YES After renaming modulo { 0->0, 2->1, 3->2, 1->3 }, it remains to prove termination of the 81-rule system { 0 0 0 0 1 2 1 0 3 0 3 2 3 1 0 2 0 1 -> 0 2 1 0 2 1 1 2 3 0 0 0 0 3 0 0 3 1 , 0 0 1 3 3 3 0 1 2 0 3 0 3 2 2 1 0 0 -> 0 2 3 0 0 2 3 0 1 2 1 3 0 1 3 3 0 0 , 0 0 2 0 3 0 0 2 0 3 3 1 2 2 3 1 1 2 -> 0 2 1 3 0 2 0 0 0 3 1 2 1 3 0 3 2 2 , 0 0 2 3 3 0 0 3 2 1 0 0 0 0 1 2 3 0 -> 0 1 0 3 0 2 2 1 3 0 0 3 3 0 0 2 0 0 , 0 3 3 3 0 1 0 0 1 2 2 1 3 2 1 0 2 0 -> 0 2 0 3 2 0 3 0 0 2 1 3 1 1 2 1 3 0 , 0 3 3 1 2 1 0 1 2 2 3 0 0 0 0 2 0 3 -> 0 2 0 0 3 3 0 2 1 1 0 0 2 0 2 1 3 3 , 0 3 1 0 1 1 2 0 1 0 1 1 0 1 2 1 1 2 -> 0 2 0 1 2 1 1 1 0 0 1 3 0 1 1 2 1 1 , 0 3 1 0 2 3 1 0 3 0 3 2 0 0 0 1 1 1 -> 0 1 0 0 3 1 3 1 1 0 3 0 0 0 3 2 2 1 , 0 3 1 0 2 1 3 3 3 0 1 0 1 2 2 3 3 0 -> 0 2 1 0 3 2 3 3 1 3 0 2 0 1 1 3 3 0 , 0 3 2 0 1 1 3 0 1 1 0 2 2 2 3 0 1 0 -> 0 0 2 1 3 1 1 1 2 2 0 2 0 3 3 0 1 0 , 0 3 2 3 2 0 0 1 0 1 0 0 0 1 0 0 3 1 -> 0 2 0 0 1 3 1 0 0 1 2 3 0 0 3 0 0 1 , 0 3 2 1 3 2 0 3 1 0 0 1 0 3 2 0 1 3 -> 0 3 1 1 0 0 2 1 3 0 0 0 3 3 2 2 1 3 , 0 3 2 1 2 2 0 2 3 2 3 2 2 0 0 2 2 2 -> 0 2 2 2 2 3 2 0 3 3 2 2 2 1 0 0 2 2 , 0 1 0 0 3 0 0 3 2 2 0 0 3 2 3 0 0 0 -> 0 3 0 3 1 0 0 0 0 0 3 0 2 3 0 2 2 0 , 0 1 0 3 0 3 3 0 0 2 0 1 0 3 0 3 2 0 -> 0 2 3 1 2 3 1 0 0 0 0 0 0 0 0 3 3 3 , 0 1 0 3 1 3 3 1 1 2 0 3 2 3 3 1 0 3 -> 0 0 2 1 1 2 3 0 1 1 3 3 3 3 3 0 1 3 , 0 1 0 3 1 3 2 0 1 1 1 1 1 1 2 0 3 1 -> 0 1 0 1 1 1 0 0 2 1 3 1 1 3 2 3 1 1 , 0 1 0 1 3 2 1 2 0 0 2 3 2 1 3 3 2 1 -> 0 2 3 1 2 2 3 1 3 3 0 0 2 2 0 1 1 1 , 0 1 1 0 1 2 3 2 3 3 2 2 1 0 3 2 2 1 -> 0 3 1 3 2 2 3 1 2 3 0 1 0 2 2 2 1 1 , 0 1 1 3 1 0 1 2 0 0 3 1 1 1 2 1 0 1 -> 0 1 1 1 1 0 2 1 0 0 1 1 1 3 3 2 0 1 , 0 1 1 3 1 2 0 0 0 3 2 3 2 0 1 0 2 1 -> 0 2 1 2 3 1 0 0 0 0 2 3 1 3 1 0 2 1 , 0 1 2 0 0 1 2 0 3 2 0 2 1 1 1 0 1 2 -> 2 0 0 0 2 3 1 1 0 2 0 2 1 1 0 1 1 2 , 0 1 2 1 2 3 2 3 2 2 3 0 0 3 0 1 0 2 -> 0 3 0 3 3 0 0 2 3 1 0 2 2 2 1 2 1 2 , 0 2 0 1 0 2 3 1 0 3 1 3 1 1 3 2 0 2 -> 0 2 3 0 2 3 3 1 3 1 1 2 0 0 0 1 1 2 , 0 2 0 2 2 0 1 2 3 1 1 3 2 2 2 0 1 0 -> 0 2 2 1 0 1 2 0 1 3 1 3 0 2 2 2 2 0 , 0 2 1 3 3 2 1 1 1 2 0 2 3 1 2 3 1 2 -> 0 2 0 1 1 1 2 2 2 3 3 3 1 1 3 1 2 2 , 0 2 2 1 3 0 1 2 1 1 3 2 1 0 1 0 1 1 -> 0 2 0 2 1 3 1 3 0 1 1 2 0 1 1 2 1 1 , 0 2 2 2 1 0 0 1 3 2 0 3 2 2 0 0 0 1 -> 0 0 0 0 2 2 3 1 2 3 2 0 0 2 1 0 2 1 , 3 0 1 0 2 2 3 1 2 0 1 1 3 3 0 0 1 2 -> 3 3 3 0 2 1 1 1 2 1 3 1 0 2 0 0 0 2 , 3 0 1 0 2 2 1 0 1 1 2 1 0 1 2 1 1 0 -> 3 0 0 0 2 0 1 1 1 1 1 2 0 2 1 1 1 2 , 3 0 1 3 1 3 3 1 1 1 2 0 1 2 0 3 3 3 -> 1 3 1 3 1 3 1 2 0 3 1 3 1 3 0 0 2 3 , 3 3 0 3 3 2 2 0 3 2 2 0 3 2 3 1 0 1 -> 1 0 2 3 3 3 0 0 1 3 0 2 3 3 3 2 2 2 , 3 3 3 3 1 2 3 3 2 1 3 1 1 0 1 1 2 3 -> 3 3 2 1 1 3 3 3 2 2 3 1 3 0 1 1 1 3 , 3 3 3 3 2 1 0 3 0 3 3 0 0 3 1 2 3 2 -> 3 3 0 2 3 3 3 0 3 0 1 2 3 1 3 0 3 2 , 3 1 0 0 3 3 3 0 0 0 1 0 1 0 3 1 2 0 -> 3 0 1 1 1 0 0 3 1 2 0 0 3 0 3 3 0 0 , 3 1 0 3 0 1 3 0 3 3 3 0 3 2 0 0 3 1 -> 3 0 0 3 2 0 0 3 0 3 0 3 3 3 3 1 1 1 , 3 1 0 1 2 0 1 3 1 1 2 1 0 1 3 1 1 2 -> 1 1 3 3 0 0 0 1 1 1 2 1 1 1 3 2 1 2 , 3 1 0 2 3 3 0 3 1 2 3 2 3 1 0 2 2 0 -> 3 3 1 1 3 1 2 3 0 0 2 2 3 2 3 2 0 0 , 3 1 3 0 1 3 3 3 0 1 2 0 1 1 3 0 0 2 -> 3 3 3 1 1 1 3 3 0 0 1 3 0 0 1 0 2 2 , 3 1 2 0 1 2 1 0 1 3 0 2 3 2 2 3 1 0 -> 3 0 2 3 1 0 2 1 1 1 0 2 2 3 0 1 2 3 , 3 1 2 3 1 2 3 1 1 3 2 0 2 1 3 2 0 1 -> 3 1 2 3 1 0 1 1 3 2 2 2 2 1 3 3 0 1 , 3 2 0 0 3 1 0 3 3 0 3 2 1 0 1 2 1 0 -> 3 3 0 2 3 0 3 0 0 1 1 1 3 2 0 2 1 0 , 3 2 0 0 3 2 0 1 3 0 1 2 3 1 0 3 1 0 -> 3 3 1 0 0 3 3 2 1 0 3 0 0 2 1 2 1 0 , 3 2 0 1 3 0 3 2 3 0 1 3 3 2 3 0 3 3 -> 3 3 3 1 3 1 0 0 0 3 3 2 2 3 3 0 2 3 , 3 2 0 2 0 1 2 3 0 2 0 3 3 2 2 0 1 3 -> 3 2 0 2 1 0 3 3 3 2 3 0 0 0 2 2 2 1 , 3 2 1 0 2 0 1 3 3 1 0 1 2 1 0 2 0 3 -> 3 2 2 2 1 3 0 2 1 1 3 0 0 0 1 1 0 3 , 1 0 3 0 3 3 3 1 3 2 3 1 3 1 2 0 1 3 -> 1 1 0 0 3 3 3 1 1 0 3 2 2 3 3 3 1 3 , 1 0 3 0 3 2 1 3 2 0 1 0 0 1 0 3 2 3 -> 1 1 3 3 0 0 2 0 1 0 3 3 1 2 2 0 0 3 , 1 0 3 2 1 1 3 1 0 3 1 2 0 2 0 3 1 0 -> 1 3 1 3 3 1 1 1 2 2 0 1 3 0 2 0 0 0 , 1 0 1 0 0 1 2 3 0 0 1 3 0 3 1 0 1 0 -> 1 0 2 0 0 3 1 3 0 1 3 1 1 1 0 0 0 0 , 1 0 1 1 0 3 0 0 1 1 2 2 0 2 1 2 3 1 -> 3 0 2 1 1 1 1 0 2 1 2 0 2 0 0 3 1 1 , 1 0 1 2 1 1 3 3 3 0 1 0 1 1 3 0 0 1 -> 1 0 0 0 1 3 3 2 1 3 1 3 1 1 1 0 0 1 , 1 0 2 1 0 3 1 2 2 0 0 3 3 0 3 2 0 1 -> 3 3 1 0 1 2 0 0 0 2 3 1 0 2 3 2 0 1 , 1 0 2 2 0 0 1 0 3 2 1 3 1 3 2 2 3 0 -> 1 0 2 2 1 3 3 1 1 3 0 3 2 0 2 0 2 0 , 1 3 3 2 0 3 2 3 3 2 1 1 3 1 2 2 3 3 -> 1 3 0 1 1 1 2 3 3 2 2 3 2 3 2 3 3 3 , 1 1 0 3 0 1 0 2 1 0 1 0 2 0 0 3 2 0 -> 1 1 3 0 0 0 2 1 0 0 0 3 1 2 2 0 1 0 , 1 1 0 3 0 2 0 1 2 0 2 1 2 1 2 3 1 2 -> 1 1 0 0 2 1 2 2 3 0 3 0 1 1 1 2 2 2 , 1 1 3 0 3 3 1 2 0 1 0 3 1 0 1 3 2 0 -> 1 3 2 0 0 3 3 1 3 1 0 1 3 1 0 2 1 0 , 1 1 3 3 0 1 2 1 0 2 2 0 1 1 2 1 2 1 -> 1 1 0 0 1 0 1 1 1 2 2 2 2 3 1 3 2 1 , 1 1 3 2 1 1 1 3 1 1 0 0 1 1 0 0 3 1 -> 1 1 1 1 1 0 0 2 1 3 3 3 1 1 0 1 0 1 , 1 1 1 1 1 0 3 1 0 1 3 1 0 1 1 2 1 2 -> 1 1 1 0 1 1 1 1 1 1 3 3 1 1 0 0 2 2 , 1 2 3 0 1 0 1 0 2 0 1 3 2 2 0 2 1 1 -> 1 1 2 2 0 3 1 0 0 2 2 2 1 3 0 0 1 1 , 1 2 3 3 0 1 1 0 3 2 0 1 2 1 2 2 1 0 -> 3 2 1 2 0 2 1 3 0 2 0 2 1 1 1 3 1 0 , 1 2 3 2 1 2 0 2 0 1 0 3 3 1 2 2 3 2 -> 1 2 3 1 3 1 2 0 3 0 3 2 0 2 2 1 2 2 , 1 2 1 0 3 1 0 2 0 2 2 2 0 1 2 2 1 1 -> 1 2 2 2 0 2 1 1 2 1 3 1 1 0 0 2 0 2 , 1 2 2 0 1 2 3 1 0 2 0 2 0 2 1 3 0 2 -> 1 3 3 2 0 2 2 1 1 0 2 1 2 0 0 0 2 2 , 1 2 2 1 3 1 0 1 2 1 1 1 2 2 2 2 0 1 -> 1 2 2 1 0 2 2 2 3 2 1 1 1 0 2 1 1 1 , 1 2 2 1 2 0 1 3 1 2 0 2 2 3 2 2 0 0 -> 1 2 1 2 2 3 3 0 0 2 1 2 2 0 2 2 1 0 , 2 3 0 2 2 0 2 3 2 1 2 3 2 0 3 3 0 3 -> 2 3 0 0 2 3 2 2 3 2 0 1 3 2 2 3 0 3 , 2 3 3 3 1 0 3 3 2 2 3 1 2 1 2 3 1 1 -> 2 3 3 3 3 3 3 2 1 2 3 2 0 1 2 1 1 1 , 2 3 1 0 0 3 2 2 3 2 0 1 3 1 0 1 0 1 -> 2 0 3 0 2 1 3 0 1 2 2 0 1 3 1 3 0 1 , 2 3 1 2 2 3 3 0 2 1 2 1 2 2 3 1 2 2 -> 2 2 2 3 3 2 2 3 2 3 1 0 2 2 1 1 1 2 , 2 3 2 0 1 2 2 2 0 3 1 2 0 0 0 3 3 0 -> 2 0 1 2 0 0 2 1 3 3 3 0 2 0 2 0 2 3 , 2 3 2 3 0 1 0 1 2 0 1 3 2 0 2 2 1 2 -> 2 0 2 1 3 0 1 2 1 0 2 1 2 2 3 0 3 2 , 2 3 2 1 0 3 2 2 1 0 1 1 0 3 2 0 2 3 -> 2 0 3 2 1 1 3 3 0 0 2 1 2 2 0 2 3 1 , 2 1 2 2 1 2 1 0 2 0 0 3 3 3 2 0 0 3 -> 2 1 1 2 0 1 3 2 0 3 3 0 2 2 0 2 0 3 , 2 2 0 0 1 2 0 0 0 1 2 2 0 3 0 2 0 0 -> 2 0 2 0 0 0 0 0 2 3 1 0 0 2 2 2 1 0 , 2 2 1 2 0 3 2 2 0 1 3 3 2 3 0 1 2 0 -> 2 2 1 3 0 2 3 1 3 0 2 1 0 0 2 2 2 3 , 2 2 2 3 1 3 0 0 1 3 3 0 1 2 2 3 1 0 -> 2 2 3 2 1 3 1 3 2 1 1 3 3 2 0 0 0 0 , 2 2 2 2 1 1 2 2 2 3 3 3 1 0 3 2 3 3 -> 2 3 2 2 2 2 3 2 0 2 1 3 2 1 3 1 3 3 , 0 3 1 2 ->= 0 3 1 2 } The system was reversed. After renaming modulo { 1->0, 0->1, 2->2, 3->3 }, it remains to prove termination of the 81-rule system { 0 1 2 1 0 3 2 3 1 3 1 0 2 0 1 1 1 1 -> 0 3 1 1 3 1 1 1 1 3 2 0 0 2 1 0 2 1 , 1 1 0 2 2 3 1 3 1 2 0 1 3 3 3 0 1 1 -> 1 1 3 3 0 1 3 0 2 0 1 3 2 