YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 110-rule system { 0 0 0 1 0 -> 2 2 1 1 1 0 , 0 1 0 1 2 2 -> 1 1 2 0 0 2 , 2 2 0 0 2 2 -> 2 2 1 1 1 2 0 , 0 1 0 0 2 2 2 1 -> 2 1 1 1 2 0 0 1 1 , 0 1 2 0 1 1 2 1 -> 1 0 2 2 1 1 0 1 , 0 2 2 2 2 0 1 2 2 -> 1 1 1 1 0 1 0 0 2 2 , 2 0 0 0 1 0 2 0 0 -> 1 0 0 1 2 0 1 1 1 1 2 , 2 2 1 2 0 0 1 1 2 -> 0 1 1 1 1 1 2 2 2 1 , 0 0 0 0 0 1 1 0 1 0 1 -> 0 1 2 1 0 1 0 0 1 1 1 1 , 0 0 1 0 2 0 0 0 0 0 2 -> 1 0 0 1 2 1 2 1 0 1 1 1 , 0 2 0 1 0 2 0 1 0 1 2 -> 1 0 0 2 1 1 1 1 2 1 1 2 0 , 1 0 0 0 2 0 2 1 2 2 0 -> 1 0 1 0 0 2 2 2 1 1 1 1 2 , 2 2 1 2 0 2 0 1 0 1 2 -> 1 1 1 1 0 2 1 2 2 2 1 0 , 1 0 1 0 2 2 0 1 0 0 0 0 -> 1 0 0 2 1 2 0 0 0 1 1 1 1 2 , 1 2 1 2 0 1 2 2 2 0 0 1 -> 1 1 1 1 2 1 1 1 1 1 1 1 1 0 1 1 2 , 0 1 2 2 2 2 2 2 0 0 2 2 1 -> 2 2 0 2 2 0 1 0 1 1 1 1 1 2 2 1 , 0 2 0 1 1 0 2 2 0 0 1 2 0 -> 2 1 2 1 0 2 1 1 1 1 1 1 0 1 , 0 2 0 2 0 1 0 2 2 1 1 0 0 -> 1 1 1 1 0 2 2 2 2 2 1 1 1 2 0 1 , 2 0 2 0 0 2 2 2 2 1 2 0 2 -> 0 0 2 0 1 0 0 2 1 1 1 1 1 2 1 2 , 2 1 0 1 1 0 1 0 2 1 2 0 2 -> 1 1 1 1 1 1 0 0 0 1 0 2 2 2 0 2 , 2 1 1 0 2 2 1 2 0 2 2 1 2 -> 1 1 1 0 2 1 1 1 1 1 0 1 2 2 2 0 , 2 1 2 0 0 0 1 0 1 0 0 0 0 -> 2 2 0 1 2 0 0 1 1 1 1 1 1 0 , 0 0 0 2 0 1 1 2 1 1 2 0 1 1 -> 1 1 2 0 2 0 2 2 1 2 0 1 1 1 1 , 2 1 2 0 1 2 1 2 1 2 1 1 0 0 -> 1 1 2 0 2 1 2 2 1 2 1 1 0 0 , 1 2 0 1 0 0 1 2 2 0 0 0 0 0 2 -> 1 1 1 2 1 0 1 1 1 1 2 2 1 1 0 0 0 , 2 1 1 0 0 0 0 1 0 1 2 2 1 2 1 -> 2 0 1 1 1 1 2 2 1 1 2 2 1 1 1 2 , 0 1 0 1 0 1 0 1 0 2 1 1 0 0 0 2 -> 0 0 1 1 1 1 2 0 1 0 1 0 0 0 0 2 , 1 0 2 2 1 0 1 0 1 1 2 2 1 2 0 0 -> 1 1 1 1 1 1 1 1 1 1 2 1 2 2 2 2 2 0 2 , 2 0 0 0 2 2 0 2 1 0 1 0 2 2 1 1 -> 2 1 1 1 1 0 0 0 1 1 2 1 2 0 2 1 1 1 , 2 1 2 1 2 0 1 2 0 2 0 0 1 0 2 0 -> 1 1 1 0 1 2 2 1 0 1 2 2 2 1 1 1 2 , 2 2 0 2 2 0 2 2 1 2 0 2 1 0 2 2 -> 1 2 1 1 1 2 2 0 1 2 2 1 1 1 2 2 1 1 1 , 0 2 2 0 0 2 1 2 2 0 2 1 0 0 0 0 2 -> 0 1 0 2 1 2 2 1 2 1 2 2 0 1 1 1 1 2 2 , 1 1 2 0 0 0 2 0 0 1 1 0 0 2 1 2 2 -> 1 1 2 1 1 1 1 2 2 1 1 2 1 0 0 0 1 1 0 , 2 2 2 2 0 1 0 2 2 0 2 0 0 0 0 0 0 -> 0 1 2 1 2 2 0 1 0 0 0 1 1 1 1 2 2 1 , 0 2 2 2 2 0 2 0 0 1 1 1 0 2 2 1 1 2 -> 0 1 0 2 1 1 1 1 1 1 0 2 2 1 1 1 2 1 2 2 , 1 2 2 0 2 2 0 0 1 2 1 2 0 1 0 2 1 2 -> 1 0 0 2 2 1 0 2 1 1 2 0 1 1 1 1 0 2 0 0 , 2 1 2 0 2 0 0 2 2 1 2 2 0 2 0 2 2 1 -> 0 2 0 0 1 1 1 2 0 2 0 1 0 2 0 2 2 1 1 , 0 0 2 2 0 0 1 0 0 1 1 2 1 0 1 0 2 1 2 -> 0 0 2 2 0 0 1 1 2 0 0 1 0 2 1 0 1 1 1 1 1 1 1 , 0 1 0 0 1 1 0 0 0 1 0 0 2 1 2 1 2 0 1 -> 2 0 0 2 2 1 1 1 2 0 0 2 0 1 1 0 2 1 0 1 , 0 1 2 0 2 1 0 2 0 2 2 1 2 1 2 2 0 2 2 -> 0 2 0 2 0 1 1 1 1 1 2 2 2 0 2 2 0 2 2 2 , 0 1 2 1 2 2 0 1 0 1 0 2 0 1 0 1 0 1 0 -> 1 1 1 0 1 2 0 0 1 1 0 0 0 0 1 2 0 2 2 , 0 0 0 0 0 2 1 2 2 2 1 0 2 0 1 2 2 0 1 2 -> 0 2 2 1 1 1 1 1 1 2 2 2 2 1 0 2 0 0 0 0 0 2 , 0 1 0 1 2 1 0 1 0 0 2 1 2 0 1 0 2 0 1 2 -> 2 1 2 1 1 2 0 1 0 1 2 2 0 0 0 1 1 1 2 2 2 , 1 0 2 1 1 2 2 0 1 1 1 2 0 2 0 2 2 2 0 2 -> 1 1 2 1 2 1 2 2 1 1 1 1 2 2 0 2 1 0 0 0 1 , 1 2 1 1 2 1 1 2 1 0 1 1 1 2 0 1 2 2 0 0 -> 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 2 1 2 , 2 0 0 1 2 0 2 2 2 2 0 0 1 1 2 1 2 2 2 2 -> 1 0 1 0 0 0 1 1 1 2 2 2 1 1 1 2 2 2 2 0 2 1 , 2 0 0 2 0 0 1 0 0 0 1 1 2 0 0 1 1 0 2 1 -> 0 1 1 0 2 2 1 1 1 2 2 1 0 2 0 1 1 1 1 2 1 , 2 2 0 0 1 1 2 1 1 0 1 2 0 1 2 0 2 2 0 0 -> 1 2 0 2 2 2 0 0 0 1 1 1 0 1 1 0 1 1 1 1 1 2 2 , 0 1 0 1 1 0 1 2 1 2 2 2 1 2 1 0 2 2 0 0 0 -> 1 0 2 0 0 0 1 0 1 1 1 0 0 2 1 1 1 1 0 1 0 0 1 , 2 0 1 1 1 0 1 0 2 0 1 1 2 1 0 1 1 2 2 0 1 -> 2 1 1 1 2 0 0 0 2 0 1 2 0 1 0 2 1 1 1 1 1 , 2 0 2 2 0 1 0 1 0 2 0 1 0 2 2 2 2 0 1 2 0 -> 1 1 1 2 1 0 0 0 1 2 1 2 2 1 1 1 1 2 1 0 0 1 1 1 1 1 1 0 , 0 0 2 2 1 2 0 1 0 0 2 1 1 2 0 2 1 0 1 0 0 0 -> 2 1 0 2 2 2 1 1 1 1 1 1 1 1 2 0 1 0 0 0 1 1 0 0 , 0 1 0 2 1 1 2 1 2 2 0 1 1 2 0 1 2 0 2 1 2 1 -> 1 2 1 1 0 0 0 1 2 1 0 2 1 1 2 0 1 2 0 1 1 1 1 , 0 2 2 0 2 0 0 1 2 1 2 0 2 0 0 0 1 0 2 2 1 0 -> 0 0 1 1 1 2 2 0 1 2 