14 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 5 , 14 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 5 -> 3 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 5 , 10 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 5 -> 3 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 5 , 3 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 5 -> 3 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 5 , 14 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 5 -> 10 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 5 , 7 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 5 -> 7 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 5 , 10 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 5 -> 14 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 5 , 14 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 5 -> 3 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 5 , 14 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 5 -> 14 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 5 , 7 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 5 -> 7 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 5 , 14 0 0 6 10 14 8 9 2 7 5 0 8 9 2 14 6 7 5 -> 14 6 14 8 13 15 14 0 0 1 2 7 15 14 0 1 2 7 5 , 3 12 0 8 5 8 9 12 6 14 8 5 6 14 0 1 12 8 5 -> 3 12 0 0 0 8 5 0 0 6 10 3 12 8 13 9 12 8 5 , 7 15 7 5 1 4 5 6 10 3 4 9 4 13 15 7 5 8 5 -> 7 15 10 10 7 13 9 12 8 13 5 0 6 7 9 11 4 13 5 , 14 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 5 -> 14 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 5 , 10 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 5 -> 10 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 5 , 14 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 5 -> 14 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 5 , 14 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 5 -> 3 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 5 , 3 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 14 -> 3 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 14 , 10 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 14 -> 10 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 14 , 7 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 14 -> 7 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 14 , 10 7 13 15 10 7 15 3 4 9 11 4 13 15 7 5 8 15 14 -> 10 7 13 15 10 14 1 2 7 13 9 11 4 13 15 7 13 15 14 , 10 3 12 6 10 7 15 3 2 3 12 0 8 15 7 5 8 15 14 -> 14 1 12 8 9 2 10 3 2 14 0 6 7 13 15 10 7 15 14 , 3 11 12 0 1 4 9 11 12 8 15 7 15 10 10 3 2 10 14 -> 3 11 12 8 15 14 1 11 4 15 10 10 14 8 9 2 3 2 14 , 14 6 10 14 1 11 12 1 12 0 1 2 14 6 10 3 2 10 14 -> 14 6 10 3 2 3 11 12 1 2 14 0 1 2 14 6 14 6 14 , 14 6 3 4 9 12 0 0 6 3 4 13 13 5 6 7 15 10 14 -> 14 6 14 0 1 11 12 1 12 8 15 10 7 13 13 13 15 10 14 , 10 3 4 5 0 8 9 4 5 1 2 10 14 1 2 10 10 10 14 -> 10 14 0 1 12 1 4 5 1 4 15 10 3 4 15 10 10 10 14 , 3 12 0 0 8 13 9 2 14 8 5 1 11 12 8 5 6 10 14 -> 3 12 1 12 0 0 8 13 13 13 5 6 14 6 10 3 11 12 0 , 3 4 5 0 1 2 3 12 8 15 7 5 0 8 9 4 5 6 14 -> 14 0 6 3 2 3 4 5 1 12 8 15 14 1 4 13 13 5 0 , 14 8 9 4 9 11 11 2 10 10 10 14 1 11 2 7 5 6 14 -> 10 7 9 4 13 9 12 0 1 12 1 11 2 10 10 3 2 10 14 , 14 0 0 6 3 4 9 12 1 12 6 3 12 6 14 6 14 6 14 -> 14 0 6 14 1 2 14 1 11 4 15 14 6 14 0 1 12 6 14 , 10 7 9 4 5 1 12 8 5 1 11 12 8 15 7 5 0 6 14 -> 3 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 14 , 14 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 14 -> 14 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 14 , 10 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 0 -> 10 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 0 , 7 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 0 -> 7 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 0 , 14 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 0 -> 3 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 0 , 7 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 0 -> 7 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 12 , 7 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 0 -> 7 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 0 , 7 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 0 -> 7 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 0 , 10 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 0 -> 14 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 14 , 3 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 0 -> 3 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 14 , 14 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 0 -> 10 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 14 , 7 9 12 8 13 15 14 0 0 8 5 6 10 7 5 1 4 5 0 -> 7 9 12 0 1 4 13 5 0 8 13 5 0 6 7 15 14 6 14 , 14 0 8 5 8 9 2 14 6 7 15 3 11 12 8 15 7 5 0 -> 3 4 15 10 14 8 15 3 12 6 14 8 5 1 12 8 13 5 0 , 14 1 11 11 2 3 4 9 4 15 10 10 10 10 14 6 7 5 0 -> 14 1 11 2 10 7 15 10 3 4 15 3 4 9 2 14 6 14 0 , 14 1 12 0 0 6 7 5 0 1 4 9 4 15 7 5 8 5 0 -> 14 1 2 14 0 8 5 8 13 15 3 12 1 4 13 5 0 0 0 , 3 11 4 15 7 13 5 8 5 0 6 3 12 6 7 5 8 5 0 -> 3 11 4 15 14 8 13 5 0 0 8 15 7 5 8 5 1 2 14 , 7 13 5 0 1 12 0 6 10 7 9 4 5 8 15 14 8 5 0 -> 7 13 13 13 9 12 0 0 6 14 8 15 3 2 7 5 0 0 0 , 10 10 10 10 14 1 11 12 1 2 14 6 10 10 10 14 8 5 0 -> 10 10 10 14 0 0 6 3 11 12 6 10 10 14 1 4 15 10 14 , 14 0 8 13 9 4 5 6 7 13 5 8 9 4 15 10 10 14 0 -> 14 1 4 13 13 5 6 10 10 3 12 8 13 13 5 6 7 5 0 , 7 9 11 12 8 9 2 3 2 7 5 6 10 7 15 3 12 0 0 -> 7 13 13 15 3 11 2 3 11 11 12 6 14 0 6 14 8 15 14 , 3 4 15 14 6 7 5 8 5 0 8 15 7 15 3 4 5 0 0 -> 10 3 2 7 5 1 2 14 0 0 8 13 13 13 13 15 14 0 0 , 14 8 15 14 6 7 13 5 6 10 10 14 1 12 1 4 5 0 0 -> 14 0 6 7 15 14 0 0 6 3 2 14 1 12 8 13 13 15 14 , 7 13 15 10 3 11 12 6 7 15 7 15 14 6 7 13 5 0 0 -> 7 13 13 13 15 3 2 14 0 6 3 12 6 7 15 7 15 14 0 , 10 14 1 12 0 8 15 10 10 10 7 5 6 3 4 15 14 0 0 -> 10 14 6 10 14 1 4 15 14 0 8 13 15 10 3 12 6 14 0 , 10 3 2 7 15 7 9 12 0 6 7 5 1 12 6 10 14 0 0 -> 10 10 3 12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 0 , 10 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 0 -> 14 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 0 , 14 6 7 9 12 ->= 14 6 7 9 12 , 14 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 11 -> 14 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 11 , 10 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 11 -> 14 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 11 , 14 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 11 -> 14 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 11 , 10 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 11 -> 10 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 3 , 10 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 11 -> 10 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 3 , 14 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 11 -> 3 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 11 , 7 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 11 -> 7 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 3 , 14 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 11 -> 3 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 11 , 10 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 11 -> 14 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 11 , 7 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 11 -> 7 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 9 , 3 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 11 -> 14 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 3 , 7 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 11 -> 7 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 11 , 7 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 11 -> 7 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 11 , 3 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 11 -> 3 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 3 , 7 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 11 -> 7 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 3 , 3 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 11 -> 3 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 11 , 7 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 11 -> 7 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 11 , 14 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 11 -> 14 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 11 , 14 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 11 -> 10 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 3 , 10 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 11 -> 10 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 11 , 7 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 11 -> 7 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 11 , 7 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 