1 1 3 2 1 , 2 0 0 3 2 2 0 3 3 1 2 1 1 3 1 2 1 1 -> 2 2 3 1 3 0 2 0 3 1 1 1 2 1 3 0 2 1 , 1 3 2 0 1 1 1 1 0 2 3 1 1 3 3 2 1 1 -> 1 1 2 1 1 3 3 1 1 3 0 2 2 1 3 1 0 1 , 1 2 1 0 2 3 0 2 2 0 1 1 0 1 3 3 3 1 -> 1 3 0 2 0 0 3 0 2 1 1 3 1 2 3 1 2 1 , 3 1 2 1 1 1 1 3 2 2 0 1 0 2 0 3 3 1 -> 3 3 0 2 1 2 1 1 0 0 2 1 3 3 1 1 2 1 , 2 0 0 2 0 1 0 0 1 0 1 2 0 0 1 0 3 1 -> 0 0 2 0 0 1 3 0 1 1 0 0 0 2 0 1 2 1 , 0 0 0 1 1 1 2 3 1 3 1 0 3 2 1 0 3 1 -> 0 2 2 3 1 1 1 3 1 0 0 3 0 3 1 1 0 1 , 1 3 3 2 2 0 1 0 1 3 3 3 0 2 1 0 3 1 -> 1 3 3 0 0 1 2 1 3 0 3 3 2 3 1 0 2 1 , 1 0 1 3 2 2 2 1 0 0 1 3 0 0 1 2 3 1 -> 1 0 1 3 3 1 2 1 2 2 0 0 0 3 0 2 1 1 , 0 3 1 1 0 1 1 1 0 1 0 1 1 2 3 2 3 1 -> 0 1 1 3 1 1 3 2 0 1 1 0 3 0 1 1 2 1 , 3 0 1 2 3 1 0 1 1 0 3 1 2 3 0 2 3 1 -> 3 0 2 2 3 3 1 1 1 3 0 2 1 1 0 0 3 1 , 2 2 2 1 1 2 2 3 2 3 2 1 2 2 0 2 3 1 -> 2 2 1 1 0 2 2 2 3 3 1 2 3 2 2 2 2 1 , 1 1 1 3 2 3 1 1 2 2 3 1 1 3 1 1 0 1 -> 1 2 2 1 3 2 1 3 1 1 1 1 1 0 3 1 3 1 , 1 2 3 1 3 1 0 1 2 1 1 3 3 1 3 1 0 1 -> 3 3 3 1 1 1 1 1 1 1 1 0 3 2 0 3 2 1 , 3 1 0 3 3 2 3 1 2 0 0 3 3 0 3 1 0 1 -> 3 0 1 3 3 3 3 3 0 0 1 3 2 0 0 2 1 1 , 0 3 1 2 0 0 0 0 0 0 1 2 3 0 3 1 0 1 -> 0 0 3 2 3 0 0 3 0 2 1 1 0 0 0 1 0 1 , 0 2 3 3 0 2 3 2 1 1 2 0 2 3 0 1 0 1 -> 0 0 0 1 2 2 1 1 3 3 0 3 2 2 0 3 2 1 , 0 2 2 3 1 0 2 2 3 3 2 3 2 0 1 0 0 1 -> 0 0 2 2 2 1 0 1 3 2 0 3 2 2 3 0 3 1 , 0 1 0 2 0 0 0 3 1 1 2 0 1 0 3 0 0 1 -> 0 1 2 3 3 0 0 0 1 1 0 2 1 0 0 0 0 1 , 0 2 1 0 1 2 3 2 3 1 1 1 2 0 3 0 0 1 -> 0 2 1 0 3 0 3 2 1 1 1 1 0 3 2 0 2 1 , 2 0 1 0 0 0 2 1 2 3 1 2 0 1 1 2 0 1 -> 2 0 0 1 0 0 2 1 2 1 0 0 3 2 1 1 1 2 , 2 1 0 1 3 1 1 3 2 2 3 2 3 2 0 2 0 1 -> 2 0 2 0 2 2 2 1 0 3 2 1 1 3 3 1 3 1 , 2 1 2 3 0 0 3 0 3 1 0 3 2 1 0 1 2 1 -> 2 0 0 1 1 1 2 0 0 3 0 3 3 2 1 3 2 1 , 1 0 1 2 2 2 3 0 0 3 2 0 1 2 2 1 2 1 -> 1 2 2 2 2 1 3 0 3 0 1 2 0 1 0 2 2 1 , 2 0 3 2 0 3 2 1 2 0 0 0 2 3 3 0 2 1 -> 2 2 0 3 0 0 3 3 3 2 2 2 0 0 0 1 2 1 , 0 0 1 0 1 0 2 3 0 0 2 0 1 3 0 2 2 1 -> 0 0 2 0 0 1 2 0 0 1 3 0 3 0 2 1 2 1 , 0 1 1 1 2 2 3 1 2 3 0 1 1 0 2 2 2 1 -> 0 2 1 0 2 1 1 2 3 2 0 3 2 2 1 1 1 1 , 2 0 1 1 3 3 0 0 1 2 0 3 2 2 1 0 1 3 -> 2 1 1 1 2 1 0 3 0 2 0 0 0 2 1 3 3 3 , 1 0 0 2 0 1 0 2 0 0 1 0 2 2 1 0 1 3 -> 2 0 0 0 2 1 2 0 0 0 0 0 1 2 1 1 1 3 , 3 3 3 1 2 0 1 2 0 0 0 3 3 0 3 0 1 3 -> 3 2 1 1 3 0 3 0 3 1 2 0 3 0 3 0 3 0 , 0 1 0 3 2 3 1 2 2 3 1 2 2 3 3 1 3 3 -> 2 2 2 3 3 3 2 1 3 0 1 1 3 3 3 2 1 0 , 3 2 0 0 1 0 0 3 0 2 3 3 2 0 3 3 3 3 -> 3 0 0 0 1 3 0 3 2 2 3 3 3 0 0 2 3 3 , 2 3 2 0 3 1 1 3 3 1 3 1 0 2 3 3 3 3 -> 2 3 1 3 0 3 2 0 1 3 1 3 3 3 2 1 3 3 , 1 2 0 3 1 0 1 0 1 1 1 3 3 3 1 1 0 3 -> 1 1 3 3 1 3 1 1 2 0 3 1 1 0 0 0 1 3 , 0 3 1 1 2 3 1 3 3 3 1 3 0 1 3 1 0 3 -> 0 0 0 3 3 3 3 1 3 1 3 1 1 2 3 1 1 3 , 2 0 0 3 0 1 0 2 0 0 3 0 1 2 0 1 0 3 -> 2 0 2 3 0 0 0 2 0 0 0 1 1 1 3 3 0 0 , 1 2 2 1 0 3 2 3 2 0 3 1 3 3 2 1 0 3 -> 1 1 2 3 2 3 2 2 1 1 3 2 0 3 0 0 3 3 , 2 1 1 3 0 0 1 2 0 1 3 3 3 0 1 3 0 3 -> 2 2 1 0 1 1 3 0 1 1 3 3 0 0 0 3 3 3 , 1 0 3 2 2 3 2 1 3 0 1 0 2 0 1 2 0 3 -> 3 2 0 1 3 2 2 1 0 0 0 2 1 0 3 2 1 3 , 0 1 2 3 0 2 1 2 3 0 0 3 2 0 3 2 0 3 -> 0 1 3 3 0 2 2 2 2 3 0 0 1 0 3 2 0 3 , 1 0 2 0 1 0 2 3 1 3 3 1 0 3 1 1 2 3 -> 1 0 2 1 2 3 0 0 0 1 1 3 1 3 2 1 3 3 , 1 0 3 1 0 3 2 0 1 3 0 1 2 3 1 1 2 3 -> 1 0 2 0 2 1 1 3 1 0 2 3 3 1 1 0 3 3 , 3 3 1 3 2 3 3 0 1 3 2 3 1 3 0 1 2 3 -> 3 2 1 3 3 2 2 3 3 1 1 1 0 3 0 3 3 3 , 3 0 1 2 2 3 3 1 2 1 3 2 0 1 2 1 2 3 -> 0 2 2 2 1 1 1 3 2 3 3 3 1 0 2 1 2 3 , 3 1 2 1 0 2 0 1 0 3 3 0 1 2 1 0 2 3 -> 3 1 0 0 1 1 1 3 0 0 2 1 3 0 2 2 2 3 , 3 0 1 2 0 3 0 3 2 3 0 3 3 3 1 3 1 0 -> 3 0 3 3 3 2 2 3 1 0 0 3 3 3 1 1 0 0 , 3 2 3 1 0 1 1 0 1 2 3 0 2 3 1 3 1 0 -> 3 1 1 2 2 0 3 3 1 0 1 2 1 1 3 3 0 0 , 1 0 3 1 2 1 2 0 3 1 0 3 0 0 2 3 1 0 -> 1 1 1 2 1 3 0 1 2 2 0 0 0 3 3 0 3 0 , 1 0 1 0 3 1 3 0 1 1 3 2 0 1 1 0 1 0 -> 1 1 1 1 0 0 0 3 0 1 3 0 3 1 1 2 1 0 , 0 3 2 0 2 1 2 2 0 0 1 1 3 1 0 0 1 0 -> 0 0 3 1 1 2 1 2 0 2 1 0 0 0 0 2 1 3 , 0 1 1 3 0 0 1 0 1 3 3 3 0 0 2 0 1 0 -> 0 1 1 0 0 0 3 0 3 0 2 3 3 0 1 1 1 0 , 0 1 2 3 1 3 3 1 1 2 2 0 3 1 0 2 1 0 -> 0 1 2 3 2 1 0 3 2 1 1 1 2 0 1 0 3 3 , 1 3 2 2 3 0 3 0 2 3 1 0 1 1 2 2 1 0 -> 1 2 1 2 1 2 3 1 3 0 0 3 3 0 2 2 1 0 , 3 3 2 2 0 3 0 0 2 3 3 2 3 1 2 3 3 0 -> 3 3 3 2 3 2 3 2 2 3 3 2 0 0 0 1 3 0 , 1 2 3 1 1 2 1 0 1 0 2 1 0 1 3 1 0 0 -> 1 0 1 2 2 0 3 1 1 1 0 2 1 1 1 3 0 0 , 2 0 3 2 0 2 0 2 1 2 0 1 2 1 3 1 0 0 -> 2 2 2 0 0 0 1 3 1 3 2 2 0 2 1 1 0 0 , 1 2 3 0 1 0 3 1 0 1 2 0 3 3 1 3 0 0 -> 1 0 2 1 0 3 0 1 0 3 0 3 3 1 1 2 3 0 , 0 2 0 2 0 0 1 2 2 1 0 2 0 1 3 3 0 0 -> 0 2 3 0 3 2 2 2 2 0 0 0 1 0 1 1 0 0 , 0 3 1 1 0 0 1 1 0 0 3 0 0 0 2 3 0 0 -> 0 1 0 1 0 0 3 3 3 0 2 1 1 0 0 0 0 0 , 2 0 2 0 0 1 0 3 0 1 0 3 1 0 0 0 0 0 -> 2 2 1 1 0 0 3 3 0 0 0 0 0 0 1 0 0 0 , 0 0 2 1 2 2 3 0 1 2 1 0 1 0 1 3 2 0 -> 0 0 1 1 3 0 2 2 2 1 1 0 3 1 2 2 0 0 , 1 0 2 2 0 2 0 1 2 3 1 0 0 1 3 3 2 0 -> 1 0 3 0 0 0 2 1 2 1 3 0 2 1 2 0 2 3 , 2 3 2 2 0 3 3 1 0 1 2 1 2 0 2 3 2 0 -> 2 2 0 2 2 1 2 3 1 3 1 2 0 3 0 3 2 0 , 0 0 2 2 0 1 2 2 2 1 2 1 0 3 1 0 2 0 -> 2 1 2 1 1 0 0 3 0 2 0 0 2 1 2 2 2 0 , 2 1 3 0 2 1 2 1 2 1 0 3 2 0 1 2 2 0 -> 2 2 1 1 1 2 0 2 1 0 0 2 2 1 2 3 3 0 , 0 1 2 2 2 2 0 0 0 2 0 1 0 3 0 2 2 0 -> 0 0 0 2 1 0 0 0 2 3 2 2 2 1 0 2 2 0 , 1 1 2 2 3 2 2 1 2 0 3 0 1 2 0 2 2 0 -> 1 0 2 2 1 2 2 0 2 1 1 3 3 2 2 0 2 0 , 3 1 3 3 1 2 3 2 0 2 3 2 1 2 2 1 3 2 -> 3 1 3 2 2 3 0 1 2 3 2 2 3 2 1 1 3 2 , 0 0 3 2 0 2 0 3 2 2 3 3 1 0 3 3 3 2 -> 0 0 0 2 0 1 2 3 2 0 2 3 3 3 3 3 3 2 , 0 1 0 1 0 3 0 1 2 3 2 2 3 1 1 0 3 2 -> 0 1 3 0 3 0 1 2 2 0 1 3 0 2 1 3 1 2 , 2 2 0 3 2 2 0 2 0 2 1 3 3 2 2 0 3 2 -> 2 0 0 0 2 2 1 0 3 2 3 2 2 3 3 2 2 2 , 1 3 3 1 1 1 2 0 3 1 2 2 2 0 1 2 3 2 -> 3 2 1 2 1 2 1 3 3 3 0 2 1 1 2 0 1 2 , 2 0 2 2 1 2 3 0 1 2 0 1 0 1 3 2 3 2 -> 2 3 1 3 2 2 0 2 1 0 2 0 1 3 0 2 1 2 , 3 2 1 2 3 1 0 0 1 0 2 2 3 1 0 2 3 2 -> 0 3 2 1 2 2 0 2 1 1 3 3 0 0 2 3 1 2 , 3 1 1 2 3 3 3 1 1 2 1 0 2 0 2 2 0 2 -> 3 1 2 1 2 2 1 3 3 1 2 3 0 1 2 0 0 2 , 1 1 2 1 3 1 2 2 0 1 1 1 2 0 1 1 2 2 -> 1 0 2 2 2 1 1 0 3 2 1 1 1 1 1 2 1 2 , 1 2 0 1 3 2 3 3 0 1 2 2 3 1 2 0 2 2 -> 3 2 2 2 1 1 0 2 1 3 0 3 2 1 3 0 2 2 , 1 0 3 2 2 0 1 3 3 0 1 1 3 0 3 2 2 2 -> 1 1 1 1 2 3 3 0 0 2 3 0 3 0 2 3 2 2 , 3 3 2 3 1 0 3 3 3 2 2 2 0 0 2 2 2 2 -> 3 3 0 3 0 2 3 0 2 1 2 3 2 2 2 2 3 2 , 2 0 3 1 ->= 2 0 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, 0]->4, [0, 3]->5, [3, 2]->6, [2, 3]->7, [3, 1]->8, [1, 3]->9, [0, 2]->10, [2, 0]->11, [1, 1]->12, [2, 2]->13, [3, 3]->14, [3, 0]->15 }, it remains to prove termination of the 1296-rule system { 0 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 4 -> 0 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 4 , 1 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 4 -> 1 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 4 , 10 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 