0 1 2 1 1 1 1 0 2 0 1 0 1 , 1 1 2 1 0 1 1 2 2 2 2 2 0 1 1 0 2 2 0 2 1 2 -> 1 1 1 1 0 2 0 1 0 1 0 2 0 0 1 2 2 0 0 1 1 2 1 , 2 1 1 1 2 2 0 1 0 1 0 2 0 0 0 0 1 2 0 2 2 2 -> 1 2 1 2 0 1 1 1 1 0 0 1 1 0 2 1 2 1 1 0 0 0 1 , 2 1 2 0 1 1 2 2 0 1 1 0 1 2 1 0 2 2 2 2 1 2 -> 1 1 1 1 1 2 0 1 1 1 2 2 2 1 0 1 1 2 0 2 1 0 0 , 2 1 2 2 0 2 1 2 0 2 0 2 0 2 2 0 0 1 0 0 2 1 -> 0 2 1 0 0 1 0 2 1 2 1 1 0 0 0 2 2 2 1 2 1 1 1 , 2 1 2 2 1 0 2 0 1 0 2 1 1 0 0 2 0 0 1 1 0 2 -> 2 2 2 0 2 0 0 0 1 2 0 0 2 0 2 0 2 0 2 1 1 1 1 , 0 0 1 2 2 1 2 1 2 0 1 1 0 2 2 0 0 2 1 0 0 1 2 -> 2 0 1 1 0 1 2 2 0 2 1 1 2 0 1 1 1 1 0 2 2 1 1 1 , 0 2 0 0 1 1 0 2 1 1 0 1 2 2 1 0 0 0 0 0 2 0 2 -> 0 1 1 1 0 2 2 2 0 0 1 0 2 1 2 0 1 0 0 0 0 0 2 , 0 2 2 1 2 1 0 2 1 2 0 1 0 1 1 1 2 2 0 2 0 2 1 -> 2 0 1 1 1 1 1 1 1 2 0 2 2 1 1 1 0 2 0 2 2 2 1 1 0 , 1 0 2 2 2 1 2 1 1 0 0 1 0 0 0 2 0 2 2 2 2 2 1 -> 1 1 1 2 0 0 1 0 2 1 1 2 2 1 1 1 2 0 1 0 0 1 1 0 1 , 0 0 2 1 0 0 2 1 2 2 0 1 2 0 0 0 2 1 0 2 1 0 2 1 -> 0 1 2 1 2 2 1 1 2 2 1 0 2 0 1 2 1 1 1 0 0 2 0 1 1 , 0 1 0 2 0 0 1 2 1 2 2 2 0 0 0 0 0 0 1 2 0 0 0 0 -> 2 1 0 0 2 0 1 0 1 2 2 1 1 1 2 2 1 1 1 1 2 2 2 2 0 0 , 0 1 0 2 1 0 2 0 1 1 2 2 1 2 1 0 0 0 1 1 1 0 2 2 -> 1 1 1 1 1 2 2 0 0 2 2 0 1 2 0 0 2 2 2 0 1 0 2 1 2 , 0 1 2 1 1 0 1 1 2 1 2 1 0 0 0 1 1 2 0 1 0 0 0 1 -> 0 1 2 2 1 1 0 2 2 1 0 2 1 2 0 1 1 2 1 1 1 1 2 1 1 , 0 2 1 0 1 0 0 1 0 0 0 2 0 0 2 0 2 2 1 0 2 0 2 0 -> 1 0 2 2 0 1 1 2 2 1 2 2 2 2 1 1 1 1 0 0 2 2 1 0 0 2 , 1 2 0 1 1 0 0 0 0 1 2 0 0 2 2 2 1 0 0 0 2 2 0 0 -> 1 0 1 2 2 2 1 2 1 2 1 1 1 1 1 1 0 0 0 1 1 0 0 2 1 0 1 , 1 2 2 0 0 1 2 0 1 2 0 2 0 1 0 1 2 2 1 1 2 1 2 2 -> 1 1 1 1 1 2 0 0 2 2 0 2 1 1 1 0 0 0 1 2 2 0 0 1 1 , 2 1 1 2 1 2 1 2 1 2 0 0 1 0 1 0 1 2 0 2 2 0 2 0 -> 2 0 0 0 0 2 1 0 2 1 1 2 0 2 0 1 0 2 0 1 0 1 1 1 1 , 0 0 0 0 0 0 0 0 2 0 0 1 0 2 1 0 0 2 1 2 2 1 0 1 1 -> 1 1 1 1 0 0 1 0 1 2 2 1 1 1 1 0 2 0 2 0 1 1 0 0 0 0 , 0 1 0 0 2 1 2 0 1 1 0 2 2 1 2 0 1 0 0 0 2 0 2 2 0 -> 0 2 1 1 0 2 2 2 1 1 2 1 2 0 0 1 1 1 1 1 0 0 1 2 0 2 2 , 0 2 2 1 0 1 0 2 2 0 2 0 0 0 1 0 2 2 2 0 2 2 1 2 1 -> 1 0 0 0 2 2 1 1 1 1 2 1 0 2 0 0 2 0 2 1 1 0 0 0 2 1 , 0 2 2 2 2 0 1 0 2 0 0 1 2 2 1 2 2 0 0 0 0 2 1 0 1 -> 2 1 1 1 2 1 2 0 2 1 1 0 0 2 1 1 0 2 1 2 2 0 2 2 1 1 , 1 0 0 0 2 0 1 0 1 0 2 0 1 0 0 1 0 1 2 2 0 1 2 0 2 -> 1 0 2 2 1 0 1 2 1 2 2 0 0 0 1 1 1 1 0 0 2 1 1 1 2 1 , 1 1 2 0 0 1 0 1 2 0 0 2 2 0 0 0 2 2 2 0 2 0 2 0 2 -> 1 1 1 1 2 2 1 1 0 2 2 1 2 0 0 0 1 0 2 1 0 1 2 1 0 0 0 , 1 2 1 1 0 0 1 1 2 0 0 0 1 0 1 0 1 0 0 2 1 2 2 0 2 -> 1 1 1 2 2 2 2 0 0 1 0 1 1 2 1 1 1 0 0 1 1 1 2 0 0 1 , 1 2 2 0 0 2 2 2 1 1 0 0 1 2 0 1 2 1 2 1 1 2 1 2 0 -> 1 2 1 0 2 0 2 1 1 2 2 2 1 0 2 1 0 2 0 0 2 2 1 1 1 , 2 0 0 0 0 2 0 1 0 0 1 0 0 1 0 0 0 0 2 1 0 2 0 2 1 -> 1 0 2 0 1 2 1 1 1 0 1 0 2 2 2 0 1 0 2 2 2 2 1 1 1 0 1 , 2 1 2 2 1 1 2 2 0 1 2 2 0 2 0 1 0 2 1 1 0 0 2 0 2 -> 1 0 1 2 1 0 1 1 1 1 0 1 2 2 2 1 1 1 1 1 0 0 2 1 0 2 2 , 0 0 1 1 2 1 0 1 2 2 2 0 0 1 1 2 0 0 2 1 2 1 0 0 0 2 -> 0 1 2 1 1 0 2 1 1 1 0 0 1 1 0 1 1 2 2 2 1 1 1 0 0 0 0 0 , 0 2 1 0 0 2 1 0 2 0 0 1 1 0 1 2 0 0 2 0 0 2 2 2 2 0 -> 2 1 1 1 0 2 2 0 0 2 1 0 1 0 1 2 0 0 2 1 1 1 2 0 1 2 2 2 , 0 2 1 2 0 0 0 2 0 2 0 1 1 2 1 2 0 1 2 2 0 2 2 0 1 2 -> 1 0 0 1 1 2 2 2 2 2 2 1 1 2 1 1 0 0 1 1 1 2 0 0 2 0 2 , 0 0 2 0 2 0 2 2 1 0 2 1 2 1 0 2 1 1 0 2 1 0 2 0 0 1 0 -> 1 1 1 1 1 0 1 0 0 2 2 2 0 1 2 0 2 1 2 0 0 0 1 1 1 2 0 0 0 , 0 1 0 2 2 2 2 0 2 1 2 2 0 0 0 1 0 1 1 2 0 1 0 1 0 0 2 -> 1 1 1 1 2 0 2 2 2 0 0 0 0 1 0 2 1 2 1 2 1 0 2 2 1 2 0 2 1 , 0 1 1 2 1 0 2 0 1 0 0 0 1 2 1 1 0 1 2 2 1 2 2 2 2 1 2 -> 0 0 0 2 1 1 1 1 0 2 2 1 1 2 2 0 1 2 1 2 1 1 1 1 2 0 1 1 , 0 2 1 2 1 2 2 2 0 2 2 0 2 0 2 1 0 1 1 1 1 2 1 0 1 2 0 -> 0 2 2 1 0 1 0 2 2 1 2 2 0 0 1 1 2 1 1 1 1 1 1 2 1 1 1 1 , 1 0 2 2 2 1 0 1 1 0 2 0 1 2 0 0 0 2 1 1 2 1 2 1 1 2 1 -> 1 1 1 0 1 2 1 1 2 2 2 0 1 0 0 1 2 2 2 2 1 1 1 0 0 0 2 2 , 1 2 1 0 1 0 0 0 0 1 2 2 2 1 2 1 0 1 1 2 2 2 0 2 0 1 1 -> 1 2 2 