9 -> 7 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 9 , 10 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 9 -> 10 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 9 , 3 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 9 -> 3 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 9 , 3 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 9 -> 14 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 9 , 14 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 9 -> 3 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 9 , 10 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13 9 12 8 13 5 0 6 7 9 11 4 13 9 , 14 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 9 -> 14 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 9 , 10 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 9 -> 10 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 9 , 14 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 9 -> 14 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 9 , 14 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 9 -> 3 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 9 , 3 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 3 -> 3 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 3 , 10 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 3 -> 10 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 3 , 7 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 3 -> 7 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 3 , 10 7 13 15 10 7 15 3 4 9 11 4 13 15 7 5 8 15 3 -> 10 7 13 15 10 14 1 2 7 13 9 11 4 13 15 7 13 15 3 , 10 3 12 6 10 7 15 3 2 3 12 0 8 15 7 5 8 15 3 -> 14 1 12 8 9 2 10 3 2 14 0 6 7 13 15 10 7 15 3 , 3 11 12 0 1 4 9 11 12 8 15 7 15 10 10 3 2 10 3 -> 3 11 12 8 15 14 1 11 4 15 10 10 14 8 9 2 3 2 3 , 14 6 10 14 1 11 12 1 12 0 1 2 14 6 10 3 2 10 3 -> 14 6 10 3 2 3 11 12 1 2 14 0 1 2 14 6 14 6 3 , 14 6 3 4 9 12 0 0 6 3 4 13 13 5 6 7 15 10 3 -> 14 6 14 0 1 11 12 1 12 8 15 10 7 13 13 13 15 10 3 , 10 3 4 5 0 8 9 4 5 1 2 10 14 1 2 10 10 10 3 -> 10 14 0 1 12 1 4 5 1 4 15 10 3 4 15 10 10 10 3 , 3 12 0 0 8 13 9 2 14 8 5 1 11 12 8 5 6 10 3 -> 3 12 1 12 0 0 8 13 13 13 5 6 14 6 10 3 11 12 1 , 3 4 5 0 1 2 3 12 8 15 7 5 0 8 9 4 5 6 3 -> 14 0 6 3 2 3 4 5 1 12 8 15 14 1 4 13 13 5 1 , 14 8 9 4 9 11 11 2 10 10 10 14 1 11 2 7 5 6 3 -> 10 7 9 4 13 9 12 0 1 12 1 11 2 10 10 3 2 10 3 , 14 0 0 6 3 4 9 12 1 12 6 3 12 6 14 6 14 6 3 -> 14 0 6 14 1 2 14 1 11 4 15 14 6 14 0 1 12 6 3 , 10 7 9 4 5 1 12 8 5 1 11 12 8 15 7 5 0 6 3 -> 3 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 3 , 14 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 3 -> 14 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 3 , 10 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 1 -> 10 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 1 , 7 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 1 -> 7 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12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 1 , 10 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 1 -> 14 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 1 , 14 6 7 9 11 ->= 14 6 7 9 11 , 14 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 2 -> 14 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 2 , 10 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 2 -> 14 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 2 , 14 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 2 -> 14 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 2 , 10 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 2 -> 10 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 10 , 10 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 2 -> 10 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 10 , 14 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 2 -> 3 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 2 , 7 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 2 -> 7 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 10 , 14 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 2 -> 3 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 2 , 10 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 2 -> 14 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 2 , 7 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 2 -> 7 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 15 , 3 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 2 -> 14 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 10 , 7 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 2 -> 7 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 2 , 7 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 2 -> 7 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 2 , 3 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 2 -> 3 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 10 , 7 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 2 -> 7 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 10 , 3 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 2 -> 3 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 2 , 7 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 2 -> 7 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 2 , 14 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 2 -> 14 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 2 , 14 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 2 -> 10 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 10 , 10 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 2 -> 10 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 2 , 7 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 2 -> 7 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 2 , 7 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 15 -> 7 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 15 , 10 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 15 -> 10 3 11 12 1 12 0 0 1 4 13 15 10 3 4 13 15 7 15 , 3 12 8 9 2 14 1 12 1 11 12 0 6 10 10 10 3 4 15 -> 3 11 12 6 14 6 3 11 2 3 12 0 6 3 2 14 8 13 15 , 3 4 9 4 5 8 13 5 0 8 9 2 14 6 10 14 1 4 15 -> 14 6 7 15 14 0 8 13 9 4 15 14 1 11 12 1 4 13 15 , 14 0 8 13 5 8 9 4 9 4 15 10 3 4 9 11 4 13 15 -> 3 12 1 11 4 13 15 7 13 15 3 12 8 9 12 8 13 13 15 , 10 7 9 11 4 9 4 5 6 7 15 7 5 0 0 1 4 13 15 -> 3 11 12 0 6 10 10 3 12 0 8 13 13 13 9 4 13 13 15 , 3 11 2 7 9 2 14 1 12 8 9 12 8 9 11 2 7 13 15 -> 3 11 4 13 9 2 14 6 3 12 8 9 2 14 1 11 4 13 15 , 14 6 7 5 0 8 9 11 11 4 15 3 11 2 7 5 8 13 15 -> 10 3 11 11 4 5 1 12 8 5 0 1 2 10 7 13 13 13 15 , 7 9 4 5 8 9 12 0 6 3 4 9 11 4 5 0 8 13 15 -> 7 9 4 13 13 13 9 12 6 7 5 0 1 12 1 11 12 8 15 , 10 7 5 1 4 13 5 8 15 7 13 9 2 7 9 11 2 7 15 -> 14 6 3 12 1 4 15 7 15 3 2 7 13 9 4 13 13 13 15 , 14 1 2 3 4 15 7 9 11 11 12 8 13 9 12 1 2 7 15 -> 3 11 4 13 9 4 15 14 0 1 11 11 11 4 15 10 14 8 15 , 14 0 8 15 7 15 14 0 6 10 10 14 1 4 5 8 15 7 15 -> 14 8 13 5 1 2 14 8 5 0 6 10 10 14 8 15 10 7 15 , 7 13 9 4 13 15 10 7 5 8 15 3 12 0 6 10 10 7 15 -> 7 13 13 13 15 14 1 2 10 7 5 8 9 12 6 10 10 7 15 , 14 0 0 6 10 14 8 9 2 7 5 0 8 9 2 14 6 7 15 -> 14 6 14 8 13 15 14 0 0 1 2 7 15 14 0 1 2 7 15 , 3 12 0 8 5 8 9 12 6 14 8 5 6 14 0 1 12 8 15 -> 3 12 0 0 0 8 5 0 0 6 10 3 12 8 13 9 12 8 15 , 7 15 7 5 1 4 5 6 10 3 4 9 4 13 15 7 5 8 15 -> 7 15 10 10 7 13 9 12 8 13 5 0 6 7 9 11 4 13 15 , 14 0 1 11 4 5 0 6 7 5 1 12 8 15 10 7 5 8 15 -> 14 0 6 7 13 5 0 0 1 12 6 7 9 4 15 3 12 8 15 , 10 10 14 8 15 7 13 5 8 13 13 9 2 14 8 15 14 8 15 -> 10 14 6 10 14 8 13 13 15 14 8 13 15 3 4 5 8 13 15 , 14 8 9 2 14 8 5 1 11 2 7 15 10 3 12 6 14 8 15 -> 14 6 10 3 2 14 1 4 13 5 0 6 7 15 3 11 12 8 15 , 14 8 9 4 5 8 5 8 9 11 2 3 11 4 9 12 0 8 15 -> 3 4 9 4 5 0 1 2 14 8 13 9 11 12 1 12 8 13 15 , 3 4 13 9 4 13 5 8 9 2 7 5 1 2 3 2 3 2 10 -> 3 11 2 10 14 8 13 13 9 11 12 6 3 11 4 13 13 15 10 , 10 7 13 9 4 15 7 13 5 6 3 4 13 15 7 9 4 15 10 -> 10 7 5 8 15 7 13 13 9 4 13 15 10 7 9 11 4 15 10 , 7 13 9 2 7 13 9 4 5 0 6 7 9 4 15 10 7 15 10 -> 7 13 15 7 13 13 15 7 15 10 3 12 8 9 11 12 8 15 10 , 10 7 13 15 10 7 15 3 4 9 11 4 13 15 7 5 8 15 10 -> 10 7 13 15 10 14 1 2 7 13 9 11 4 13 15 7 13 15 10 , 10 3 12 6 10 7 15 3 2 3 12 0 8 15 7 5 8 15 10 -> 14 1 12 8 9 2 10 3 2 14 0 6 7 13 15 10 7 15 10 , 3 11 12 0 1 4 9 11 12 8 15 7 15 10 10 3 2 10 10 -> 3 11 12 8 15 14 1 11 4 15 10 10 14 8 9 2 3 2 10 , 14 6 10 14 1 11 12 1 12 0 1 2 14 6 10 3 2 10 10 -> 14 6 10 3 2 3 11 12 1 2 14 0 1 2 14 6 14 6 10 , 14 6 3 4 9 12 0 0 6 3 4 13 13 5 6 7 15 10 10 -> 14 6 14 0 1 11 12 1 12 8 15 10 7 13 13 13 15 10 10 , 10 3 4 5 0 8 9 4 5 1 2 10 14 1 2 10 10 10 10 -> 10 14 0 1 12 1 4 5 1 4 15 10 3 4 15 10 10 10 10 , 3 12 0 0 8 13 9 2 14 8 5 1 11 12 8 5 6 10 10 -> 3 12 1 12 0 0 8 13 13 13 5 6 14 6 10 3 11 12 6 , 3 4 5 0 1 2 3 12 8 15 7 5 0 8 9 4 5 6 10 -> 14 0 6 3 2 3 4 5 1 12 8 15 14 