4 -> 10 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 4 , 1 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 4 -> 1 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 4 , 1 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 4 -> 1 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 4 , 5 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 4 -> 5 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 4 , 10 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 4 -> 0 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 4 , 0 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 4 -> 0 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 4 , 1 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 4 -> 1 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 4 , 1 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 4 -> 1 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 4 , 0 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 4 -> 0 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 4 , 5 15 1 2 7 8 4 1 12 4 5 8 2 7 15 10 7 8 4 -> 5 15 10 13 7 14 8 12 12 9 15 10 3 12 4 0 5 8 4 , 10 13 13 3 12 2 13 7 6 7 6 3 2 13 11 10 7 8 4 -> 10 13 3 12 4 10 13 13 7 14 8 2 7 6 13 13 13 3 4 , 1 12 12 9 6 7 8 12 2 13 7 8 12 9 8 12 4 1 4 -> 1 2 13 3 9 6 3 9 8 12 12 12 12 4 5 8 9 8 4 , 1 2 7 8 9 8 4 1 2 3 12 9 14 8 9 8 4 1 4 -> 5 14 14 8 12 12 12 12 12 12 12 4 5 6 11 5 6 3 4 , 5 8 4 5 14 6 7 8 2 11 0 5 14 15 5 8 4 1 4 -> 5 15 1 9 14 14 14 14 15 0 1 9 6 11 0 10 3 12 4 , 0 5 8 2 11 0 0 0 0 0 1 2 7 15 5 8 4 1 4 -> 0 0 5 6 7 15 0 5 15 10 3 12 4 0 0 1 4 1 4 , 0 10 7 14 15 10 7 6 3 12 2 11 10 7 15 1 4 1 4 -> 0 0 0 1 2 13 3 12 9 14 15 5 6 13 11 5 6 3 4 , 0 10 13 7 8 4 10 13 7 14 6 7 6 11 1 4 0 1 4 -> 0 0 10 13 13 3 4 1 9 6 11 5 6 13 7 15 5 8 4 , 0 1 4 10 11 0 0 5 8 12 2 11 1 4 5 15 0 1 4 -> 0 1 2 7 14 15 0 0 1 12 4 10 3 4 0 0 0 1 4 , 0 10 3 4 1 2 7 6 7 8 12 12 2 11 5 15 0 1 4 -> 0 10 3 4 5 15 5 6 3 12 12 12 4 5 6 11 10 3 4 , 10 11 1 4 0 0 10 3 2 7 8 2 11 1 12 2 11 1 4 -> 10 11 0 1 4 0 10 3 2 3 4 0 5 6 3 12 12 2 11 , 10 3 4 1 9 8 12 9 6 13 7 6 7 6 11 10 11 1 4 -> 10 11 10 11 10 13 13 3 4 5 6 3 12 9 14 8 9 8 4 , 10 3 2 7 15 0 5 15 5 8 4 5 6 3 4 1 2 3 4 -> 10 11 0 1 12 12 2 11 0 5 15 5 14 6 3 9 6 3 4 , 1 4 1 2 13 13 7 15 0 5 6 11 1 2 13 3 2 3 4 -> 1 2 13 13 13 3 9 15 5 15 1 2 11 1 4 10 13 3 4 , 10 11 5 6 11 5 6 3 2 11 0 0 10 7 14 15 10 3 4 -> 10 13 11 5 15 0 5 14 14 6 13 13 11 0 0 1 2 3 4 , 0 0 1 4 1 4 10 7 15 0 10 11 1 9 15 10 13 3 4 -> 0 0 10 11 0 1 2 11 0 1 9 15 5 15 10 3 2 3 4 , 0 1 12 12 2 13 7 8 2 7 15 1 12 4 10 13 13 3 4 -> 0 10 3 4 10 3 12 2 7 6 11 5 6 13 3 12 12 12 4 , 10 11 1 12 9 14 15 0 1 2 11 5 6 13 3 4 1 9 15 -> 10 3 12 12 2 3 4 5 15 10 11 0 0 10 3 9 14 14 15 , 1 4 0 10 11 1 4 10 11 0 1 4 10 13 3 4 1 9 15 -> 10 11 0 0 10 3 2 11 0 0 0 0 1 2 3 12 12 9 15 , 5 14 14 8 2 11 1 2 11 0 0 5 14 15 5 15 1 9 15 -> 5 6 3 12 9 15 5 15 5 8 2 11 5 15 5 15 5 15 0 , 0 1 4 5 6 7 8 2 13 7 8 2 13 7 14 8 9 14 15 -> 10 13 13 7 14 14 6 3 9 15 1 12 9 14 14 6 3 4 0 , 5 6 11 0 1 4 0 5 15 10 7 14 6 11 5 14 14 14 15 -> 5 15 0 0 1 9 15 5 6 13 7 14 14 15 0 10 7 14 15 , 10 7 6 11 5 8 12 9 14 8 9 8 4 10 7 14 14 14 15 -> 10 7 8 9 15 5 6 11 1 9 8 9 14 14 6 3 9 14 15 , 1 2 11 5 8 4 1 4 1 12 12 9 14 14 8 12 4 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12 4 5 6 3 -> 0 1 9 15 5 15 1 2 13 11 1 9 15 10 3 9 8 2 3 , 10 13 11 5 6 13 11 10 11 10 3 9 14 6 13 11 5 6 3 -> 10 11 0 0 10 13 3 4 5 6 7 6 13 7 14 6 13 13 3 , 1 9 14 8 12 12 2 11 5 8 2 13 13 11 1 2 7 6 3 -> 5 6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 3 , 10 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 3 -> 10 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 3 , 5 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 3 -> 0 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 3 , 5 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 3 -> 5 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 3 , 1 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 3 -> 1 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 3 , 1 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 3 -> 5 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 3 , 1 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 3 -> 1 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 3 , 5 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 3 -> 5 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 3 , 10 11 5 8 12 ->= 10 11 5 8 12 , 0 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 2 -> 0 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 2 , 1 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 2 -> 1 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 2 , 10 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 2 -> 10 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 2 , 1 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 2 -> 1 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 2 , 1 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 2 -> 1 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 2 , 5 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 2 -> 5 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 2 , 10 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 2 -> 0 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 2 , 0 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 2 -> 0 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 2 , 1 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 2 -> 1 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 2 , 1 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 2 -> 1 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 2 , 0 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 2 -> 0 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 2 , 5 15 1 2 7 8 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12 2 13 , 10 3 4 1 9 8 12 9 6 13 7 6 7 6 11 10 11 1 2 -> 10 11 10 11 10 13 13 3 4 5 6 3 12 9 14 8 9 8 2 , 10 3 2 7 15 0 5 15 5 8 4 5 6 3 4 1 2 3 2 -> 10 11 0 1 12 12 2 11 0 5 15 5 14 6 3 9 6 3 2 , 1 4 1 2 13 13 7 15 0 5 6 11 1 2 13 3 2 3 2 -> 1 2 13 13 13 3 9 15 5 15 1 2 11 1 4 10 13 3 2 , 10 11 5 6 11 5 6 3 2 11 0 0 10 7 14 15 10 3 2 -> 10 13 11 5 15 0 5 14 14 6 13 13 11 0 0 1 2 3 2 , 0 0 1 4 1 4 10 7 15 0 10 11 1 9 15 10 13 3 2 -> 0 0 10 11 0 1 2 11 0 1 9 15 5 15 10 3 2 3 2 , 0 1 12 12 2 13 7 8 2 7 15 1 12 4 10 13 13 3 2 -> 0 10 3 4 10 3 12 2 7 6 11 5 6 13 3 12 12 12 2 , 10 11 1 12 9 14 15 0 1 2 11 5 6 13 3 4 1 9 6 -> 10 3 12 12 2 3 4 5 15 10 11 0 0 10 3 9 14 14 6 , 1 4 0 10 11 1 4 10 11 