2 0 1 1 1 2 0 1 1 2 1 2 0 0 0 2 1 2 1 0 2 1 2 1 1 , 1 2 1 2 2 2 0 0 2 1 2 1 1 0 0 0 2 2 1 0 2 2 1 0 0 0 1 -> 1 1 1 1 1 2 2 0 1 2 0 2 0 2 1 2 1 1 1 1 0 0 0 2 1 0 0 0 1 , 2 1 1 0 2 2 2 1 0 2 0 1 0 0 2 1 0 0 0 2 1 1 0 0 1 1 1 -> 1 2 1 1 1 2 0 0 0 0 2 0 2 2 1 1 1 2 2 1 1 1 1 1 1 0 1 2 , 2 2 0 2 0 0 1 1 0 1 0 2 0 2 0 1 0 2 1 2 0 2 2 1 0 0 2 -> 2 2 2 0 1 1 0 1 1 2 2 2 2 2 1 1 0 0 1 1 1 0 0 1 1 1 2 0 0 , 0 2 2 1 1 2 2 0 1 2 1 2 2 0 2 2 1 2 2 2 2 2 2 0 0 2 1 0 -> 2 2 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 1 1 1 1 2 1 1 0 1 2 0 2 2 , 2 0 0 2 2 0 0 0 0 0 0 2 0 1 0 2 2 0 2 2 0 0 0 2 2 0 2 2 -> 1 2 0 1 0 2 2 1 2 0 1 1 1 1 2 2 0 1 1 2 0 1 0 1 0 1 1 2 2 2 , 2 0 1 2 2 2 0 1 2 0 0 2 0 1 1 2 1 0 0 0 1 2 1 1 2 0 2 0 -> 0 2 1 2 0 1 1 0 1 1 1 1 0 0 0 1 2 2 2 1 0 0 1 0 0 1 1 0 0 , 2 1 0 2 1 0 2 0 0 0 1 2 2 2 1 2 0 0 1 1 2 1 0 0 0 0 0 0 -> 1 0 2 1 1 1 1 1 2 0 2 1 0 1 1 1 2 2 1 1 0 2 2 1 2 1 0 2 0 , 2 1 1 0 1 1 0 1 2 1 2 1 2 2 0 1 2 0 1 0 0 0 2 0 2 2 2 0 -> 1 1 1 0 2 2 0 1 1 0 1 1 2 2 2 1 0 2 0 2 0 0 1 0 2 2 0 2 , 2 1 2 1 2 2 1 2 1 2 1 1 0 2 2 0 2 1 2 1 2 0 1 0 0 2 1 0 -> 1 1 1 2 2 1 1 2 1 2 1 2 1 2 0 1 1 2 1 0 0 2 2 0 2 1 1 1 1 2 , 2 1 2 2 0 1 2 0 2 2 2 2 1 2 2 1 0 0 0 0 2 0 1 0 2 1 2 2 -> 2 2 1 1 2 1 0 0 0 1 1 1 1 1 0 2 2 2 2 0 1 1 1 0 1 0 2 0 1 , 2 2 0 0 0 2 0 1 0 1 2 1 0 2 0 2 2 1 0 0 0 1 0 2 0 1 0 2 -> 1 0 1 2 0 0 1 2 0 0 2 0 0 2 0 2 0 0 0 2 2 2 1 1 1 1 0 1 2 1 , 2 2 1 0 2 1 2 1 2 0 2 0 0 1 0 2 0 1 2 1 0 0 0 0 1 1 2 0 -> 2 2 2 1 2 2 0 2 2 0 2 0 2 2 1 0 2 1 1 1 2 1 0 0 1 1 1 1 1 1 , 0 0 1 0 0 0 2 0 2 0 1 2 2 0 1 2 1 0 1 0 0 0 0 2 2 0 2 0 2 -> 0 1 0 2 0 0 1 2 2 0 1 2 2 0 1 0 0 0 0 0 0 0 2 0 0 2 1 2 2 , 0 1 0 1 1 0 1 0 0 2 0 2 2 2 0 0 1 2 2 0 2 1 2 1 1 0 0 1 1 -> 0 1 2 2 2 2 1 1 2 1 2 2 1 1 1 0 2 2 2 1 1 1 1 0 1 0 2 0 2 2 , 0 1 1 0 1 0 1 2 0 2 0 2 0 0 0 2 1 1 2 1 1 1 0 0 2 0 1 0 0 -> 2 1 1 0 2 0 0 0 0 2 0 2 0 1 0 1 1 1 1 1 2 1 0 0 1 2 0 0 0 , 1 2 0 1 1 1 0 0 0 2 0 0 0 1 2 2 2 1 0 1 1 2 1 2 0 1 2 0 2 -> 1 2 2 1 2 2 0 0 0 2 0 0 1 0 0 1 1 1 1 1 2 2 0 0 0 2 1 2 1 , 1 2 1 1 0 1 2 2 1 0 1 2 2 2 1 0 2 0 1 0 1 0 2 0 0 0 1 0 0 -> 1 1 0 0 0 1 1 1 1 0 0 0 2 0 0 2 2 0 2 0 1 0 1 2 0 2 0 1 2 2 , 2 0 1 2 2 1 0 0 2 2 2 1 0 1 0 0 2 0 2 1 0 0 1 0 0 1 2 2 0 -> 2 0 0 1 2 2 0 2 2 1 0 1 0 0 2 1 1 2 2 0 0 1 1 1 2 1 0 2 2 0 , 2 2 1 0 1 0 1 2 1 2 0 0 1 0 0 2 2 1 2 2 2 0 0 0 2 1 0 0 2 -> 2 0 2 1 1 1 2 2 1 1 0 2 0 2 1 0 0 2 2 0 1 1 2 2 2 0 1 1 2 0 , 1 1 0 1 1 2 0 2 2 0 0 1 2 0 0 0 2 1 2 1 2 2 0 0 2 2 2 0 1 1 -> 1 1 2 1 1 2 1 2 2 1 1 0 0 2 0 0 2 0 2 0 0 0 2 0 2 2 2 0 1 1 } The system was reversed. After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 110-rule system { 0 1 0 0 0 -> 0 1 1 1 2 2 , 2 2 1 0 1 0 -> 2 0 0 2 1 1 , 2 2 0 0 2 2 -> 0 2 1 1 1 2 2 , 1 2 2 2 0 0 1 0 -> 1 1 0 0 2 1 1 1 2 , 1 2 1 1 0 2 1 0 -> 1 0 1 1 2 2 0 1 , 2 2 1 0 2 2 2 2 0 -> 2 2 0 0 1 0 1 1 1 1 , 0 0 2 0 1 0 0 0 2 -> 2 1 1 1 1 0 2 1 0 0 1 , 2 1 1 0 0 2 1 2 2 -> 1 2 2 2 1 1 1 1 1 0 , 1 0 1 0 1 1 0 0 0 0 0 -> 1 1 1 1 0 0 1 0 1 2 1 0 , 2 0 0 0 0 0 2 0 1 0 0 -> 1 1 1 0 1 2 1 2 1 0 0 1 , 2 1 0 1 0 2 0 1 0 2 0 -> 0 2 1 1 2 1 1 1 1 2 0 0 1 , 0 2 2 1 2 0 2 0 0 0 1 -> 2 1 1 1 1 2 2 2 0 0 1 0 1 , 2 1 0 1 0 2 0 2 1 2 2 -> 0 1 2 2 2 1 2 0 1 1 1 1 , 0 0 0 0 1 0 2 2 0 1 0 1 -> 2 1 1 1 1 0 0 0 2 1 2 0 0 1 , 1 0 0 2 2 2 1 0 2 1 2 1 -> 2 1 1 0 1 1 1 1 1 1 1 1 2 1 1 1 1 , 1 2 2 0 0 2 2 2 2 2 2 1 0 -> 1 2 2 1 1 1 1 1 0 1 0 2 2 0 2 2 , 0 2 1 0 0 2 2 0 1 1 0 2 0 -> 1 0 1 1 1 1 1 1 2 0 1 2 1 2 , 0 0 1 1 2 2 0 1 0 2 0 2 0 -> 1 0 2 1 1 1 2 2 2 2 2 0 1 1 1 1 , 2 0 2 1 2 2 2 2 0 0 2 0 2 -> 2 1 2 1 1 1 1 1 2 0 0 1 0 2 0 0 , 2 0 2 1 2 0 1 0 1 1 0 1 2 -> 2 0 2 2 2 0 1 0 0 0 1 1 1 1 1 1 , 2 1 2 2 0 2 1 2 2 0 1 1 2 -> 0 2 2 2 1 0 1 1 1 1 1 2 0 1 1 1 , 0 0 0 0 1 0 1 0 0 0 2 1 2 -> 0 1 1 1 1 1 1 0 0 2 1 0 2 2 , 1 1 0 2 1 1 2 1 1 0 2 0 0 0 -> 1 1 1 1 0 2 1 2 2 0 2 0 2 1 1 , 0 0 1 1 2 1 2 1 2 1 0 2 1 2 -> 