1 4 13 13 5 6 , 14 8 9 4 9 11 11 2 10 10 10 14 1 11 2 7 5 6 10 -> 10 7 9 4 13 9 12 0 1 12 1 11 2 10 10 3 2 10 10 , 14 0 0 6 3 4 9 12 1 12 6 3 12 6 14 6 14 6 10 -> 14 0 6 14 1 2 14 1 11 4 15 14 6 14 0 1 12 6 10 , 10 7 9 4 5 1 12 8 5 1 11 12 8 15 7 5 0 6 10 -> 3 4 13 5 1 11 12 8 13 5 0 1 4 5 0 6 10 10 10 , 14 6 14 8 15 14 0 6 14 6 14 8 5 0 6 14 0 6 10 -> 14 6 14 0 0 0 0 0 8 15 14 8 15 10 14 6 14 6 10 , 10 3 11 4 9 12 6 14 6 7 15 10 3 4 9 11 11 12 6 -> 10 3 2 3 11 4 13 9 2 14 0 6 10 3 11 4 9 12 6 , 7 9 11 11 12 6 7 9 11 2 7 5 6 3 12 1 11 12 6 -> 7 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 6 , 14 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 6 -> 3 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 6 , 7 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 6 -> 7 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 2 , 7 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 6 -> 7 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 6 , 7 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 6 -> 7 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 6 , 10 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 6 -> 14 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 10 , 3 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 6 -> 3 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 10 , 14 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 6 -> 10 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 10 , 7 9 12 8 13 15 14 0 0 8 5 6 10 7 5 1 4 5 6 -> 7 9 12 0 1 4 13 5 0 8 13 5 0 6 7 15 14 6 10 , 14 0 8 5 8 9 2 14 6 7 15 3 11 12 8 15 7 5 6 -> 3 4 15 10 14 8 15 3 12 6 14 8 5 1 12 8 13 5 6 , 14 1 11 11 2 3 4 9 4 15 10 10 10 10 14 6 7 5 6 -> 14 1 11 2 10 7 15 10 3 4 15 3 4 9 2 14 6 14 6 , 14 1 12 0 0 6 7 5 0 1 4 9 4 15 7 5 8 5 6 -> 14 1 2 14 0 8 5 8 13 15 3 12 1 4 13 5 0 0 6 , 3 11 4 15 7 13 5 8 5 0 6 3 12 6 7 5 8 5 6 -> 3 11 4 15 14 8 13 5 0 0 8 15 7 5 8 5 1 2 10 , 7 13 5 0 1 12 0 6 10 7 9 4 5 8 15 14 8 5 6 -> 7 13 13 13 9 12 0 0 6 14 8 15 3 2 7 5 0 0 6 , 10 10 10 10 14 1 11 12 1 2 14 6 10 10 10 14 8 5 6 -> 10 10 10 14 0 0 6 3 11 12 6 10 10 14 1 4 15 10 10 , 14 0 8 13 9 4 5 6 7 13 5 8 9 4 15 10 10 14 6 -> 14 1 4 13 13 5 6 10 10 3 12 8 13 13 5 6 7 5 6 , 7 9 11 12 8 9 2 3 2 7 5 6 10 7 15 3 12 0 6 -> 7 13 13 15 3 11 2 3 11 11 12 6 14 0 6 14 8 15 10 , 3 4 15 14 6 7 5 8 5 0 8 15 7 15 3 4 5 0 6 -> 10 3 2 7 5 1 2 14 0 0 8 13 13 13 13 15 14 0 6 , 14 8 15 14 6 7 13 5 6 10 10 14 1 12 1 4 5 0 6 -> 14 0 6 7 15 14 0 0 6 3 2 14 1 12 8 13 13 15 10 , 7 13 15 10 3 11 12 6 7 15 7 15 14 6 7 13 5 0 6 -> 7 13 13 13 15 3 2 14 0 6 3 12 6 7 15 7 15 14 6 , 10 14 1 12 0 8 15 10 10 10 7 5 6 3 4 15 14 0 6 -> 10 14 6 10 14 1 4 15 14 0 8 13 15 10 3 12 6 14 6 , 10 3 2 7 15 7 9 12 0 6 7 5 1 12 6 10 14 0 6 -> 10 10 3 12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 6 , 10 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 6 -> 14 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 6 , 14 6 7 9 2 ->= 14 6 7 9 2 , 14 0 1 2 3 4 5 6 7 5 8 9 2 10 3 11 11 11 4 -> 14 8 13 13 9 2 10 3 11 12 1 11 12 0 6 10 3 11 4 , 10 7 13 5 6 14 8 13 9 2 7 5 6 7 5 1 11 11 4 -> 14 6 10 14 8 13 15 10 3 11 4 13 13 5 8 9 12 1 4 , 14 1 12 0 8 5 0 8 5 8 9 12 6 10 7 13 9 11 4 -> 14 0 8 5 0 0 6 7 9 11 4 5 6 3 4 13 5 1 4 , 10 7 13 5 0 0 1 2 7 9 2 7 5 8 15 7 9 11 4 -> 10 3 11 4 5 1 4 15 3 12 8 13 13 13 5 6 14 6 7 , 10 10 7 13 15 3 12 8 15 7 15 7 15 14 6 7 9 11 4 -> 10 10 14 8 13 13 5 1 11 2 7 13 13 15 10 3 2 10 7 , 14 1 12 1 12 8 9 12 1 4 13 5 8 9 12 8 9 11 4 -> 3 12 8 13 9 12 0 0 8 13 9 12 8 5 1 11 11 11 4 , 7 13 9 12 0 8 9 2 7 5 0 6 14 8 5 8 9 11 4 -> 7 13 15 14 8 9 11 12 8 9 12 1 12 8 13 5 0 6 7 , 14 1 11 2 10 7 9 12 1 12 8 9 2 3 12 1 4 9 4 -> 3 4 13 5 0 6 3 12 1 11 4 15 10 3 11 11 12 1 4 , 10 7 9 2 3 12 8 13 15 7 5 0 8 5 0 8 13 9 4 -> 14 8 5 0 6 3 12 1 4 13 13 13 13 15 7 15 14 1 4 , 7 9 4 9 12 1 4 15 7 13 15 7 13 13 9 2 7 9 4 -> 7 9 4 13 5 8 13 13 13 15 3 4 15 3 11 11 2 7 13 , 3 4 5 8 15 7 5 8 15 7 5 0 1 2 7 15 7 9 4 -> 14 1 4 5 0 1 4 13 15 10 3 4 13 13 13 15 14 6 7 , 7 5 0 8 13 9 12 1 4 9 11 2 10 7 15 10 7 9 4 -> 7 9 4 13 15 10 3 12 6 14 8 15 3 4 5 1 4 9 4 , 7 9 4 9 2 7 15 14 8 15 3 4 9 4 5 6 7 9 4 -> 7 9 4 13 13 9 2 3 2 7 5 0 6 7 13 9 2 3 4 , 3 2 14 0 8 5 6 14 1 2 3 12 8 5 6 7 15 3 4 -> 3 2 14 8 13 13 15 14 1 11 2 14 0 6 3 12 0 6 7 , 7 9 4 13 13 5 6 10 14 8 9 12 6 7 5 8 15 3 4 -> 7 5 8 13 13 13 9 12 6 7 15 14 6 3 4 5 1 2 7 , 3 4 9 4 15 10 7 9 12 6 3 12 8 5 8 9 12 1 4 -> 3 2 10 7 13 13 13 9 11 12 1 11 12 6 7 5 0 1 4 , 7 9 12 6 7 5 1 11 11 12 0 8 15 7 15 3 12 1 4 -> 7 13 15 14 6 3 11 4 5 0 0 1 11 4 9 12 6 3 4 , 14 8 5 0 8 5 1 11 2 14 0 0 8 9 11 4 5 1 4 -> 14 0 1 4 9 4 13 9 12 8 9 12 6 14 0 0 0 1 4 , 14 8 9 4 9 2 14 1 11 11 2 10 7 5 8 15 14 1 4 -> 10 14 1 11 11 2 3 12 1 4 13 13 13 15 14 1 12 6 7 , 10 3 12 1 2 14 0 8 13 15 7 9 12 6 3 12 0 1 4 -> 10 3 4 15 3 11 4 13 5 0 6 14 1 12 0 6 14 1 4 , 7 13 13 9 2 3 2 10 10 7 13 5 8 15 14 0 0 1 4 -> 7 13 9 12 6 14 6 14 8 13 13 13 5 6 10 3 2 3 4 , 7 13 9 4 13 5 8 5 1 12 0 8 13 5 6 7 9 4 13 -> 7 13 5 0 8 5 0 8 13 9 11 12 6 3 4 13 13 13 13 , 10 3 12 6 3 4 13 9 12 8 5 6 14 1 4 15 3 4 13 -> 10 3 11 12 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12 6 7 9 11 2 7 5 6 3 12 1 11 12 8 -> 13 5 1 12 0 1 2 10 3 4 15 3 11 11 11 4 9 12 8 , 5 0 8 5 8 9 11 12 8 13 5 8 13 9 11 4 9 12 8 -> 9 4 9 12 0 1 12 8 13 13 9 4 13 5 8 9 12 0 8 , 13 13 9 4 13 13 9 12 8 9 11 2 3 11 2 7 9 12 8 -> 13 13 9 2 3 12 1 12 1 4 9 11 4 13 13 13 15 3 4 , 13 9 4 5 6 14 8 13 15 7 5 8 13 5 0 8 9 12 8 -> 13 9 4 15 14 8 13 15 7 9 12 0 8 5 0 8 13 5 8 , 13 5 8 5 6 7 13 5 0 1 4 5 1 2 14 6 3 12 8 -> 13 5 8 15 3 12 1 11 12 8 13 13 5 0 6 14 6 14 8 , 15 7 5 6 10 3 4 5 0 6 7 15 7 13 9 12 1 12 8 -> 5 8 15 3 2 7 13 13 9 2 14 6 14 0 0 8 9 2 7 , 9 11 11 2 10 10 10 14 8 15 7 13 9 2 3 11 4 5 8 -> 9 11 11 2 10 10 7 13 9 11 4 5 6 3 4 15 14 6 7 , 5 8 5 6 10 7 5 6 10 10 3 4 5 1 2 3 4 5 8 -> 15 7 13 13 5 1 11 12 6 14 6 3 12 6 7 5 6 10 7 , 13 9 12 8 13 15 14 0 0 8 5 6 10 7 5 1 4 5 8 -> 13 9 12 0 1 4 13 5 0 8 13 5 0 6 7 15 14 6 7 , 5 0 8 5 8 9 2 14 6 7 15 3 11 12 8 15 7 5 8 -> 9 4 15 10 14 8 15 3 12 6 14 8 5 1 12 8 13 5 8 , 5 1 11 11 2 3 4 9 4 15 10 10 10 10 14 6 7 5 8 -> 5 1 11 2 10 7 15 10 3 4 15 3 4 9 2 14 6 14 8 , 5 1 12 0 0 6 7 5 0 1 4 9 4 15 7 5 8 5 8 -> 5 1 2 14 0 8 5 8 13 15 3 12 1 4 13 5 0 0 8 , 9 11 4 15 7 13 5 8 5 0 6 3 12 6 7 5 8 5 8 -> 9 11 4 15 14 8 13 5 0 0 8 15 7 5 8 5 1 2 7 , 13 13 5 0 1 12 0 6 10 7 9 4 5 8 15 14 8 5 8 -> 13 13 13 13 9 12 0 0 6 14 8 15 3 2 7 5 0 0 8 , 15 10 10 10 14 1 11 12 1 2 14 6 10 10 10 14 8 5 8 -> 15 10 10 14 0 0 6 3 11 12 6 10 10 14 1 4 15 10 7 , 5 0 8 13 9 4 5 6 7 13 5 8 9 4 15 10 10 14 8 -> 5 1 4 13 13 5 6 10 10 3 12 8 13 13 5 6 7 5 8 , 13 9 11 12 8 9 2 3 2 7 5 6 10 7 15 3 12 0 8 -> 13 13 13 15 3 11 2 3 11 11 12 6 14 0 6 14 8 15 7 , 9 4 15 14 6 7 5 8 5 0 8 15 7 15 3 4 5 0 8 -> 15 3 2 7 5 1 2 14 0 0 8 13 13 13 13 15 14 0 8 , 5 8 15 14 6 7 13 5 6 10 10 14 1 12 1 4 5 0 8 -> 5 0 6 7 15 14 0 0 6 3 2 14 1 12 8 13 13 15 7 , 13 13 15 10 3 11 12 6 7 15 7 15 14 6 7 13 5 0 8 -> 13 13 13 13 15 3 2 14 0 6 3 12 6 7 15 7 15 14 8 , 15 14 1 12 0 8 15 10 10 10 7 5 6 3 4 15 14 0 8 -> 15 14 6 10 14 1 4 15 14 0 8 13 15 10 3 12 6 14 8 , 15 3 2 7 15 7 9 12 0 6 7 5 1 12 6 10 14 0 8 -> 15 10 3 12 1 11 12 0 0 8 15 10 14 6 7 13 15 14 8 , 15 7 9 12 0 0 8 5 0 8 9 4 15 3 4 5 0 0 8 -> 5 8 13 13 9 4 5 0 0 6 3 4 15 14 0 1 12 0 8 , 5 6 7 9 4 ->= 5 6 7 9 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 1 | | 0 1 | \ / 10 is interpreted by / \ | 1 1 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 0 1 | \ / 15 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 12->2, 8->3, 5->4, 9->5, 6->6, 10->7, 7->8, 13->9, 11->10, 4->11, 3->12, 2->13, 15->14, 14->15 }, it remains to prove termination of the 272-rule system { 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 3 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 2 -> 3 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 2 , 6 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 2 -> 6 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 2 , 0 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 4 -> 1 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 4 , 6 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 15 -> 6 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 15 , 1 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 15 -> 1 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 15 , 0 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 15 -> 0 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 15 , 6 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 15 -> 6 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 15 , 0 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 15 -> 0 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 15 , 