0 1 4 10 13 3 4 1 9 6 -> 10 11 0 0 10 3 2 11 0 0 0 0 1 2 3 12 12 9 6 , 5 14 14 8 2 11 1 2 11 0 0 5 14 15 5 15 1 9 6 -> 5 6 3 12 9 15 5 15 5 8 2 11 5 15 5 15 5 15 10 , 0 1 4 5 6 7 8 2 13 7 8 2 13 7 14 8 9 14 6 -> 10 13 13 7 14 14 6 3 9 15 1 12 9 14 14 6 3 4 10 , 5 6 11 0 1 4 0 5 15 10 7 14 6 11 5 14 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10 7 6 13 7 , 5 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 7 -> 5 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 7 , 10 11 5 8 9 ->= 10 11 5 8 9 , 4 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 4 -> 4 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 4 , 12 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 4 -> 12 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 4 , 2 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 4 -> 2 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 4 , 12 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 4 -> 12 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 4 , 12 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 4 -> 12 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 4 , 9 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 4 -> 9 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 4 , 2 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 4 -> 4 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 4 , 4 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 4 -> 4 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 4 , 12 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 4 -> 12 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 4 , 12 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 4 -> 12 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 4 , 4 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 4 -> 4 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 4 , 9 15 1 2 7 8 4 1 12 4 5 8 2 7 15 10 7 8 4 -> 9 15 10 13 7 14 8 12 12 9 15 10 3 12 4 0 5 8 4 , 2 13 13 3 12 2 13 7 6 7 6 3 2 13 11 10 7 8 4 -> 2 13 3 12 4 10 13 13 7 14 8 2 7 6 13 13 13 3 4 , 12 12 12 9 6 7 8 12 2 13 7 8 12 9 8 12 4 1 4 -> 12 2 13 3 9 6 3 9 8 12 12 12 12 4 5 8 9 8 4 , 12 2 7 8 9 8 4 1 2 3 12 9 14 8 9 8 4 1 4 -> 9 14 14 8 12 12 12 12 12 12 12 4 5 6 11 5 6 3 4 , 9 8 4 5 14 6 7 8 2 11 0 5 14 15 5 8 4 1 4 -> 9 15 1 9 14 14 14 14 15 0 1 9 6 11 0 10 3 12 4 , 4 5 8 2 11 0 0 0 0 0 1 2 7 15 5 8 4 1 4 -> 4 0 5 6 7 15 0 5 15 10 3 12 4 0 0 1 4 1 4 , 4 10 7 14 15 10 7 6 3 12 2 11 10 7 15 1 4 1 4 -> 4 0 0 1 2 13 3 12 9 14 15 5 6 13 11 5 6 3 4 , 4 10 13 7 8 4 10 13 7 14 6 7 6 11 1 4 0 1 4 -> 4 0 10 13 13 3 4 1 9 6 11 5 6 13 7 15 5 8 4 , 4 1 4 10 11 0 0 5 8 12 2 11 1 4 5 15 0 1 4 -> 4 1 2 7 14 15 0 0 1 12 4 10 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12 12 12 9 -> 4 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 9 , 12 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 9 -> 12 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 9 , 2 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 9 -> 2 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 9 , 12 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 9 -> 12 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 9 , 12 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 9 -> 12 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 9 , 9 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 9 -> 9 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 9 , 2 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 9 -> 4 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 9 , 4 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 9 -> 4 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 9 , 12 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 9 -> 12 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 9 , 12 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 9 -> 12 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 9 , 4 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 9 -> 4 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 9 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11 5 14 14 14 14 -> 9 15 0 0 1 9 15 5 6 13 7 14 14 15 0 10 7 14 14 , 2 7 6 11 5 8 12 9 14 8 9 8 4 10 7 14 14 14 14 -> 2 7 8 9 15 5 6 11 1 9 8 9 14 14 6 3 9 14 14 , 12 2 11 5 8 4 1 4 1 12 12 9 14 14 8 12 4 5 14 -> 12 12 9 14 8 9 8 12 2 11 5 8 12 4 0 0 1 9 14 , 4 5 8 12 2 7 8 9 14 14 8 9 15 1 9 8 4 5 14 -> 4 0 0 5 14 14 14 8 9 8 9 8 12 2 7 8 12 9 14 , 2 11 0 5 15 1 4 10 11 0 5 15 1 2 11 1 4 5 14 -> 2 11 10 7 15 0 0 10 11 0 0 1 12 12 9 14 15 0 5 , 12 2 13 3 4 5 6 7 6 11 5 8 9 14 6 3 4 5 14 -> 12 12 2 7 6 7 6 13 3 12 9 6 11 5 15 0 5 14 14 , 2 3 12 9 15 0 1 2 11 1 9 14 14 15 1 9 15 5 14 -> 2 13 3 4 1 12 9 15 1 12 9 14 15 0 0 5 14 14 14 , 12 4 5 6 13 7 6 3 9 15 1 4 10 11 1 2 11 5 14 -> 9 6 11 1 9 6 13 3 4 0 0 10 3 4 5 6 3 9 14 , 4 1 2 7 15 10 3 2 7 15 0 5 6 11 5 6 11 5 14 -> 4 1 9 14 15 10 13 13 13 7 15 0 1 4 5 6 11 5 14 , 12 4 10 11 1 4 10 7 8 9 14 8 4 5 8 12 2 7 14 -> 12 4 10 3 2 7 15 0 0 1 12 9 8 9 6 3 9 14 14 , 12 4 5 8 4 5 6 11 1 9 15 1 2 7 8 12 2 7 14 -> 12 4 10 11 10 3 12 9 8 4 10 7 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10 3 12 9 14 15 0 10 7 8 2 7 , 9 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 7 -> 9 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 7 , 12 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 7 -> 12 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 7 , 12 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 7 -> 9 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 7 , 12 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 7 -> 12 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 7 , 9 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 7 -> 9 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 7 , 2 11 5 8 9 ->= 2 11 5 8 9 , 11 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 4 -> 11 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 4 , 3 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 4 -> 3 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 4 , 13 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 4 -> 13 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 4 , 3 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 4 -> 3 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 4 , 3 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 4 -> 3 9 15 10 11 0 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14 8 2 7 6 11 10 7 6 3 2 13 3 9 6 11 -> 7 8 9 6 13 7 15 1 2 7 6 13 7 6 3 12 9 6 11 , 11 0 5 6 11 10 11 5 6 13 7 14 8 4 5 14 14 6 11 -> 11 0 0 10 11 