0 0 1 1 2 1 2 2 1 2 0 2 1 1 , 2 0 0 0 0 0 2 2 1 0 0 1 0 2 1 -> 0 0 0 1 1 2 2 1 1 1 1 0 1 2 1 1 1 , 1 2 1 2 2 1 0 1 0 0 0 0 1 1 2 -> 2 1 1 1 2 2 1 1 2 2 1 1 1 1 0 2 , 2 0 0 0 1 1 2 0 1 0 1 0 1 0 1 0 -> 2 0 0 0 0 1 0 1 0 2 1 1 1 1 0 0 , 0 0 2 1 2 2 1 1 0 1 0 1 2 2 0 1 -> 2 0 2 2 2 2 2 1 2 1 1 1 1 1 1 1 1 1 1 , 1 1 2 2 0 1 0 1 2 0 2 2 0 0 0 2 -> 1 1 1 2 0 2 1 2 1 1 0 0 0 1 1 1 1 2 , 0 2 0 1 0 0 2 0 2 1 0 2 1 2 1 2 -> 2 1 1 1 2 2 2 1 0 1 2 2 1 0 1 1 1 , 2 2 0 1 2 0 2 1 2 2 0 2 2 0 2 2 -> 1 1 1 2 2 1 1 1 2 2 1 0 2 2 1 1 1 2 1 , 2 0 0 0 0 1 2 0 2 2 1 2 0 0 2 2 0 -> 2 2 1 1 1 1 0 2 2 1 2 1 2 2 1 2 0 1 0 , 2 2 1 2 0 0 1 1 0 0 2 0 0 0 2 1 1 -> 0 1 1 0 0 0 1 2 1 1 2 2 1 1 1 1 2 1 1 , 0 0 0 0 0 0 2 0 2 2 0 1 0 2 2 2 2 -> 1 2 2 1 1 1 1 0 0 0 1 0 2 2 1 2 1 0 , 2 1 1 2 2 0 1 1 1 0 0 2 0 2 2 2 2 0 -> 2 2 1 2 1 1 1 2 2 0 1 1 1 1 1 1 2 0 1 0 , 2 1 2 0 1 0 2 1 2 1 0 0 2 2 0 2 2 1 -> 0 0 2 0 1 1 1 1 0 2 1 1 2 0 1 2 2 0 0 1 , 1 2 2 0 2 0 2 2 1 2 2 0 0 2 0 2 1 2 -> 1 1 2 2 0 2 0 1 0 2 0 2 1 1 1 0 0 2 0 , 2 1 2 0 1 0 1 2 1 1 0 0 1 0 0 2 2 0 0 -> 1 1 1 1 1 1 1 0 1 2 0 1 0 0 2 1 1 0 0 2 2 0 0 , 1 0 2 1 2 1 2 0 0 1 0 0 0 1 1 0 0 1 0 -> 1 0 1 2 0 1 1 0 2 0 0 2 1 1 1 2 2 0 0 2 , 2 2 0 2 2 1 2 1 2 2 0 2 0 1 2 0 2 1 0 -> 2 2 2 0 2 2 0 2 2 2 1 1 1 1 1 0 2 0 2 0 , 0 1 0 1 0 1 0 2 0 1 0 1 0 2 2 1 2 1 0 -> 2 2 0 2 1 0 0 0 0 1 1 0 0 2 1 0 1 1 1 , 2 1 0 2 2 1 0 2 0 1 2 2 2 1 2 0 0 0 0 0 -> 2 0 0 0 0 0 2 0 1 2 2 2 2 1 1 1 1 1 1 2 2 0 , 2 1 0 2 0 1 0 2 1 2 0 0 1 0 1 2 1 0 1 0 -> 2 2 2 1 1 1 0 0 0 2 2 1 0 1 0 2 1 1 2 1 2 , 2 0 2 2 2 0 2 0 2 1 1 1 0 2 2 1 1 2 0 1 -> 1 0 0 0 1 2 0 2 2 1 1 1 1 2 2 1 2 1 2 1 1 , 0 0 2 2 1 0 2 1 1 1 0 1 2 1 1 2 1 1 2 1 -> 2 1 2 1 0 1 0 0 1 1 1 1 0 0 0 1 0 1 1 1 1 , 2 2 2 2 1 2 1 1 0 0 2 2 2 2 0 2 1 0 0 2 -> 1 2 0 2 2 2 2 1 1 1 2 2 2 1 1 1 0 0 0 1 0 1 , 1 2 0 1 1 0 0 2 1 1 0 0 0 1 0 0 2 0 0 2 -> 1 2 1 1 1 1 0 2 0 1 2 2 1 1 1 2 2 0 1 1 0 , 0 0 2 2 0 2 1 0 2 1 0 1 1 2 1 1 0 0 2 2 -> 2 2 1 1 1 1 1 0 1 1 0 1 1 1 0 0 0 2 2 2 0 2 1 , 0 0 0 2 2 0 1 2 1 2 2 2 1 2 1 0 1 1 0 1 0 -> 1 0 0 1 0 1 1 1 1 2 0 0 1 1 1 0 1 0 0 0 2 0 1 , 1 0 2 2 1 1 0 1 2 1 1 0 2 0 1 0 1 1 1 0 2 -> 1 1 1 1 1 2 0 1 0 2 1 0 2 0 0 0 2 1 1 1 2 , 0 2 1 0 2 2 2 2 0 1 0 2 0 1 0 1 0 2 2 0 2 -> 0 1 1 1 1 1 1 0 0 1 2 1 1 1 1 2 2 1 2 1 0 0 0 1 2 1 1 1 , 0 0 0 1 0 1 2 0 2 1 1 2 0 0 1 0 2 1 2 2 0 0 -> 0 0 1 1 0 0 0 1 0 2 1 1 1 1 1 1 1 1 2 2 2 0 1 2 , 1 2 1 2 0 2 1 0 2 1 1 0 2 2 1 2 1 1 2 0 1 0 -> 1 1 1 1 0 2 1 0 2 1 1 2 0 1 2 1 0 0 0 1 1 2 1 , 0 1 2 2 0 1 0 0 0 2 0 2 1 2 1 0 0 2 0 2 2 0 -> 1 0 1 0 2 0 1 1 1 1 2 1 0 2 1 0 2 2 1 1 1 0 0 , 2 1 2 0 2 2 0 1 1 0 2 2 2 2 2 1 1 0 1 2 1 1 -> 1 2 1 1 0 0 2 2 1 0 0 2 0 1 0 1 0 2 0 1 1 1 1 , 2 2 2 0 2 1 0 0 0 0 2 0 1 0 1 0 2 2 1 1 1 2 -> 1 0 0 0 1 1 2 1 2 0 1 1 0 0 1 1 1 1 0 2 1 2 1 , 2 1 2 2 2 2 0 1 2 1 0 1 1 0 2 2 1 1 0 2 1 2 -> 0 0 1 2 0 2 1 1 0 1 2 2 2 1 1 1 0 2 1 1 1 1 1 , 1 2 0 0 1 0 0 2 2 0 2 0 2 0 2 1 2 0 2 2 1 2 -> 1 1 1 2 1 2 2 2 0 0 0 1 1 2 1 2 0 1 0 0 1 2 0 , 2 0 1 1 0 0 2 0 0 1 1 2 0 1 0 2 0 1 2 2 1 2 -> 1 1 1 1 2 0 2 0 2 0 2 0 0 2 1 0 0 0 2 0 2 2 2 , 2 1 0 0 1 2 0 0 2 2 0 1 1 0 2 1 2 1 2 2 1 0 0 -> 1 1 1 2 2 0 1 1 1 1 0 2 1 1 2 0 2 2 1 0 1 1 0 2 , 2 0 2 0 0 0 0 0 1 2 2 1 0 1 1 2 0 1 1 0 0 2 0 -> 2 0 0 0 0 0 1 0 2 1 2 0 1 0 0 2 2 2 0 1 1 1 0 , 1 2 0 2 0 2 2 1 1 1 0 1 0 2 1 2 0 1 2 1 2 2 0 -> 0 1 1 2 2 2 0 2 0 1 1 1 2 2 0 2 1 1 1 1 1 1 1 0 2 , 1 2 2 2 2 2 0 2 0 0 0 1 0 0 1 1 2 1 2 2 2 0 1 -> 1 0 1 1 0 0 1 0 2 1 1 1 2 2 1 1 2 0 1 0 0 2 1 1 1 , 1 2 0 1 2 0 1 2 0 0 0 2 1 0 2 2 1 2 0 0 1 2 0 0 -> 1 1 0 2 0 0 1 1 1 2 1 0 2 0 1 2 2 1 1 2 2 1 2 1 0 , 0 0 0 0 2 1 0 0 0 0 0 0 2 2 2 1 2 1 0 0 2 0 1 0 -> 0 0 2 2 2 2 1 1 1 1 2 2 1 1 1 2 2 1 0 1 0 2 0 0 1 2 , 2 2 0 1 1 1 0 0 0 1 2 1 2 2 1 1 0 2 0 1 2 0 1 0 -> 2 1 2 0 1 0 2 2 2 0 0 2 1 0 2 2 0 0 2 2 1 1 1 1 1 , 1 0 0 0 1 0 2 1 1 0 0 0 1 2 1 2 1 1 0 1 1 2 1 0 -> 1 1 2 1 1 1 1 2 1 1 0 2 1 2 