0 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 15 -> 0 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 15 , 3 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 0 -> 3 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 0 , 3 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 0 -> 3 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 0 , 1 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 0 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 15 , 0 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 0 -> 0 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 0 , 1 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 0 -> 1 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 15 , 6 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 0 -> 6 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 15 , 0 6 8 5 2 ->= 0 6 8 5 2 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 3 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 10 -> 3 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 10 , 6 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 10 -> 6 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 10 , 0 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 5 -> 1 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 5 , 6 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 12 -> 6 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 12 , 1 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 12 -> 1 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 12 , 0 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 12 -> 0 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 12 , 6 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 12 -> 6 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 12 , 0 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 12 -> 0 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 12 , 0 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 12 -> 0 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 12 , 3 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 1 -> 3 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 1 , 3 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 1 -> 3 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 1 , 1 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 1 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 12 , 0 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 1 -> 0 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 1 , 1 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 1 -> 1 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 12 , 6 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 1 -> 6 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 12 , 0 6 8 5 10 ->= 0 6 8 5 10 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 3 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 13 -> 3 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 13 , 6 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 13 -> 6 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 13 , 0 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 14 -> 1 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 14 , 6 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 7 -> 6 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 7 , 1 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 7 -> 1 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 7 , 0 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 7 -> 0 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 7 , 6 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 7 -> 6 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 7 , 0 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 7 -> 0 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 7 , 0 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 7 -> 0 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 7 , 3 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 6 -> 3 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 6 , 3 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 6 -> 3 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 6 , 1 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 6 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 7 , 0 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 6 -> 0 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 6 , 1 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 6 -> 1 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 7 , 6 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 6 -> 6 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 7 , 0 6 8 5 13 ->= 0 6 8 5 13 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 3 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 11 -> 3 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 11 , 6 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 11 -> 6 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 11 , 0 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 9 -> 1 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 9 , 6 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 8 -> 6 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 8 , 1 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 8 -> 1 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 8 , 0 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 8 -> 0 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 8 , 6 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 8 -> 6 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 8 , 0 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 8 -> 0 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 8 , 0 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 8 -> 0 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 8 , 3 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 3 -> 3 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 3 , 3 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 3 -> 3 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 3 , 1 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 3 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 8 , 0 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 3 -> 0 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 3 , 1 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 3 -> 1 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 8 , 6 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 3 -> 6 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 8 , 0 6 8 5 11 ->= 0 6 8 5 11 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 11 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 2 -> 11 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 2 , 13 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 2 -> 13 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 2 , 2 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 4 -> 10 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 4 , 13 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 15 -> 13 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 15 , 10 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 15 -> 10 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 15 , 2 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 15 -> 2 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 15 , 13 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 15 -> 13 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 15 , 2 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 15 -> 2 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 15 , 2 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 15 -> 2 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 15 , 11 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 0 -> 11 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 0 , 11 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 0 -> 11 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 0 , 10 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 0 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 15 , 2 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 0 -> 2 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 0 , 10 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 0 -> 10 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 15 , 13 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 0 -> 13 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 15 , 2 6 8 5 2 ->= 2 6 8 5 2 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 11 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 10 -> 11 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 10 , 13 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 10 -> 13 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 