1 2 7 6 11 10 7 14 14 14 14 14 6 11 , 11 1 4 1 4 5 15 1 2 7 6 13 7 8 12 4 5 6 11 -> 11 1 9 15 5 15 1 2 13 11 1 9 15 10 3 9 8 2 11 , 13 13 11 5 6 13 11 10 11 10 3 9 14 6 13 11 5 6 11 -> 13 11 0 0 10 13 3 4 5 6 7 6 13 7 14 6 13 13 11 , 3 9 14 8 12 12 2 11 5 8 2 13 13 11 1 2 7 6 11 -> 7 6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 11 , 13 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 11 -> 13 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 11 , 7 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 11 -> 11 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 11 , 7 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 11 -> 7 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 11 , 3 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 11 -> 3 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 11 , 3 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 11 -> 7 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 11 , 3 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 11 -> 3 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 11 , 7 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 11 -> 7 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 11 , 13 11 5 8 4 ->= 13 11 5 8 4 , 11 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 12 -> 11 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 12 , 3 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 12 -> 3 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 12 , 13 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 12 -> 13 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 12 , 3 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 12 -> 3 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 12 , 3 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 12 -> 3 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 12 , 7 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 12 -> 7 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 12 , 13 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 12 -> 11 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 12 , 11 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 12 -> 11 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 12 , 3 9 14 6 13 11 1 4 1 9 14 14 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7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 7 -> 7 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 7 , 13 11 5 8 9 ->= 13 11 5 8 9 , 15 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 4 -> 15 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 4 , 8 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 4 -> 8 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 4 , 6 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 4 -> 6 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 4 , 8 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 4 -> 8 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 4 , 8 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 4 -> 8 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 4 , 14 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 4 -> 14 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 4 , 6 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 4 -> 15 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 4 , 15 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 4 -> 15 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 4 , 8 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 4 -> 8 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 4 , 8 4 1 9 6 13 13 3 4 0 1 9 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6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 11 , 6 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 11 -> 6 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 11 , 14 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 11 -> 15 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 11 , 14 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 11 -> 14 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 11 , 8 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 11 -> 8 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 11 , 8 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 11 -> 14 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 11 , 8 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 11 -> 8 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 11 , 14 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 11 -> 14 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 11 , 6 11 5 8 4 ->= 6 11 5 8 4 , 15 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 12 -> 15 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 12 , 8 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 12 -> 8 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 12 , 6 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 12 -> 6 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 12 , 8 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 12 -> 8 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 12 , 8 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 12 -> 8 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 12 , 14 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 12 -> 14 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 12 , 6 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 12 -> 15 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 12 , 15 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 12 -> 15 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 12 , 8 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 12 -> 8 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 12 , 8 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 12 -> 8 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 12 , 15 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 12 -> 15 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 12 , 14 15 1 2 7 8 4 1 12 4 5 8 2 7 15 10 7 8 12 -> 14 15 10 13 7 14 8 12 12 9 15 10 3 12 4 0 5 8 12 , 6 13 13 3 12 2 13 7 6 7 6 3 2 13 11 10 7 8 12 -> 6 13 3 12 4 10 13 13 7 14 8 2 7 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10 13 13 3 12 12 9 6 7 14 14 8 4 10 3 2 7 8 , 14 8 2 3 4 10 11 1 4 5 14 15 1 2 3 4 10 7 8 -> 14 8 4 0 1 12 12 9 15 0 10 3 9 15 10 13 13 7 8 , 14 15 1 2 11 5 15 5 6 7 15 5 14 14 8 9 8 4 1 -> 14 15 5 14 14 6 13 7 8 4 0 5 14 14 8 12 4 0 1 , 14 6 7 8 4 1 12 4 1 2 7 15 10 7 8 9 8 4 1 -> 14 8 12 2 13 11 5 14 8 4 1 2 3 12 9 14 15 0 1 , 8 4 5 8 2 3 2 11 5 8 4 5 15 0 10 7 8 4 1 -> 8 