0 1 2 2 0 1 1 2 2 1 0 , 0 2 0 2 0 1 2 2 0 2 0 0 2 0 0 0 1 0 0 1 0 1 2 0 -> 2 0 0 1 2 2 0 0 1 1 1 1 2 2 2 2 1 2 2 1 1 0 2 2 0 1 , 0 0 2 2 0 0 0 1 2 2 2 0 0 2 1 0 0 0 0 1 1 0 2 1 -> 1 0 1 2 0 0 1 1 0 0 0 1 1 1 1 1 1 2 1 2 1 2 2 2 1 0 1 , 2 2 1 2 1 1 2 2 1 0 1 0 2 0 2 1 0 2 1 0 0 2 2 1 -> 1 1 0 0 2 2 1 0 0 0 1 1 1 2 0 2 2 0 0 2 1 1 1 1 1 , 0 2 0 2 2 0 2 1 0 1 0 1 0 0 2 1 2 1 2 1 2 1 1 2 -> 1 1 1 1 0 1 0 2 0 1 0 2 0 2 1 1 2 0 1 2 0 0 0 0 2 , 1 1 0 1 2 2 1 2 0 0 1 2 0 1 0 0 2 0 0 0 0 0 0 0 0 -> 0 0 0 0 1 1 0 2 0 2 0 1 1 1 1 2 2 1 0 1 0 0 1 1 1 1 , 0 2 2 0 2 0 0 0 1 0 2 1 2 2 0 1 1 0 2 1 2 0 0 1 0 -> 2 2 0 2 1 0 0 1 1 1 1 1 0 0 2 1 2 1 1 2 2 2 0 1 1 2 0 , 1 2 1 2 2 0 2 2 2 0 1 0 0 0 2 0 2 2 0 1 0 1 2 2 0 -> 1 2 0 0 0 1 1 2 0 2 0 0 2 0 1 2 1 1 1 1 2 2 0 0 0 1 , 1 0 1 2 0 0 0 0 2 2 1 2 2 1 0 0 2 0 1 0 2 2 2 2 0 -> 1 1 2 2 0 2 2 1 2 0 1 1 2 0 0 1 1 2 0 2 1 2 1 1 1 2 , 2 0 2 1 0 2 2 1 0 1 0 0 1 0 2 0 1 0 1 0 2 0 0 0 1 -> 1 2 1 1 1 2 0 0 1 1 1 1 0 0 0 2 2 1 2 1 0 1 2 2 0 1 , 2 0 2 0 2 0 2 2 2 0 0 0 2 2 0 0 2 1 0 1 0 0 2 1 1 -> 0 0 0 1 2 1 0 1 2 0 1 0 0 0 2 1 2 2 0 1 1 2 2 1 1 1 1 , 2 0 2 2 1 2 0 0 1 0 1 0 1 0 0 0 2 1 1 0 0 1 1 2 1 -> 1 0 0 2 1 1 1 0 0 1 1 1 2 1 1 0 1 0 0 2 2 2 2 1 1 1 , 0 2 1 2 1 1 2 1 2 1 0 2 1 0 0 1 1 2 2 2 0 0 2 2 1 -> 1 1 1 2 2 0 0 2 0 1 2 0 1 2 2 2 1 1 2 0 2 0 1 2 1 , 1 2 0 2 0 1 2 0 0 0 0 1 0 0 1 0 0 1 0 2 0 0 0 0 2 -> 1 0 1 1 1 2 2 2 2 0 1 0 2 2 2 0 1 0 1 1 1 2 1 0 2 0 1 , 2 0 2 0 0 1 1 2 0 1 0 2 0 2 2 1 0 2 2 1 1 2 2 1 2 -> 2 2 0 1 2 0 0 1 1 1 1 1 2 2 2 1 0 1 1 1 1 0 1 2 1 0 1 , 2 0 0 0 1 2 1 2 0 0 2 1 1 0 0 2 2 2 1 0 1 2 1 1 0 0 -> 0 0 0 0 0 1 1 1 2 2 2 1 1 0 1 1 0 0 1 1 1 2 0 1 1 2 1 0 , 0 2 2 2 2 0 0 2 0 0 2 1 0 1 1 0 0 2 0 1 2 0 0 1 2 0 -> 2 2 2 1 0 2 1 1 1 2 0 0 2 1 0 1 0 1 2 0 0 2 2 0 1 1 1 2 , 2 1 0 2 2 0 2 2 1 0 2 1 2 1 1 0 2 0 2 0 0 0 2 1 2 0 -> 2 0 2 0 0 2 1 1 1 0 0 1 1 2 1 1 2 2 2 2 2 2 1 1 0 0 1 , 0 1 0 0 2 0 1 2 0 1 1 2 0 1 2 1 2 0 1 2 2 0 2 0 2 0 0 -> 0 0 0 2 1 1 1 0 0 0 2 1 2 0 2 1 0 2 2 2 0 0 1 0 1 1 1 1 1 , 2 0 0 1 0 1 0 2 1 1 0 1 0 0 0 2 2 1 2 0 2 2 2 2 0 1 0 -> 1 2 0 2 1 2 2 0 1 2 1 2 1 2 0 1 0 0 0 0 2 2 2 0 2 1 1 1 1 , 2 1 2 2 2 2 1 2 2 1 0 1 1 2 1 0 0 0 1 0 2 0 1 2 1 1 0 -> 1 1 0 2 1 1 1 1 2 1 2 1 0 2 2 1 1 2 2 0 1 1 1 1 2 0 0 0 , 0 2 1 0 1 2 1 1 1 1 0 1 2 0 2 0 2 2 0 2 2 2 1 2 1 2 0 -> 1 1 1 1 2 1 1 1 1 1 1 2 1 1 0 0 2 2 1 2 2 0 1 0 1 2 2 0 , 1 2 1 1 2 1 2 1 1 2 0 0 0 2 1 0 2 0 1 1 0 1 2 2 2 0 1 -> 2 2 0 0 0 1 1 1 2 2 2 2 1 0 0 1 0 2 2 2 1 1 2 1 0 1 1 1 , 1 1 0 2 0 2 2 2 1 1 0 1 2 1 2 2 2 1 0 0 0 0 1 0 1 2 1 -> 1 1 2 1 2 0 1 2 1 2 0 0 0 2 1 2 1 1 0 2 1 1 1 0 2 2 2 1 , 1 0 0 0 1 2 2 0 1 2 2 0 0 0 1 1 2 1 2 0 0 2 2 2 1 2 1 -> 1 0 0 0 1 2 0 0 0 1 1 1 1 2 1 2 0 2 0 2 1 0 2 2 1 1 1 1 1 , 1 1 1 0 0 1 1 2 0 0 0 1 2 0 0 1 0 2 0 1 2 2 2 0 1 1 2 -> 2 1 0 1 1 1 1 1 1 2 2 1 1 1 2 2 0 2 0 0 0 0 2 1 1 1 2 1 , 2 0 0 1 2 2 0 2 1 2 0 1 0 2 0 2 0 1 0 1 1 0 0 2 0 2 2 -> 0 0 2 1 1 1 0 0 1 1 1 0 0 1 1 2 2 2 2 2 1 1 0 1 1 0 2 2 2 , 0 1 2 0 0 2 2 2 2 2 2 1 2 2 0 2 2 1 2 1 0 2 2 1 1 2 2 0 -> 2 2 0 2 1 0 1 1 2 1 1 1 1 0 1 1 1 1 1 1 0 0 0 0 0 0 1 0 2 2 , 2 2 0 2 2 0 0 0 2 2 0 2 2 0 1 0 2 0 0 0 0 0 0 2 2 0 0 2 -> 2 2 2 1 1 0 1 0 1 0 2 1 1 0 2 2 1 1 1 1 0 2 1 2 2 0 1 0 2 1 , 0 2 0 2 1 1 2 1 0 0 0 1 2 1 1 0 2 0 0 2 1 0 2 2 2 1 0 2 -> 0 0 1 1 0 0 1 0 0 1 2 2 2 1 0 0 0 1 1 1 1 0 1 1 0 2 1 2 0 , 0 0 0 0 0 0 1 2 1 1 0 0 2 1 2 2 2 1 0 0 0 2 0 1 2 0 1 2 -> 0 2 0 1 2 1 2 2 0 1 1 2 2 1 1 1 0 1 2 0 2 1 1 1 1 1 2 0 1 , 0 2 2 2 0 2 0 0 0 1 0 2 1 0 2 2 1 2 1 2 1 0 1 1 0 1 1 2 -> 2 0 2 2 0 1 0 0 2 0 2 0 1 2 2 2 1 1 0 1 1 0 2 2 0 1 1 1 , 0 1 2 0 0 1 0 2 1 2 1 2 0 2 2 0 1 1 2 1 2 1 2 2 1 2 1 2 -> 2 1 1 1 1 2 0 2 2 0 0 1 2 1 1 0 2 1 2 1 2 1 2 1 1 2 2 1 1 1 , 2 2 1 2 0 1 0 2 0 0 0 0 1 2 2 1 2 2 2 2 0 2 1 0 2 2 1 2 -> 1 0 2 0 1 0 1 1 1 0 2 2 2 2 0 1 1 1 1 1 0 0 0 1 2 1 1 2 2 , 2 0 1 0 2 0 1 0 0 0 1 2 2 0 2 0 1 2 1 0 1 0 2 0 0 0 2 