10 , 2 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 5 -> 10 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 5 , 13 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 12 -> 13 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 12 , 10 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 12 -> 10 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 12 , 2 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 12 -> 2 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 12 , 13 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 12 -> 13 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 12 , 2 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 12 -> 2 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 12 , 2 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 12 -> 2 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 12 , 11 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 1 -> 11 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 1 , 11 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 1 -> 11 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 1 , 10 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 1 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 12 , 2 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 1 -> 2 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 1 , 10 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 1 -> 10 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 12 , 13 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 1 -> 13 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 12 , 2 6 8 5 10 ->= 2 6 8 5 10 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 11 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 13 -> 11 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 13 , 13 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 13 -> 13 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 13 , 2 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 14 -> 10 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 14 , 13 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 7 -> 13 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 7 , 10 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 7 -> 10 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 7 , 2 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 7 -> 2 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 7 , 13 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 7 -> 13 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 7 , 2 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 7 -> 2 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 7 , 2 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 7 -> 2 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 7 , 11 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 6 -> 11 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 6 , 11 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 6 -> 11 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 6 , 10 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 6 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 7 , 2 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 6 -> 2 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 6 , 10 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 6 -> 10 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 7 , 13 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 6 -> 13 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 7 , 2 6 8 5 13 ->= 2 6 8 5 13 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 11 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 11 -> 11 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 11 , 13 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 11 -> 13 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 11 , 2 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 9 -> 10 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 9 , 13 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 8 -> 13 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 8 , 10 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 8 -> 10 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 8 , 2 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 8 -> 2 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 8 , 13 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 8 -> 13 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 8 , 2 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 8 -> 2 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 8 , 2 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 8 -> 2 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 8 , 11 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 3 -> 11 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 3 , 11 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 3 -> 11 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 3 , 10 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 3 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 8 , 2 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 3 -> 2 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 3 , 10 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 3 -> 10 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 8 , 13 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 3 -> 13 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 8 , 2 6 8 5 11 ->= 2 6 8 5 11 , 15 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 15 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 8 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 2 -> 8 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 2 , 7 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 2 -> 7 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 2 , 15 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 4 -> 12 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 4 , 7 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 15 -> 7 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 15 , 12 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 15 -> 12 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 15 , 15 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 15 -> 15 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 15 , 7 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 15 -> 7 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 15 , 15 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 15 -> 15 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 15 , 15 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 15 -> 15 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 15 , 8 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 0 -> 8 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 0 , 8 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 0 -> 8 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 0 , 12 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 0 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 15 , 15 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 0 -> 15 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 0 , 12 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 0 -> 12 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 15 , 7 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 0 -> 7 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 15 , 15 6 8 5 2 ->= 15 6 8 5 2 , 15 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 15 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 8 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 10 -> 8 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 10 , 7 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 10 -> 7 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 10 , 15 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 5 -> 12 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 5 , 7 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 12 -> 7 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 12 , 12 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 12 -> 12 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 12 , 15 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 12 -> 15 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 12 , 7 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 12 -> 7 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 12 , 15 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 12 -> 15 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 12 , 15 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 12 -> 15 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 12 , 8 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 1 -> 8 