12 12 2 3 9 15 1 2 13 11 0 0 5 14 15 5 15 1 , 8 4 1 4 5 8 9 15 1 12 9 6 11 1 12 4 1 4 1 -> 8 12 12 12 4 0 0 5 15 1 9 15 5 8 12 2 3 4 1 , 15 5 6 11 10 3 2 13 11 0 1 12 9 8 4 0 1 4 1 -> 15 0 5 8 12 2 3 2 11 10 3 4 0 0 0 10 3 9 8 , 15 1 12 9 15 0 1 4 1 9 14 14 15 0 10 11 1 4 1 -> 15 1 12 4 0 0 5 15 5 15 10 7 14 15 1 12 12 4 1 , 15 1 2 7 8 9 14 8 12 2 13 11 5 8 4 10 3 4 1 -> 15 1 2 7 6 3 4 5 6 3 12 12 2 11 1 4 5 14 8 , 8 9 6 13 7 15 5 15 10 7 8 4 1 12 2 13 3 4 1 -> 8 2 3 2 3 2 7 8 9 15 0 5 14 15 10 13 3 4 1 , 14 14 6 13 11 5 15 0 10 7 14 6 7 8 2 7 14 15 1 -> 14 14 14 6 7 6 7 6 13 7 14 6 11 0 0 1 9 15 1 , 8 2 7 8 12 2 3 4 1 4 10 3 4 1 9 8 4 0 1 -> 8 4 1 2 13 11 5 8 12 12 4 10 3 12 12 9 15 0 1 , 6 11 5 6 11 10 11 10 3 2 11 1 2 3 9 8 4 0 1 -> 6 13 13 11 0 0 1 9 8 9 6 13 11 10 3 12 4 0 1 , 8 2 7 15 1 4 5 8 4 1 2 11 5 14 8 9 15 0 1 -> 8 4 10 3 4 5 15 1 4 5 15 5 14 8 12 2 7 15 1 , 15 10 11 10 11 0 1 2 13 3 4 10 11 1 9 14 15 0 1 -> 15 10 7 15 5 6 13 13 13 11 0 0 1 4 1 12 4 0 1 , 15 5 8 12 4 0 1 12 4 0 5 15 0 0 10 7 15 0 1 -> 15 1 4 1 4 0 5 14 14 15 10 3 12 4 0 0 0 0 1 , 6 11 10 11 0 1 4 5 15 1 4 5 8 4 0 0 0 0 1 -> 6 13 3 12 4 0 5 14 15 0 0 0 0 0 1 4 0 0 1 , 15 0 10 3 2 13 7 15 1 2 3 4 1 4 1 9 6 11 1 -> 15 0 1 12 9 15 10 13 13 3 12 4 5 8 2 13 11 0 1 , 8 4 10 13 11 10 11 1 2 7 8 4 0 1 9 14 6 11 1 -> 8 4 5 15 0 0 10 3 2 3 9 15 10 3 2 11 10 7 8 , 6 7 6 13 11 5 14 8 4 1 2 3 2 11 10 7 6 11 1 -> 6 13 11 10 13 3 2 7 8 9 8 2 11 5 15 5 6 11 1 , 15 0 10 13 11 1 2 13 13 3 2 3 4 5 8 4 10 11 1 -> 6 3 2 3 12 4 0 5 15 10 11 0 10 3 2 13 13 11 1 , 6 3 9 15 10 3 2 3 2 3 4 5 6 11 1 2 13 11 1 -> 6 13 3 12 12 2 11 10 3 4 0 10 13 3 2 7 14 15 1 , 15 1 2 13 13 13 11 0 0 10 11 1 4 5 15 10 13 11 1 -> 15 0 0 10 3 4 0 0 10 7 6 13 13 3 4 10 13 11 1 , 8 12 2 13 7 6 13 3 2 11 5 15 1 2 11 10 13 11 1 -> 8 4 10 13 3 2 13 11 10 3 12 9 14 6 13 11 10 11 1 , 14 8 9 14 8 2 7 6 11 10 7 6 3 2 13 3 9 6 3 -> 14 8 9 6 13 7 15 1 2 7 6 13 7 6 3 12 9 6 3 , 15 0 5 6 11 10 11 5 6 13 7 14 8 4 5 14 14 6 3 -> 15 0 0 10 11 1 2 7 6 11 10 7 14 14 14 14 14 6 3 , 15 1 4 1 4 5 15 1 2 7 6 13 7 8 12 4 5 6 3 -> 15 1 9 15 5 15 1 2 13 11 1 9 15 10 3 9 8 2 3 , 6 13 11 5 6 13 11 10 11 10 3 9 14 6 13 11 5 6 3 -> 6 11 0 0 10 13 3 4 5 6 7 6 13 7 14 6 13 13 3 , 8 9 14 8 12 12 2 11 5 8 2 13 13 11 1 2 7 6 3 -> 14 6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 3 , 6 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 3 -> 6 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 3 , 14 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 3 -> 15 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 3 , 14 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 3 -> 14 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 3 , 8 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 3 -> 8 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 3 , 8 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 3 -> 14 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 3 , 8 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 3 -> 8 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 3 , 14 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 3 -> 14 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 3 , 6 11 5 8 12 ->= 6 11 5 8 12 , 15 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 2 -> 15 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 2 , 8 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 2 -> 8 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 2 , 6 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 2 -> 6 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 2 , 8 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 2 -> 8 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 2 , 8 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 2 -> 8 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 2 , 14 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 2 -> 14 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 2 , 6 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 2 -> 15 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 2 , 15 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 2 -> 15 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 2 , 8 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 2 -> 8 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 2 , 8 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 2 -> 8 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 2 , 15 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 2 -> 15 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 2 , 14 15 1 2 7 8 4 1 12 4 5 8 2 7 15 10 7 8 2 -> 14 15 10 13 7 14 8 12 12 9 15 10 3 12 4 0 5 8 2 , 6 13 13 3 12 2 13 7 6 7 6 3 2 13 11 10 7 8 2 -> 6 13 3 12 4 10 13 13 7 14 8 2 7 6 13 13 13 3 2 , 8 12 12 9 6 7 8 12 2 13 7 8 12 9 8 12 4 1 2 -> 8 2 13 3 9 6 3 9 8 12 12 12 12 4 5 8 9 8 2 , 8 2 7 8 9 8 4 1 2 3 12 9 14 8 9 8 4 1 2 -> 14 14 14 8 12 12 12 12 12 12 12 4 5 6 11 5 6 3 2 , 14 8 4 5 14 6 7 8 2 11 0 5 14 15 5 8 4 1 2 -> 14 15 1 9 14 14 14 14 15 0 1 9 6 11 0 10 3 12 2 , 15 5 8 2 11 0 0 0 0 0 1 2 7 15 5 8 4 1 2 -> 15 0 5 6 7 15 0 5 15 10 3 12 4 0 0 1 4 1 2 , 15 10 7 14 15 10 7 6 3 12 2 11 10 7 15 1 4 1 2 -> 15 0 0 1 2 13 3 12 9 14 15 5 6 13 11 5 6 3 2 , 15 10 13 7 8 4 10 13 7 14 6 7 6 11 1 4 0 1 2 -> 15 0 10 13 13 3 4 1 9 6 11 5 6 13 7 15 5 8 2 , 15 1 4 10 11 0 0 5 8 12 2 11 1 4 5 15 0 1 2 -> 15 1 2 7 14 15 0 0 1 12 4 10 3 4 0 0 0 1 2 , 15 10 3 4 1 2 7 6 7 8 12 12 2 11 5 15 0 1 2 -> 15 10 3 4 5 15 5 6 3 12 12 12 4 5 6 11 10 3 2 , 6 11 1 4 0 0 10 3 2 7 8 2 11 1 12 2 11 1 2 -> 6 11 0 1 4 0 10 3 2 3 4 0 5 6 3 12 12 2 13 , 6 3 4 1 9 8 12 9 6 13 7 6 7 6 11 10 11 1 2 -> 6 11 10 11 10 13 13 3 4 5 6 3 12 9 14 8 9 8 2 , 6 3 2 7 15 0 5 15 5 8 4 5 6 3 4 1 2 3 2 -> 6 11 0 1 12 12 2 11 0 5 15 5 14 6 3 9 6 3 2 , 8 4 1 2 13 13 7 15 0 5 6 11 1 2 13 3 2 3 2 -> 8 2 13 13 13 3 9 15 5 15 1 2 11 1 4 10 13 3 2 , 6 11 5 6 11 5 6 3 2 11 0 0 10 7 14 15 10 3 2 -> 6 13 11 5 15 0 5 14 14 6 13 13 11 0 0 1 2 3 2 , 15 0 1 4 1 4 10 7 15 0 10 11 1 9 15 10 13 3 2 -> 15 0 10 11 0 1 2 11 0 1 9 15 5 15 10 3 2 3 2 , 15 1 12 12 2 13 7 8 2 7 15 1 12 4 10 13 13 3 2 -> 15 10 3 4 10 3 12 2 7 6 11 5 6 13 3 12 12 12 2 , 6 11 1 12 9 14 15 0 1 2 11 5 6 13 3 4 1 9 6 -> 6 3 12 12 2 3 4 5 15 10 11 0 0 10 3 9 14 14 6 , 8 4 0 10 11 1 4 10 11 0 1 4 10 13 3 4 1 9 6 -> 6 11 0 0 10 3 2 11 0 0 0 0 1 2 3 12 12 9 6 , 14 14 14 8 2 11 1 2 11 0 0 5 14 15 5 15 1 9 6 -> 14 6 3 12 9 15 5 15 5 8 2 11 5 15 5 15 5 15 10 , 15 1 4 5 6 7 8 2 13 7 8 2 13 7 14 8 9 14 6 -> 6 13 13 7 14 14 6 3 9 15 1 12 9 14 14 6 3 4 10 , 14 6 11 0 1 4 0 5 15 10 7 14 