2 -> 1 2 1 0 1 1 1 1 2 2 2 0 0 0 2 0 2 0 0 2 0 0 2 1 0 0 2 1 0 1 , 0 2 1 1 0 0 0 0 1 2 1 0 2 0 1 0 0 2 0 2 1 2 1 2 0 1 2 2 -> 1 1 1 1 1 1 0 0 1 2 1 1 1 2 0 1 2 2 0 2 0 2 2 0 2 2 1 2 2 2 , 2 0 2 0 2 2 0 0 0 0 1 0 1 2 1 0 2 2 1 0 2 0 2 0 0 0 1 0 0 -> 2 2 1 2 0 0 2 0 0 0 0 0 0 0 1 0 2 2 1 0 2 2 1 0 0 2 0 1 0 , 1 1 0 0 1 1 2 1 2 0 2 2 1 0 0 2 2 2 0 2 0 0 1 0 1 1 0 1 0 -> 2 2 0 2 0 1 0 1 1 1 1 2 2 2 0 1 1 1 2 2 1 2 1 1 2 2 2 2 1 0 , 0 0 1 0 2 0 0 1 1 1 2 1 1 2 0 0 0 2 0 2 0 2 1 0 1 0 1 1 0 -> 0 0 0 2 1 0 0 1 2 1 1 1 1 1 0 1 0 2 0 2 0 0 0 0 2 0 1 1 2 , 2 0 2 1 0 2 1 2 1 1 0 1 2 2 2 1 0 0 0 2 0 0 0 1 1 1 0 2 1 -> 1 2 1 2 0 0 0 2 2 1 1 1 1 1 0 0 1 0 0 2 0 0 0 2 2 1 2 2 1 , 0 0 1 0 0 0 2 0 1 0 1 0 2 0 1 2 2 2 1 0 1 2 2 1 0 1 1 2 1 -> 2 2 1 0 2 0 2 1 0 1 0 2 0 2 2 0 0 2 0 0 0 1 1 1 1 0 0 0 1 1 , 0 2 2 1 0 0 1 0 0 1 2 0 2 0 0 1 0 1 2 2 2 0 0 1 2 2 1 0 2 -> 0 2 2 0 1 2 1 1 1 0 0 2 2 1 1 2 0 0 1 0 1 2 2 0 2 2 1 0 0 2 , 2 0 0 1 2 0 0 0 2 2 2 1 2 2 0 0 1 0 0 2 1 2 1 0 1 0 1 2 2 -> 0 2 1 1 0 2 2 2 1 1 0 2 2 0 0 1 2 0 2 0 1 1 2 2 1 1 1 2 0 2 , 1 1 0 2 2 2 0 0 2 2 1 2 1 2 0 0 0 2 1 0 0 2 2 0 2 1 1 0 1 1 -> 1 1 0 2 2 2 0 2 0 0 0 2 0 2 0 0 2 0 0 1 1 2 2 1 2 1 1 2 1 1 } Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,0)->2, (1,1)->3, (1,2)->4, (2,2)->5, (2,0)->6, (2,1)->7, (0,2)->8, (0,4)->9, (2,4)->10, (3,0)->11, (1,4)->12, (3,2)->13, (3,1)->14 }, it remains to prove termination of the 1760-rule system { 0 1 2 0 0 0 -> 0 1 3 3 4 5 6 , 0 1 2 0 0 1 -> 0 1 3 3 4 5 7 , 0 1 2 0 0 8 -> 0 1 3 3 4 5 5 , 0 1 2 0 0 9 -> 0 1 3 3 4 5 10 , 2 1 2 0 0 0 -> 2 1 3 3 4 5 6 , 2 1 2 0 0 1 -> 2 1 3 3 4 5 7 , 2 1 2 0 0 8 -> 2 1 3 3 4 5 5 , 2 1 2 0 0 9 -> 2 1 3 3 4 5 10 , 6 1 2 0 0 0 -> 6 1 3 3 4 5 6 , 6 1 2 0 0 1 -> 6 1 3 3 4 5 7 , 6 1 2 0 0 8 -> 6 1 3 3 4 5 5 , 6 1 2 0 0 9 -> 6 1 3 3 4 5 10 , 11 1 2 0 0 0 -> 11 1 3 3 4 5 6 , 11 1 2 0 0 1 -> 11 1 3 3 4 5 7 , 11 1 2 0 0 8 -> 11 1 3 3 4 5 5 , 11 1 2 0 0 9 -> 11 1 3 3 4 5 10 , 8 5 7 2 1 2 0 -> 8 6 0 8 7 3 2 , 8 5 7 2 1 2 1 -> 8 6 0 8 7 3 3 , 8 5 7 2 1 2 8 -> 8 6 0 8 7 3 4 , 8 5 7 2 1 2 9 -> 8 6 0 8 7 3 12 , 4 5 7 2 1 2 0 -> 4 6 0 8 7 3 2 , 4 5 7 2 1 2 1 -> 4 6 0 8 7 3 3 , 4 5 7 2 1 2 8 -> 4 6 0 8 7 3 4 , 4 5 7 2 1 2 9 -> 4 6 0 8 7 3 12 , 5 5 7 2 1 2 0 -> 5 6 0 8 7 3 2 , 5 5 7 2 1 2 1 -> 5 6 0 8 7 3 3 , 5 5 7 2 1 2 8 -> 5 6 0 8 7 3 4 , 5 5 7 2 1 2 9 -> 5 6 0 8 7 3 12 , 13 5 7 2 1 2 0 -> 13 6 0 8 7 3 2 , 13 5 7 2 1 2 1 -> 13 6 0 8 7 3 3 , 13 5 7 2 1 2 8 -> 13 6 0 8 7 3 4 , 13 5 7 2 1 2 9 -> 13 6 0 8 7 3 12 , 8 5 6 0 8 5 6 -> 0 8 7 3 3 4 5 6 , 8 5 6 0 8 5 7 -> 0 8 7 3 3 4 5 7 , 8 5 6 0 8 5 5 -> 0 8 7 3 3 4 5 5 , 8 5 6 0 8 5 10 -> 0 8 7 3 3 4 5 10 , 4 5 6 0 8 5 6 -> 2 8 7 3 3 4 5 6 , 4 5 6 0 8 5 7 -> 2 8 7 3 3 4 5 7 , 4 5 6 0 8 5 5 -> 2 8 7 3 3 4 5 5 , 4 5 6 0 8 5 10 -> 2 8 7 3 3 4 5 10 , 5 5 6 0 8 5 6 -> 6 8 7 3 3 4 5 6 , 5 5 6 0 8 5 7 -> 6 8 7 3 3 4 5 7 , 5 5 6 0 8 5 5 -> 6 8 7 3 3 4 5 5 , 5 5 6 0 8 5 10 -> 6 8 7 3 3 4 5 10 , 13 5 6 0 8 5 6 -> 11 8 7 3 3 4 5 6 , 13 5 6 0 8 5 7 -> 11 8 7 3 3 4 5 7 , 13 5 6 0 8 5 5 -> 11 8 7 3 3 4 5 5 , 13 5 6 0 8 5 10 -> 11 8 7 3 3 4 5 10 , 1 4 5 5 6 0 1 2 0 -> 1 3 2 0 8 7 3 3 4 6 , 1 4 5 5 6 0 1 2 1 -> 1 3 2 0 8 7 3 3 4 7 , 1 4 5 5 6 0 1 2 8 -> 1 3 2 0 8 7 3 3 4 5 , 1 4 5 5 6 0 1 2 9 -> 1 3 2 0 8 7 3 3 4 10 , 3 4 5 5 6 0 1 2 0 -> 3 3 2 0 8 7 3 3 4 6 , 3 4 5 5 6 0 1 2 1 -> 3 3 2 0 8 7 3 3 4 7 , 3 4 5 5 6 0 1 2 8 -> 3 3 2 0 8 7 3 3 4 5 , 3 4 5 5 6 0 1 2 9 -> 3 3 2 0 8 7 3 3 4 10 , 7 4 5 5 6 0 1 2 0 -> 7 3 2 0 8 7 3 3 4 6 , 7 4 5 5 6 0 1 2 1 -> 7 3 2 0 8 7 3 3 4 7 , 7 4 5 5 6 0 1 2 8 -> 7 3 2 0 8 7 3 3 4 5 , 7 4 5 5 6 0 1 2 9 -> 7 3 2 0 8 7 3 3 4 10 , 14 4 5 5 6 0 1 2 0 -> 14 3 2 0 8 7 3 3 4 6 , 14 4 5 5 6 0 1 2 1 -> 14 3 2 0 8 7 3 3 4 7 , 14 4 5 5 6 0 1 2 8 -> 14 3 2 0 8 7 3 3 4 5 , 14 4 5 5 6 0 1 2 9 -> 14 3 2 0 8 7 3 3 4 10 , 1 4 7 3 2 8 7 2 0 -> 1 2 1 3 4 5 6 1 2 , 1 4 7 3 