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 1 , 8 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 1 -> 8 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 1 , 12 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 1 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 12 , 15 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 1 -> 15 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 1 , 12 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 1 -> 12 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 12 , 7 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 1 -> 7 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 12 , 15 6 8 5 10 ->= 15 6 8 5 10 , 15 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 15 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 8 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 13 -> 8 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 13 , 7 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 13 -> 7 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 13 , 15 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 14 -> 12 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 14 , 7 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 7 -> 7 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 7 , 12 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 7 -> 12 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 7 , 15 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 7 -> 15 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 7 , 7 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 7 -> 7 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 7 , 15 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 7 -> 15 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 7 , 15 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 7 -> 15 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 7 , 8 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 6 -> 8 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 6 , 8 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 6 -> 8 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 6 , 12 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 6 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 7 , 15 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 6 -> 15 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 6 , 12 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 6 -> 12 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 7 , 7 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 6 -> 7 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 7 , 15 6 8 5 13 ->= 15 6 8 5 13 , 15 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 15 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 8 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 11 -> 8 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 11 , 7 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 11 -> 7 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 11 , 15 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 9 -> 12 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 9 , 7 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 8 -> 7 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 8 , 12 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 8 -> 12 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 8 , 15 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 8 -> 15 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 8 , 7 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 8 -> 7 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 8 , 15 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 8 -> 15 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 8 , 15 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 8 -> 15 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 8 , 8 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 3 -> 8 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 3 , 8 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 3 -> 8 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 3 , 12 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 3 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 8 , 15 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 3 -> 15 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 3 , 12 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 3 -> 12 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 8 , 7 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 3 -> 7 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 8 , 15 6 8 5 11 ->= 15 6 8 5 11 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 9 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 2 -> 9 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 2 , 14 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 2 -> 14 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 2 , 4 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 4 -> 5 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 4 , 14 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 15 -> 14 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 15 , 5 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 15 -> 5 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 15 , 4 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 15 -> 4 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 15 , 14 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 15 -> 14 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 15 , 4 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 15 -> 4 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 15 , 4 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 15 -> 4 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 15 , 9 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 0 -> 9 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 0 , 9 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 0 -> 9 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 0 , 5 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 0 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 15 , 4 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 0 -> 4 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 0 , 5 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 0 -> 5 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 15 , 14 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 0 -> 14 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 15 , 4 6 8 5 2 ->= 4 6 8 5 2 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 9 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 10 -> 9 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 10 , 14 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 10 -> 14 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 10 , 4 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 5 -> 5 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 5 , 14 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 12 -> 14 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 12 , 5 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 12 -> 5 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 12 , 4 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 12 -> 4 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 12 , 14 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 12 -> 14 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 12 , 4 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 12 -> 4 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 12 , 4 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 12 -> 4 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 12 , 9 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 1 -> 9 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 1 , 9 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 1 -> 9 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 1 , 5 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 1 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 12 , 4 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 1 -> 4 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 1 , 5 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 1 -> 5 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 12 , 14 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 1 -> 14 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 12 , 4 6 8 5 10 ->= 4 6 8 5 10 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 9 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 13 -> 9 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 13 , 14 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 13 -> 14 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 13 , 4 