6 11 5 14 14 14 6 -> 14 15 0 0 1 9 15 5 6 13 7 14 14 15 0 10 7 14 6 , 6 7 6 11 5 8 12 9 14 8 9 8 4 10 7 14 14 14 6 -> 6 7 8 9 15 5 6 11 1 9 8 9 14 14 6 3 9 14 6 , 8 2 11 5 8 4 1 4 1 12 12 9 14 14 8 12 4 5 6 -> 8 12 9 14 8 9 8 12 2 11 5 8 12 4 0 0 1 9 6 , 15 5 8 12 2 7 8 9 14 14 8 9 15 1 9 8 4 5 6 -> 15 0 0 5 14 14 14 8 9 8 9 8 12 2 7 8 12 9 6 , 6 11 0 5 15 1 4 10 11 0 5 15 1 2 11 1 4 5 6 -> 6 11 10 7 15 0 0 10 11 0 0 1 12 12 9 14 15 0 10 , 8 2 13 3 4 5 6 7 6 11 5 8 9 14 6 3 4 5 6 -> 8 12 2 7 6 7 6 13 3 12 9 6 11 5 15 0 5 14 6 , 6 3 12 9 15 0 1 2 11 1 9 14 14 15 1 9 15 5 6 -> 6 13 3 4 1 12 9 15 1 12 9 14 15 0 0 5 14 14 6 , 8 4 5 6 13 7 6 3 9 15 1 4 10 11 1 2 11 5 6 -> 14 6 11 1 9 6 13 3 4 0 0 10 3 4 5 6 3 9 6 , 15 1 2 7 15 10 3 2 7 15 0 5 6 11 5 6 11 5 6 -> 15 1 9 14 15 10 13 13 13 7 15 0 1 4 5 6 11 5 6 , 8 4 10 11 1 4 10 7 8 9 14 8 4 5 8 12 2 7 6 -> 8 4 10 3 2 7 15 0 0 1 12 9 8 9 6 3 9 14 6 , 8 4 5 8 4 5 6 11 1 9 15 1 2 7 8 12 2 7 6 -> 8 4 10 11 10 3 12 9 8 4 10 7 14 8 12 4 5 14 6 , 14 14 8 9 6 7 14 15 1 9 6 7 8 9 15 1 2 7 6 -> 14 6 3 9 14 6 13 7 14 8 12 12 4 5 15 5 14 14 6 , 14 15 1 2 13 7 14 8 2 3 9 6 11 1 2 3 2 7 6 -> 15 10 13 13 3 12 12 9 6 7 14 14 8 4 10 3 2 7 6 , 14 8 2 3 4 10 11 1 4 5 14 15 1 2 3 4 10 7 6 -> 14 8 4 0 1 12 12 9 15 0 10 3 9 15 10 13 13 7 6 , 14 15 1 2 11 5 15 5 6 7 15 5 14 14 8 9 8 4 10 -> 14 15 5 14 14 6 13 7 8 4 0 5 14 14 8 12 4 0 10 , 14 6 7 8 4 1 12 4 1 2 7 15 10 7 8 9 8 4 10 -> 14 8 12 2 13 11 5 14 8 4 1 2 3 12 9 14 15 0 10 , 8 4 5 8 2 3 2 11 5 8 4 5 15 0 10 7 8 4 10 -> 8 12 12 2 3 9 15 1 2 13 11 0 0 5 14 15 5 15 10 , 8 4 1 4 5 8 9 15 1 12 9 6 11 1 12 4 1 4 10 -> 8 12 12 12 4 0 0 5 15 1 9 15 5 8 12 2 3 4 10 , 15 5 6 11 10 3 2 13 11 0 1 12 9 8 4 0 1 4 10 -> 15 0 5 8 12 2 3 2 11 10 3 4 0 0 0 10 3 9 6 , 15 1 12 9 15 0 1 4 1 9 14 14 15 0 10 11 1 4 10 -> 15 1 12 4 0 0 5 15 5 15 10 7 14 15 1 12 12 4 10 , 15 1 2 7 8 9 14 8 12 2 13 11 5 8 4 10 3 4 10 -> 15 1 2 7 6 3 4 5 6 3 12 12 2 11 1 4 5 14 6 , 8 9 6 13 7 15 5 15 10 7 8 4 1 12 2 13 3 4 10 -> 8 2 3 2 3 2 7 8 9 15 0 5 14 15 10 13 3 4 10 , 14 14 6 13 11 5 15 0 10 7 14 6 7 8 2 7 14 15 10 -> 14 14 14 6 7 6 7 6 13 7 14 6 11 0 0 1 9 15 10 , 8 2 7 8 12 2 3 4 1 4 10 3 4 1 9 8 4 0 10 -> 8 4 1 2 13 11 5 8 12 12 4 10 3 12 12 9 15 0 10 , 6 11 5 6 11 10 11 10 3 2 11 1 2 3 9 8 4 0 10 -> 6 13 13 11 0 0 1 9 8 9 6 13 11 10 3 12 4 0 10 , 8 2 7 15 1 4 5 8 4 1 2 11 5 14 8 9 15 0 10 -> 8 4 10 3 4 5 15 1 4 5 15 5 14 8 12 2 7 15 10 , 15 10 11 10 11 0 1 2 13 3 4 10 11 1 9 14 15 0 10 -> 15 10 7 15 5 6 13 13 13 11 0 0 1 4 1 12 4 0 10 , 15 5 8 12 4 0 1 12 4 0 5 15 0 0 10 7 15 0 10 -> 15 1 4 1 4 0 5 14 14 15 10 3 12 4 0 0 0 0 10 , 6 11 10 11 0 1 4 5 15 1 4 5 8 4 0 0 0 0 10 -> 6 13 3 12 4 0 5 14 15 0 0 0 0 0 1 4 0 0 10 , 15 0 10 3 2 13 7 15 1 2 3 4 1 4 1 9 6 11 10 -> 15 0 1 12 9 15 10 13 13 3 12 4 5 8 2 13 11 0 10 , 8 4 10 13 11 10 11 1 2 7 8 4 0 1 9 14 6 11 10 -> 8 4 5 15 0 0 10 3 2 3 9 15 10 3 2 11 10 7 6 , 6 7 6 13 11 5 14 8 4 1 2 3 2 11 10 7 6 11 10 -> 6 13 11 10 13 3 2 7 8 9 8 2 11 5 15 5 6 11 10 , 15 0 10 13 11 1 2 13 13 3 2 3 4 5 8 4 10 11 10 -> 6 3 2 3 12 4 0 5 15 10 11 0 10 3 2 13 13 11 10 , 6 3 9 15 10 3 2 3 2 3 4 5 6 11 1 2 13 11 10 -> 6 13 3 12 12 2 11 10 3 4 0 10 13 3 2 7 14 15 10 , 15 1 2 13 13 13 11 0 0 10 11 1 4 5 15 10 13 11 10 -> 15 0 0 10 3 4 0 0 10 7 6 13 13 3 4 10 13 11 10 , 8 12 2 13 7 6 13 3 2 11 5 15 1 2 11 10 13 11 10 -> 8 4 10 13 3 2 13 11 10 3 12 9 14 6 13 11 10 11 10 , 14 8 9 14 8 2 7 6 11 10 7 6 3 2 13 3 9 6 13 -> 14 8 9 6 13 7 15 1 2 7 6 13 7 6 3 12 9 6 13 , 15 0 5 6 11 10 11 5 6 13 7 14 8 4 5 14 14 6 13 -> 15 0 0 10 11 1 2 7 6 11 10 7 14 14 14 14 14 6 13 , 15 1 4 1 4 5 15 1 2 7 6 13 7 8 12 4 5 6 13 -> 15 1 9 15 5 15 1 2 13 11 1 9 15 10 3 9 8 2 13 , 6 13 11 5 6 13 11 10 11 10 3 9 14 6 13 11 5 6 13 -> 6 11 0 0 10 13 3 4 5 6 7 6 13 7 14 6 13 13 13 , 8 9 14 8 12 12 2 11 5 8 2 13 13 11 1 2 7 6 13 -> 14 6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 13 , 6 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 13 -> 6 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 13 , 14 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 13 -> 15 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 13 , 14 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 13 -> 14 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 13 , 8 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 13 -> 8 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 13 , 8 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 13 -> 14 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 13 , 8 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 13 -> 8 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 13 , 14 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 13 -> 14 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 13 , 6 11 5 8 2 ->= 6 11 5 8 2 , 15 1 2 3 4 5 6 7 8 9 8 4 10 11 1 12 12 12 9 -> 15 5 8 12 9 8 12 12 12 9 6 11 0 10 3 4 10 3 9 , 8 12 4 10 13 7 8 9 8 2 11 1 9 14 14 15 1 12 9 -> 8 12 9 14 15 1 9 15 10 11 1 9 6 3 12 9 6 3 9 , 6 11 0 5 6 13 11 5 14 8 2 3 12 9 8 2 3 12 9 -> 6 13 7 8 9 15 10 11 5 8 12 12 2 3 9 15 10 3 9 , 8 9 6 11 1 12 12 12 4 10 7 8 12 9 14 6 3 12 9 -> 8 12 2 3 12 9 14 8 12 9 15 10 13 3 9 8 4 1 9 , 8 2 3 4 10 7 15 10 13 11 1 12 4 1 9 14 14 8 9 -> 8 9 15 10 11 0 5 15 10 3 12 9 8 2 7 8 2 3 9 , 14 8 2 3 12 12 12 9 6 13 11 1 4 10 11 5 14 8 9 -> 14 14 15 10 3 2 3 12 4 0 10 3 9 14 8 12 2 3 9 , 6 11 0 10 11 1 4 0 1 4 1 2 11 0 1 4 5 8 9 -> 15 0 10 11 0 1 9 15 1 12 4 0 0 10 11 1 2 3 9 , 15 0 0 1 12 12 2 7 8 9 8 4 5 6 3 4 5 8 9 -> 15 10 13 7 8 12 12 9 8 4 0 5 15 5 8 12 4 1 9 , 8 9 14 6 13 11 1 4 1 9 14 14 15 10 3 4 5 8 9 -> 8 9 14 15 0 1 2 3 9 15 5 14 6 7 8 4 10 3 9 , 8 4 1 9 6 13 13 3 4 0 1 9 15 0 1 2 7 8 9 -> 8 4 1 9 14 8 2 3 2 13 11 0 0 5 15 10 3 12 9 , 15 5 8 12 4 1 12 12 4 1 4 1 12 2 7 6 7 8 9 -> 15 1 12 9 8 12 9 6 11 1 12 4 5 15 1 12 2 3 9 , 14 15 1 2 7 8 4 1 12 4 5 8 2 7 15 10 7 8 9 -> 14 15 10 13 7 14 8 12 12 9 15 10 3 12 4 0 5 8 9 , 6 13 13 3 12 2 13 7 6 7 6 3 2 13 11 10 7 8 9 -> 6 13 3 12 4 10 13 13 7 14 8 2 7 6 13 13 13 3 9 , 8 12 12 9 6 7 8 12 2 13 7 8 12 9 8 12 4 1 9 -> 8 2 13 3 9 6 3 9 8 12 12 12 12 4 5 8 9 8 9 , 8 2 7 8 9 8 4 1 2 3 12 9 14 8 9 8 4 1 9 -> 14 14 14 8 12 12 12 12 12 12 12 4 5 6 11 5 6 3 9 , 14 8 4 5 14 6 7 8 2 11 0 5 14 15 5 8 4 1 9 -> 14 15 1 9 14 14 14 14 15 0 1 9 6 11 0 10 3 12 9 , 15 5 8 2 11 0 0 0 0 0 1 2 7 15 5 8 4 1 9 -> 15 0 5 6 7 15 0 5 15 10 3 12 4 0 0 1 4 1 9 , 15 10 7 14 15 10 7 6 3 12 2 11 10 7 15 1 4 1 9 -> 15 0 0 1 2 13 3 12 9 14 15 5 6 13 11 5 6 3 9 , 15 10 13 7 8 4 10 13 7 14 6 7 6 11 1 4 0 1 9 -> 15 0 10 13 13 3 4 1 9 6 