2 8 7 2 1 -> 1 2 1 3 4 5 6 1 3 , 1 4 7 3 2 8 7 2 8 -> 1 2 1 3 4 5 6 1 4 , 1 4 7 3 2 8 7 2 9 -> 1 2 1 3 4 5 6 1 12 , 3 4 7 3 2 8 7 2 0 -> 3 2 1 3 4 5 6 1 2 , 3 4 7 3 2 8 7 2 1 -> 3 2 1 3 4 5 6 1 3 , 3 4 7 3 2 8 7 2 8 -> 3 2 1 3 4 5 6 1 4 , 3 4 7 3 2 8 7 2 9 -> 3 2 1 3 4 5 6 1 12 , 7 4 7 3 2 8 7 2 0 -> 7 2 1 3 4 5 6 1 2 , 7 4 7 3 2 8 7 2 1 -> 7 2 1 3 4 5 6 1 3 , 7 4 7 3 2 8 7 2 8 -> 7 2 1 3 4 5 6 1 4 , 7 4 7 3 2 8 7 2 9 -> 7 2 1 3 4 5 6 1 12 , 14 4 7 3 2 8 7 2 0 -> 14 2 1 3 4 5 6 1 2 , 14 4 7 3 2 8 7 2 1 -> 14 2 1 3 4 5 6 1 3 , 14 4 7 3 2 8 7 2 8 -> 14 2 1 3 4 5 6 1 4 , 14 4 7 3 2 8 7 2 9 -> 14 2 1 3 4 5 6 1 12 , 8 5 7 2 8 5 5 5 6 0 -> 8 5 6 0 1 2 1 3 3 3 2 , 8 5 7 2 8 5 5 5 6 1 -> 8 5 6 0 1 2 1 3 3 3 3 , 8 5 7 2 8 5 5 5 6 8 -> 8 5 6 0 1 2 1 3 3 3 4 , 8 5 7 2 8 5 5 5 6 9 -> 8 5 6 0 1 2 1 3 3 3 12 , 4 5 7 2 8 5 5 5 6 0 -> 4 5 6 0 1 2 1 3 3 3 2 , 4 5 7 2 8 5 5 5 6 1 -> 4 5 6 0 1 2 1 3 3 3 3 , 4 5 7 2 8 5 5 5 6 8 -> 4 5 6 0 1 2 1 3 3 3 4 , 4 5 7 2 8 5 5 5 6 9 -> 4 5 6 0 1 2 1 3 3 3 12 , 5 5 7 2 8 5 5 5 6 0 -> 5 5 6 0 1 2 1 3 3 3 2 , 5 5 7 2 8 5 5 5 6 1 -> 5 5 6 0 1 2 1 3 3 3 3 , 5 5 7 2 8 5 5 5 6 8 -> 5 5 6 0 1 2 1 3 3 3 4 , 5 5 7 2 8 5 5 5 6 9 -> 5 5 6 0 1 2 1 3 3 3 12 , 13 5 7 2 8 5 5 5 6 0 -> 13 5 6 0 1 2 1 3 3 3 2 , 13 5 7 2 8 5 5 5 6 1 -> 13 5 6 0 1 2 1 3 3 3 3 , 13 5 7 2 8 5 5 5 6 8 -> 13 5 6 0 1 2 1 3 3 3 4 , 13 5 7 2 8 5 5 5 6 9 -> 13 5 6 0 1 2 1 3 3 3 12 , 0 0 8 6 1 2 0 0 8 6 -> 8 7 3 3 3 2 8 7 2 0 1 2 , 0 0 8 6 1 2 0 0 8 7 -> 8 7 3 3 3 2 8 7 2 0 1 3 , 0 0 8 6 1 2 0 0 8 5 -> 8 7 3 3 3 2 8 7 2 0 1 4 , 0 0 8 6 1 2 0 0 8 10 -> 8 7 3 3 3 2 8 7 2 0 1 12 , 2 0 8 6 1 2 0 0 8 6 -> 4 7 3 3 3 2 8 7 2 0 1 2 , 2 0 8 6 1 2 0 0 8 7 -> 4 7 3 3 3 2 8 7 2 0 1 3 , 2 0 8 6 1 2 0 0 8 5 -> 4 7 3 3 3 2 8 7 2 0 1 4 , 2 0 8 6 1 2 0 0 8 10 -> 4 7 3 3 3 2 8 7 2 0 1 12 , 6 0 8 6 1 2 0 0 8 6 -> 5 7 3 3 3 2 8 7 2 0 1 2 , 6 0 8 6 1 2 0 0 8 7 -> 5 7 3 3 3 2 8 7 2 0 1 3 , 6 0 8 6 1 2 0 0 8 5 -> 5 7 3 3 3 2 8 7 2 0 1 4 , 6 0 8 6 1 2 0 0 8 10 -> 5 7 3 3 3 2 8 7 2 0 1 12 , 11 0 8 6 1 2 0 0 8 6 -> 13 7 3 3 3 2 8 7 2 0 1 2 , 11 0 8 6 1 2 0 0 8 7 -> 13 7 3 3 3 2 8 7 2 0 1 3 , 11 0 8 6 1 2 0 0 8 5 -> 13 7 3 3 3 2 8 7 2 0 1 4 , 11 0 8 6 1 2 0 0 8 10 -> 13 7 3 3 3 2 8 7 2 0 1 12 , 8 7 3 2 0 8 7 4 5 6 -> 1 4 5 5 7 3 3 3 3 2 0 , 8 7 3 2 0 8 7 4 5 7 -> 1 4 5 5 7 3 3 3 3 2 1 , 8 7 3 2 0 8 7 4 5 5 -> 1 4 5 5 7 3 3 3 3 2 8 , 8 7 3 2 0 8 7 4 5 10 -> 1 4 5 5 7 3 3 3 3 2 9 , 4 7 3 2 0 8 7 4 5 6 -> 3 4 5 5 7 3 3 3 3 2 0 , 4 7 3 2 0 8 7 4 5 7 -> 3 4 5 5 7 3 3 3 3 2 1 , 4 7 3 2 0 8 7 4 5 5 -> 3 4 5 5 7 3 3 3 3 2 8 , 4 7 3 2 0 8 7 4 5 10 -> 3 4 5 5 7 3 3 3 3 2 9 , 5 7 3 2 0 8 7 4 5 6 -> 7 4 5 5 7 3 3 3 3 2 0 , 5 7 3 2 0 8 7 4 5 7 -> 7 4 5 5 7 3 3 3 3 2 1 , 5 7 3 2 0 8 7 4 5 5 -> 7 4 5 5 7 3 3 3 3 2 8 , 5 7 3 2 0 8 7 4 5 10 -> 7 4 5 5 7 3 3 3 3 2 9 , 13 7 3 2 0 8 7 4 5 6 -> 14 4 5 5 7 3 3 3 3 2 0 , 13 7 3 2 0 8 7 4 5 7 -> 14 4 5 5 7 3 3 3 3 2 1 , 13 7 3 2 0 8 7 4 5 5 -> 14 4 5 5 7 3 3 3 3 2 8 , 13 7 3 2 0 8 7 4 5 10 -> 14 4 5 5 7 3 3 3 3 2 9 , 1 2 1 2 1 3 2 0 0 0 0 0 -> 1 3 3 3 2 0 1 2 1 4 7 2 0 , 1 2 1 2 1 3 2 0 0 0 0 1 -> 1 3 3 3 2 0 1 2 1 4 7 2 1 , 1 2 1 2 1 3 2 0 0 0 0 8 -> 1 3 3 3 2 0 1 2 1 4 7 2 8 , 1 2 1 2 1 3 2 0 0 0 0 9 -> 1 3 3 3 2 0 1 2 1 4 7 2 9 , 3 2 1 2 1 3 2 0 0 0 0 0 -> 3 3 3 3 2 0 1 2 1 4 7 2 0 , 3 2 1 2 1 3 2 0 0 0 0 1 -> 3 3 3 3 2 0 1 2 1 4 7 2 1 , 3 2 1 2 1 3 2 0 0 0 0 8 -> 3 3 3 3 2 0 1 2 1 4 7 2 8 , 3 2 1 2 1 3 2 0 0 0 0 9 -> 3 3 3 3 2 0 1 2 1 4 7 2 9 , 7 2 1 2 1 3 2 0 0 0 0 0 -> 7 3 3 3 2 0 1 2 1 4 7 2 0 , 7 2 1 2 1 3 2 0 0 0 0 1 -> 7 3 3 3 2 0 1 2 1 4 7 2 1 , 7 2 1 2 1 3 2 0 0 0 0 8 -> 7 3 3 3 2 0 1 2 1 4 7 2 8 , 7 2 1 2 1 3 2 0 0 0 0 9 -> 7 3 3 3 2 0 1 2 1 4 7 2 9 , 14 2 1 2 1 3 2 0 0 0 0 0 -> 14 3 3 3 2 0 1 2 1 4 7 2 0 , 14 2 1 2 1 3 2 0 0 0 0 1 -> 14 3 3 3 2 0 1 2 1 4 7 2 1 , 14 2 1 2 1 3 2 0 0 0 0 8 -> 14 3 3 3 2 0 1 2 1 4 7 2 8 , 14 2 1 2 