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 14 -> 5 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 14 , 14 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 7 -> 14 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 7 , 5 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 7 -> 5 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 7 , 4 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 7 -> 4 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 7 , 14 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 7 -> 14 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 7 , 4 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 7 -> 4 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 7 , 4 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 7 -> 4 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 7 , 9 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 6 -> 9 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 6 , 9 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 6 -> 9 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 6 , 5 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 6 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 7 , 4 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 6 -> 4 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 6 , 5 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 6 -> 5 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 7 , 14 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 6 -> 14 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 7 , 4 6 8 5 13 ->= 4 6 8 5 13 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 9 4 0 3 9 5 2 1 11 5 10 13 7 8 14 7 8 5 11 -> 9 5 11 9 14 7 12 2 6 15 3 14 12 11 4 1 11 5 11 , 14 12 2 1 13 15 0 3 9 14 8 5 2 6 12 2 0 1 11 -> 14 12 11 14 12 10 11 9 4 0 6 15 1 2 0 6 15 1 11 , 4 1 13 12 11 14 8 5 10 10 2 3 9 5 2 1 13 8 9 -> 5 10 11 9 5 11 14 15 0 1 10 10 10 11 14 7 15 3 9 , 14 8 9 5 11 14 8 9 4 6 12 11 9 14 8 5 11 14 8 -> 14 8 4 3 14 8 9 9 5 11 9 14 7 8 5 10 11 14 8 , 5 10 2 0 1 11 5 10 2 3 14 8 14 7 7 12 13 7 8 -> 5 10 2 3 14 15 1 10 11 14 7 7 15 3 5 13 12 13 8 , 4 6 7 15 1 10 2 1 2 0 1 13 15 6 7 12 13 7 8 -> 4 6 7 12 13 12 10 2 1 13 15 0 1 13 15 6 15 6 8 , 14 12 11 4 0 3 5 11 4 1 13 7 15 1 13 7 7 7 8 -> 14 15 0 1 2 1 11 4 1 11 14 7 12 11 14 7 7 7 8 , 4 0 0 6 12 11 5 2 1 2 6 12 2 6 15 6 15 6 8 -> 4 0 6 15 1 13 15 1 10 11 14 15 6 15 0 1 2 6 8 , 4 6 15 3 14 15 0 6 15 6 15 3 4 0 6 15 0 6 8 -> 4 6 15 0 0 0 0 0 3 14 15 3 14 7 15 6 15 6 8 , 9 5 10 10 2 6 8 5 10 13 8 4 6 12 2 1 10 2 3 -> 9 4 1 2 0 1 13 7 12 11 14 12 10 10 10 11 5 2 3 , 9 5 11 4 6 15 3 9 14 8 4 3 9 4 0 3 5 2 3 -> 9 5 11 14 15 3 9 14 8 5 2 0 3 4 0 3 9 4 3 , 5 10 10 13 7 7 7 15 3 14 8 9 5 13 12 10 11 4 3 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 14 15 6 8 , 4 1 10 10 13 12 11 5 11 14 7 7 7 7 15 6 8 4 3 -> 4 1 10 13 7 8 14 7 12 11 14 12 11 5 13 15 6 15 3 , 5 10 11 14 8 9 4 3 4 0 6 12 2 6 8 4 3 4 3 -> 5 10 11 14 15 3 9 4 0 0 3 14 8 4 3 4 1 13 8 , 14 7 7 7 15 1 10 2 1 13 15 6 7 7 7 15 3 4 3 -> 14 7 7 15 0 0 6 12 10 2 6 7 7 15 1 11 14 7 8 , 4 6 8 5 11 ->= 4 6 8 5 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 1 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 15->14, 14->15 }, it remains to prove termination of the 112-rule system { 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 6 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 2 -> 6 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 2 , 6 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 14 -> 6 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 14 , 1 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 14 -> 1 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 14 , 0 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 14 -> 0 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 14 , 1 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 0 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 14 , 0 6 8 5 2 ->= 0 6 8 5 2 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 6 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 10 -> 6 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 10 , 6 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 12 -> 6 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 12 , 1 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 12 -> 1 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 12 , 0 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 12 -> 0 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 12 , 1 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 1 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 12 , 0 6 8 5 10 ->= 0 6 8 5 10 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 6 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 13 -> 6 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 13 , 6 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 7 -> 6 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 7 , 1 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 7 -> 1 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 7 , 0 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 7 -> 0 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 7 , 1 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 6 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 7 , 0 6 8 5 13 ->= 0 6 8 5 13 , 0 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 0 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 6 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 11 -> 6 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 11 , 6 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 8 -> 6 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 8 , 1 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 8 -> 1 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 8 , 0 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 8 -> 0 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 8 , 1 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 3 -> 1 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 8 , 0 6 8 5 11 ->= 0 6 8 5 11 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 13 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 2 -> 13 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 2 , 13 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 14 -> 13 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 14 , 10 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 14 -> 10 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 14 , 2 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 14 -> 2 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 14 , 10 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 0 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 14 , 2 6 8 5 2 ->= 2 6 8 5 2 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 13 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 10 -> 13 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 10 , 13 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 12 -> 13 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 12 , 10 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 12 -> 10 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 12 , 2 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 12 -> 2 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 12 , 10 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 1 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 12 , 2 6 8 5 10 ->= 2 6 8 5 10 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 13 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 13 -> 13 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 13 , 13 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 7 -> 13 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 7 , 10 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 7 -> 10 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 7 , 2 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 7 -> 2 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 7 , 10 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 6 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 7 , 2 6 8 5 13 ->= 2 6 8 5 13 , 2 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 2 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 13 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 11 -> 13 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 11 , 13 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 8 -> 13 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 8 , 10 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 8 -> 10 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 8 , 2 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 8 -> 2 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 