11 5 6 13 7 15 5 8 9 , 15 1 4 10 11 0 0 5 8 12 2 11 1 4 5 15 0 1 9 -> 15 1 2 7 14 15 0 0 1 12 4 10 3 4 0 0 0 1 9 , 15 10 3 4 1 2 7 6 7 8 12 12 2 11 5 15 0 1 9 -> 15 10 3 4 5 15 5 6 3 12 12 12 4 5 6 11 10 3 9 , 6 11 1 4 0 0 10 3 2 7 8 2 11 1 12 2 11 1 9 -> 6 11 0 1 4 0 10 3 2 3 4 0 5 6 3 12 12 2 7 , 6 3 4 1 9 8 12 9 6 13 7 6 7 6 11 10 11 1 9 -> 6 11 10 11 10 13 13 3 4 5 6 3 12 9 14 8 9 8 9 , 6 3 2 7 15 0 5 15 5 8 4 5 6 3 4 1 2 3 9 -> 6 11 0 1 12 12 2 11 0 5 15 5 14 6 3 9 6 3 9 , 8 4 1 2 13 13 7 15 0 5 6 11 1 2 13 3 2 3 9 -> 8 2 13 13 13 3 9 15 5 15 1 2 11 1 4 10 13 3 9 , 6 11 5 6 11 5 6 3 2 11 0 0 10 7 14 15 10 3 9 -> 6 13 11 5 15 0 5 14 14 6 13 13 11 0 0 1 2 3 9 , 15 0 1 4 1 4 10 7 15 0 10 11 1 9 15 10 13 3 9 -> 15 0 10 11 0 1 2 11 0 1 9 15 5 15 10 3 2 3 9 , 15 1 12 12 2 13 7 8 2 7 15 1 12 4 10 13 13 3 9 -> 15 10 3 4 10 3 12 2 7 6 11 5 6 13 3 12 12 12 9 , 6 11 1 12 9 14 15 0 1 2 11 5 6 13 3 4 1 9 14 -> 6 3 12 12 2 3 4 5 15 10 11 0 0 10 3 9 14 14 14 , 8 4 0 10 11 1 4 10 11 0 1 4 10 13 3 4 1 9 14 -> 6 11 0 0 10 3 2 11 0 0 0 0 1 2 3 12 12 9 14 , 14 14 14 8 2 11 1 2 11 0 0 5 14 15 5 15 1 9 14 -> 14 6 3 12 9 15 5 15 5 8 2 11 5 15 5 15 5 15 5 , 15 1 4 5 6 7 8 2 13 7 8 2 13 7 14 8 9 14 14 -> 6 13 13 7 14 14 6 3 9 15 1 12 9 14 14 6 3 4 5 , 14 6 11 0 1 4 0 5 15 10 7 14 6 11 5 14 14 14 14 -> 14 15 0 0 1 9 15 5 6 13 7 14 14 15 0 10 7 14 14 , 6 7 6 11 5 8 12 9 14 8 9 8 4 10 7 14 14 14 14 -> 6 7 8 9 15 5 6 11 1 9 8 9 14 14 6 3 9 14 14 , 8 2 11 5 8 4 1 4 1 12 12 9 14 14 8 12 4 5 14 -> 8 12 9 14 8 9 8 12 2 11 5 8 12 4 0 0 1 9 14 , 15 5 8 12 2 7 8 9 14 14 8 9 15 1 9 8 4 5 14 -> 15 0 0 5 14 14 14 8 9 8 9 8 12 2 7 8 12 9 14 , 6 11 0 5 15 1 4 10 11 0 5 15 1 2 11 1 4 5 14 -> 6 11 10 7 15 0 0 10 11 0 0 1 12 12 9 14 15 0 5 , 8 2 13 3 4 5 6 7 6 11 5 8 9 14 6 3 4 5 14 -> 8 12 2 7 6 7 6 13 3 12 9 6 11 5 15 0 5 14 14 , 6 3 12 9 15 0 1 2 11 1 9 14 14 15 1 9 15 5 14 -> 6 13 3 4 1 12 9 15 1 12 9 14 15 0 0 5 14 14 14 , 8 4 5 6 13 7 6 3 9 15 1 4 10 11 1 2 11 5 14 -> 14 6 11 1 9 6 13 3 4 0 0 10 3 4 5 6 3 9 14 , 15 1 2 7 15 10 3 2 7 15 0 5 6 11 5 6 11 5 14 -> 15 1 9 14 15 10 13 13 13 7 15 0 1 4 5 6 11 5 14 , 8 4 10 11 1 4 10 7 8 9 14 8 4 5 8 12 2 7 14 -> 8 4 10 3 2 7 15 0 0 1 12 9 8 9 6 3 9 14 14 , 8 4 5 8 4 5 6 11 1 9 15 1 2 7 8 12 2 7 14 -> 8 4 10 11 10 3 12 9 8 4 10 7 14 8 12 4 5 14 14 , 14 14 8 9 6 7 14 15 1 9 6 7 8 9 15 1 2 7 14 -> 14 6 3 9 14 6 13 7 14 8 12 12 4 5 15 5 14 14 14 , 14 15 1 2 13 7 14 8 2 3 9 6 11 1 2 3 2 7 14 -> 15 10 13 13 3 12 12 9 6 7 14 14 8 4 10 3 2 7 14 , 14 8 2 3 4 10 11 1 4 5 14 15 1 2 3 4 10 7 14 -> 14 8 4 0 1 12 12 9 15 0 10 3 9 15 10 13 13 7 14 , 14 15 1 2 11 5 15 5 6 7 15 5 14 14 8 9 8 4 5 -> 14 15 5 14 14 6 13 7 8 4 0 5 14 14 8 12 4 0 5 , 14 6 7 8 4 1 12 4 1 2 7 15 10 7 8 9 8 4 5 -> 14 8 12 2 13 11 5 14 8 4 1 2 3 12 9 14 15 0 5 , 8 4 5 8 2 3 2 11 5 8 4 5 15 0 10 7 8 4 5 -> 8 12 12 2 3 9 15 1 2 13 11 0 0 5 14 15 5 15 5 , 8 4 1 4 5 8 9 15 1 12 9 6 11 1 12 4 1 4 5 -> 8 12 12 12 4 0 0 5 15 1 9 15 5 8 12 2 3 4 5 , 15 5 6 11 10 3 2 13 11 0 1 12 9 8 4 0 1 4 5 -> 15 0 5 8 12 2 3 2 11 10 3 4 0 0 0 10 3 9 14 , 15 1 12 9 15 0 1 4 1 9 14 14 15 0 10 11 1 4 5 -> 15 1 12 4 0 0 5 15 5 15 10 7 14 15 1 12 12 4 5 , 15 1 2 7 8 9 14 8 12 2 13 11 5 8 4 10 3 4 5 -> 15 1 2 7 6 3 4 5 6 3 12 12 2 11 1 4 5 14 14 , 8 9 6 13 7 15 5 15 10 7 8 4 1 12 2 13 3 4 5 -> 8 2 3 2 3 2 7 8 9 15 0 5 14 15 10 13 3 4 5 , 14 14 6 13 11 5 15 0 10 7 14 6 7 8 2 7 14 15 5 -> 14 14 14 6 7 6 7 6 13 7 14 6 11 0 0 1 9 15 5 , 8 2 7 8 12 2 3 4 1 4 10 3 4 1 9 8 4 0 5 -> 8 4 1 2 13 11 5 8 12 12 4 10 3 12 12 9 15 0 5 , 6 11 5 6 11 10 11 10 3 2 11 1 2 3 9 8 4 0 5 -> 6 13 13 11 0 0 1 9 8 9 6 13 11 10 3 12 4 0 5 , 8 2 7 15 1 4 5 8 4 1 2 11 5 14 8 9 15 0 5 -> 8 4 10 3 4 5 15 1 4 5 15 5 14 8 12 2 7 15 5 , 15 10 11 10 11 0 1 2 13 3 4 10 11 1 9 14 15 0 5 -> 15 10 7 15 5 6 13 13 13 11 0 0 1 4 1 12 4 0 5 , 15 5 8 12 4 0 1 12 4 0 5 15 0 0 10 7 15 0 5 -> 15 1 4 1 4 0 5 14 14 15 10 3 12 4 0 0 0 0 5 , 6 11 10 11 0 1 4 5 15 1 4 5 8 4 0 0 0 0 5 -> 6 13 3 12 4 0 5 14 15 0 0 0 0 0 1 4 0 0 5 , 15 0 10 3 2 13 7 15 1 2 3 4 1 4 1 9 6 11 5 -> 15 0 1 12 9 15 10 13 13 3 12 4 5 8 2 13 11 0 5 , 8 4 10 13 11 10 11 1 2 7 8 4 0 1 9 14 6 11 5 -> 8 4 5 15 0 0 10 3 2 3 9 15 10 3 2 11 10 7 14 , 6 7 6 13 11 5 14 8 4 1 2 3 2 11 10 7 6 11 5 -> 6 13 11 10 13 3 2 7 8 9 8 2 11 5 15 5 6 11 5 , 15 0 10 13 11 1 2 13 13 3 2 3 4 5 8 4 10 11 5 -> 6 3 2 3 12 4 0 5 15 10 11 0 10 3 2 13 13 11 5 , 6 3 9 15 10 3 2 3 2 3 4 5 6 11 1 2 13 11 5 -> 6 13 3 12 12 2 11 10 3 4 0 10 13 3 2 7 14 15 5 , 15 1 2 13 13 13 11 0 0 10 11 1 4 5 15 10 13 11 5 -> 15 0 0 10 3 4 0 0 10 7 6 13 13 3 4 10 13 11 5 , 8 12 2 13 7 6 13 3 2 11 5 15 1 2 11 10 13 11 5 -> 8 4 10 13 3 2 13 11 10 3 12 9 14 6 13 11 10 11 5 , 14 8 9 14 8 2 7 6 11 10 7 6 3 2 13 3 9 6 7 -> 14 8 9 6 13 7 15 1 2 7 6 13 7 6 3 12 9 6 7 , 15 0 5 6 11 10 11 5 6 13 7 14 8 4 5 14 14 6 7 -> 15 0 0 10 11 1 2 7 6 11 10 7 14 14 14 14 14 6 7 , 15 1 4 1 4 5 15 1 2 7 6 13 7 8 12 4 5 6 7 -> 15 1 9 15 5 15 1 2 13 11 1 9 15 10 3 9 8 2 7 , 6 13 11 5 6 13 11 10 11 10 3 9 14 6 13 11 5 6 7 -> 6 11 0 0 10 13 3 4 5 6 7 6 13 7 14 6 13 13 7 , 8 9 14 8 12 12 2 11 5 8 2 13 13 11 1 2 7 6 7 -> 14 6 3 2 3 2 3 9 14 14 15 10 3 12 2 11 1 2 7 , 6 11 10 13 3 2 7 15 1 2 11 1 4 1 9 6 7 6 7 -> 6 7 8 9 6 13 11 10 3 4 10 11 1 9 15 10 3 2 7 , 14 6 3 2 7 8 4 0 1 4 10 13 7 8 4 10 7 6 7 -> 15 5 6 3 2 13 11 10 3 12 9 14 15 0 10 7 8 2 7 , 14 8 12 2 7 14 14 8 12 2 3 4 10 11 10 13 11 10 7 -> 14 8 2 3 2 13 3 9 14 8 2 7 15 1 2 11 0 10 7 , 8 12 2 3 9 8 2 13 11 1 12 12 2 11 1 12 2 13 7 -> 8 4 10 13 13 3 12 4 5 6 3 12 12 12 12 2 3 2 7 , 8 2 11 1 9 6 7 14 15 1 2 13 7 8 2 11 10 13 7 -> 14 6 13 13 3 12 4 10 3 9 15 5 6 3 9 15 10 13 7 , 8 4 5 6 13 11 1 9 14 15 1 12 9 15 5 6 13 13 7 -> 8 12 12 12 2 7 14 15 0 10 7 15 5 15 10 7 6 13 7 , 14 14 6 7 8 4 5 14 14 6 13 13 11 0 10 13 13 13 7 -> 14 14 15 5 15 10 7 15 10 3 2 7 6 13 13 13 7 6 7 , 6 11 5 8 9 ->= 6 11 5 8 9 } 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 4 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 6 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 2 | | 0 1 | \ / 7 is interpreted by / \ | 1 3 | | 0 1 | \ / 8 is interpreted by / \ | 1 4 | | 0 1 | \ / 9 is interpreted by / \ | 1 2 | | 0 1 | \ / 10 is interpreted by / \ | 1 1 | | 0 1 | \ / 11 is interpreted by / \ | 1 4 | | 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 { 10->0, 11->1, 5->2, 8->3, 4->4, 12->5, 2->6, 9->7, 13->8, 6->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 , 6 1 2 3 4 ->= 6 1 2 3 4 , 6 1 2 3 5 ->= 6 1 2 3 5 , 6 1 2 3 6 ->= 6 1 2 3 6 , 6 1 2 3 7 ->= 6 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.