8 , 10 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 3 -> 10 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 8 , 2 6 8 5 11 ->= 2 6 8 5 11 , 14 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 14 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 7 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 2 -> 7 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 2 , 7 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 14 -> 7 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 14 , 12 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 14 -> 12 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 14 , 14 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 14 -> 14 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 14 , 12 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 0 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 14 , 14 6 8 5 2 ->= 14 6 8 5 2 , 14 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 14 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 7 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 10 -> 7 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 10 , 7 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 12 -> 7 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 12 , 12 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 12 -> 12 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 12 , 14 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 12 -> 14 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 12 , 12 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 1 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 12 , 14 6 8 5 10 ->= 14 6 8 5 10 , 14 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 14 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 7 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 13 -> 7 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 13 , 7 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 7 -> 7 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 7 , 12 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 7 -> 12 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 7 , 14 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 7 -> 14 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 7 , 12 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 6 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 7 , 14 6 8 5 13 ->= 14 6 8 5 13 , 14 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 14 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 7 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 11 -> 7 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 11 , 7 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 8 -> 7 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 8 , 12 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 8 -> 12 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 8 , 14 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 8 -> 14 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 8 , 12 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 3 -> 12 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 8 , 14 6 8 5 11 ->= 14 6 8 5 11 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 2 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 2 , 15 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 2 -> 15 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 2 , 15 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 14 -> 15 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 14 , 5 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 14 -> 5 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 14 , 4 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 14 -> 4 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 14 , 5 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 0 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 14 , 4 6 8 5 2 ->= 4 6 8 5 2 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 10 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 10 , 15 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 10 -> 15 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 10 , 15 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 12 -> 15 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 12 , 5 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 12 -> 5 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 12 , 4 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 12 -> 4 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 12 , 5 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 1 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 12 , 4 6 8 5 10 ->= 4 6 8 5 10 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 13 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 13 , 15 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 13 -> 15 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 13 , 15 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 7 -> 15 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 7 , 5 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 7 -> 5 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 7 , 4 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 7 -> 4 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 7 , 5 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 6 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 7 , 4 6 8 5 13 ->= 4 6 8 5 13 , 4 1 2 0 3 4 0 3 4 3 5 2 6 7 8 9 5 10 11 -> 4 0 3 4 0 0 6 8 5 10 11 4 6 12 11 9 4 1 11 , 15 12 2 1 13 14 0 3 9 15 8 5 2 6 12 2 0 1 11 -> 15 12 11 15 12 10 11 9 4 0 6 14 1 2 0 6 14 1 11 , 15 8 9 5 11 15 8 9 4 6 12 11 9 15 8 5 11 15 8 -> 15 8 4 3 15 8 9 9 5 11 9 15 7 8 5 10 11 15 8 , 5 10 2 0 1 11 5 10 2 3 15 8 15 7 7 12 13 7 8 -> 5 10 2 3 15 14 1 10 11 15 7 7 14 3 5 13 12 13 8 , 4 6 7 14 1 10 2 1 2 0 1 13 14 6 7 12 13 7 8 -> 4 6 7 12 13 12 10 2 1 13 14 0 1 13 14 6 14 6 8 , 5 10 10 13 7 7 7 14 3 15 8 9 5 13 12 10 11 4 3 -> 5 10 10 13 7 7 8 9 5 10 11 4 6 12 11 15 14 6 8 , 4 6 8 5 11 ->= 4 6 8 5 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 6->1, 8->2, 5->3, 2->4, 1->5, 10->6, 13->7, 7->8, 14->9, 3->10, 15->11, 9->12, 12->13, 11->14, 4->15 }, it remains to prove termination of the 28-rule system { 0 1 2 3 4 ->= 0 1 2 3 4 , 5 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 5 -> 5 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 13 , 0 1 2 3 6 ->= 0 1 2 3 6 , 5 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 1 -> 5 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 8 , 0 1 2 3 7 ->= 0 1 2 3 7 , 5 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 10 -> 5 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 2 , 0 1 2 3 14 ->= 0 1 2 3 14 , 4 1 2 3 4 ->= 4 1 2 3 4 , 6 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 5 -> 6 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 13 , 4 1 2 3 6 ->= 4 1 2 3 6 , 6 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 1 -> 6 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 8 , 4 1 2 3 7 ->= 4 1 2 3 7 , 6 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 10 -> 6 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 2 , 4 1 2 3 14 ->= 4 1 2 3 14 , 9 1 2 3 4 ->= 9 1 2 3 4 , 13 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 5 -> 13 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 13 , 9 1 2 3 6 ->= 9 1 2 3 6 , 13 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 1 -> 13 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 8 , 9 1 2 3 7 ->= 9 1 2 3 7 , 13 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 10 -> 13 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 2 , 9 1 2 3 14 ->= 9 1 2 3 14 , 15 1 2 3 4 ->= 15 1 2 3 4 , 3 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 5 -> 3 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 13 , 15 1 2 3 6 ->= 15 1 2 3 6 , 3 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 1 -> 3 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 8 , 15 1 2 3 7 ->= 15 1 2 3 7 , 3 6 6 7 8 8 8 9 10 11 2 12 3 7 13 6 14 15 10 -> 3 6 6 7 8 8 2 12 3 6 14 15 1 13 14 11 9 1 2 , 15 1 2 3 14 ->= 15 1 2 3 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 1 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 7->6, 14->7, 9->8, 15->9 }, it remains to prove termination of the 16-rule system { 0 1 2 3 4 ->= 0 1 2 3 4 , 0 1 2 3 5 ->= 0 1 2 3 5 , 0 1 2 3 6 ->= 0 1 2 3 6 , 0 1 2 3 7 ->= 0 1 2 3 7 , 4 1 2 3 4 ->= 4 1 2 3 4 , 4 1 2 3 5 ->= 4 1 2 3 5 , 4 1 2 3 6 ->= 4 1 2 3 6 , 4 1 2 3 7 ->= 4 1 2 3 7 , 8 1 2 3 4 ->= 8 1 2 3 4 , 8 1 2 3 5 ->= 8 1 2 3 5 , 8 1 2 3 6 ->= 8 1 2 3 6 , 8 1 2 3 7 ->= 8 1 2 3 7 , 9 1 2 3 4 ->= 9 1 2 3 4 , 9 1 2 3 5 ->= 9 1 2 3 5 , 9 1 2 3 6 ->= 9 1 2 3 6 , 9 1 2 3 7 ->= 9 1 2 3 7 } The system is trivially terminating.