1 3 2 0 0 0 0 9 -> 14 3 3 3 2 0 1 2 1 4 7 2 9 , 8 6 0 0 0 0 8 6 1 2 0 0 -> 1 3 3 2 1 4 7 4 7 2 0 1 2 , 8 6 0 0 0 0 8 6 1 2 0 1 -> 1 3 3 2 1 4 7 4 7 2 0 1 3 , 8 6 0 0 0 0 8 6 1 2 0 8 -> 1 3 3 2 1 4 7 4 7 2 0 1 4 , 8 6 0 0 0 0 8 6 1 2 0 9 -> 1 3 3 2 1 4 7 4 7 2 0 1 12 , 4 6 0 0 0 0 8 6 1 2 0 0 -> 3 3 3 2 1 4 7 4 7 2 0 1 2 , 4 6 0 0 0 0 8 6 1 2 0 1 -> 3 3 3 2 1 4 7 4 7 2 0 1 3 , 4 6 0 0 0 0 8 6 1 2 0 8 -> 3 3 3 2 1 4 7 4 7 2 0 1 4 , 4 6 0 0 0 0 8 6 1 2 0 9 -> 3 3 3 2 1 4 7 4 7 2 0 1 12 , 5 6 0 0 0 0 8 6 1 2 0 0 -> 7 3 3 2 1 4 7 4 7 2 0 1 2 , 5 6 0 0 0 0 8 6 1 2 0 1 -> 7 3 3 2 1 4 7 4 7 2 0 1 3 , 5 6 0 0 0 0 8 6 1 2 0 8 -> 7 3 3 2 1 4 7 4 7 2 0 1 4 , 5 6 0 0 0 0 8 6 1 2 0 9 -> 7 3 3 2 1 4 7 4 7 2 0 1 12 , 13 6 0 0 0 0 8 6 1 2 0 0 -> 14 3 3 2 1 4 7 4 7 2 0 1 2 , 13 6 0 0 0 0 8 6 1 2 0 1 -> 14 3 3 2 1 4 7 4 7 2 0 1 3 , 13 6 0 0 0 0 8 6 1 2 0 8 -> 14 3 3 2 1 4 7 4 7 2 0 1 4 , 13 6 0 0 0 0 8 6 1 2 0 9 -> 14 3 3 2 1 4 7 4 7 2 0 1 12 , 8 7 2 1 2 8 6 1 2 8 6 0 -> 0 8 7 3 4 7 3 3 3 4 6 0 1 2 , 8 7 2 1 2 8 6 1 2 8 6 1 -> 0 8 7 3 4 7 3 3 3 4 6 0 1 3 , 8 7 2 1 2 8 6 1 2 8 6 8 -> 0 8 7 3 4 7 3 3 3 4 6 0 1 4 , 8 7 2 1 2 8 6 1 2 8 6 9 -> 0 8 7 3 4 7 3 3 3 4 6 0 1 12 , 4 7 2 1 2 8 6 1 2 8 6 0 -> 2 8 7 3 4 7 3 3 3 4 6 0 1 2 , 4 7 2 1 2 8 6 1 2 8 6 1 -> 2 8 7 3 4 7 3 3 3 4 6 0 1 3 , 4 7 2 1 2 8 6 1 2 8 6 8 -> 2 8 7 3 4 7 3 3 3 4 6 0 1 4 , 4 7 2 1 2 8 6 1 2 8 6 9 -> 2 8 7 3 4 7 3 3 3 4 6 0 1 12 , 5 7 2 1 2 8 6 1 2 8 6 0 -> 6 8 7 3 4 7 3 3 3 4 6 0 1 2 , 5 7 2 1 2 8 6 1 2 8 6 1 -> 6 8 7 3 4 7 3 3 3 4 6 0 1 3 , 5 7 2 1 2 8 6 1 2 8 6 8 -> 6 8 7 3 4 7 3 3 3 4 6 0 1 4 , 5 7 2 1 2 8 6 1 2 8 6 9 -> 6 8 7 3 4 7 3 3 3 4 6 0 1 12 , 13 7 2 1 2 8 6 1 2 8 6 0 -> 11 8 7 3 4 7 3 3 3 4 6 0 1 2 , 13 7 2 1 2 8 6 1 2 8 6 1 -> 11 8 7 3 4 7 3 3 3 4 6 0 1 3 , 13 7 2 1 2 8 6 1 2 8 6 8 -> 11 8 7 3 4 7 3 3 3 4 6 0 1 4 , 13 7 2 1 2 8 6 1 2 8 6 9 -> 11 8 7 3 4 7 3 3 3 4 6 0 1 12 , 0 8 5 7 4 6 8 6 0 0 1 2 -> 8 7 3 3 3 4 5 5 6 0 1 2 1 2 , 0 8 5 7 4 6 8 6 0 0 1 3 -> 8 7 3 3 3 4 5 5 6 0 1 2 1 3 , 0 8 5 7 4 6 8 6 0 0 1 4 -> 8 7 3 3 3 4 5 5 6 0 1 2 1 4 , 0 8 5 7 4 6 8 6 0 0 1 12 -> 8 7 3 3 3 4 5 5 6 0 1 2 1 12 , 2 8 5 7 4 6 8 6 0 0 1 2 -> 4 7 3 3 3 4 5 5 6 0 1 2 1 2 , 2 8 5 7 4 6 8 6 0 0 1 3 -> 4 7 3 3 3 4 5 5 6 0 1 2 1 3 , 2 8 5 7 4 6 8 6 0 0 1 4 -> 4 7 3 3 3 4 5 5 6 0 1 2 1 4 , 2 8 5 7 4 6 8 6 0 0 1 12 -> 4 7 3 3 3 4 5 5 6 0 1 2 1 12 , 6 8 5 7 4 6 8 6 0 0 1 2 -> 5 7 3 3 3 4 5 5 6 0 1 2 1 2 , 6 8 5 7 4 6 8 6 0 0 1 3 -> 5 7 3 3 3 4 5 5 6 0 1 2 1 3 , 6 8 5 7 4 6 8 6 0 0 1 4 -> 5 7 3 3 3 4 5 5 6 0 1 2 1 4 , 6 8 5 7 4 6 8 6 0 0 1 12 -> 5 7 3 3 3 4 5 5 6 0 1 2 1 12 , 11 8 5 7 4 6 8 6 0 0 1 2 -> 13 7 3 3 3 4 5 5 6 0 1 2 1 2 , 11 8 5 7 4 6 8 6 0 0 1 3 -> 13 7 3 3 3 4 5 5 6 0 1 2 1 3 , 11 8 5 7 4 6 8 6 0 0 1 4 -> 13 7 3 3 3 4 5 5 6 0 1 2 1 4 , 11 8 5 7 4 6 8 6 0 0 1 12 -> 13 7 3 3 3 4 5 5 6 0 1 2 1 12 , 8 7 2 1 2 8 6 8 7 4 5 6 -> 0 1 4 5 5 7 4 6 1 3 3 3 2 , 8 7 2 1 2 8 6 8 7 4 5 7 -> 0 1 4 5 5 7 4 6 1 3 3 3 3 , 8 7 2 1 2 8 6 8 7 4 5 5 -> 0 1 4 5 5 7 4 6 1 3 3 3 4 , 8 7 2 1 2 8 6 8 7 4 5 10 -> 0 1 4 5 5 7 4 6 1 3 3 3 12 , 4 7 2 1 2 8 6 8 7 4 5 6 -> 2 1 4 5 5 7 4 6 1 3 3 3 2 , 4 7 2 1 2 8 6 8 7 4 5 7 -> 2 1 4 5 5 7 4 6 1 3 3 3 3 , 4 7 2 1 2 8 6 8 7 4 5 5 -> 2 1 4 5 5 7 4 6 1 3 3 3 4 , 4 7 2 1 2 8 6 8 7 4 5 10 -> 2 1 4 5 5 7 4 6 1 3 3 3 12 , 5 7 2 1 2 8 6 8 7 4 5 6 -> 6 1 4 5 5 7 4 6 1 3 3 3 2 , 5 7 2 1 2 8 6 8 7 4 5 7 -> 6 1 4 5 5 7 4 6 1 3 3 3 3 , 5 7 2 1 2 8 6 8 7 4 5 5 -> 6 1 4 5 5 7 4 6 1 3 3 3 4 , 5 7 2 1 2 8 6 8 7 4 5 10 -> 6 1 4 5 5 7 4 6 1 3 3 3 12 , 13 7 2 1 2 8 6 8 7 4 5 6 -> 11 1 4 5 5 7 4 6 1 3 3 3 2 , 13 7 2 1 2 8 6 8 7 4 5 7 -> 11 1 4 5 5 7 4 6 1 3 3 3 3 , 13 7 2 1 2 8 6 8 7 4 5 5 -> 11 1 4 5 5 7 4 6 1 3 3 3 4 , 13 7 2 1 2 8 6 8 7 4 5 10 -> 11 1 4 5 5 7 4 6 1 3 3 3 12 , 0 0 0 0 1 2 8 5 6 1 2 1 2 -> 8 7 3 3 3 2 0 0 8 7 4 6 0 1 2 , 0 0 0 0 1 2 8 5 6 1 2 1 3 -> 8 7 3 3 3 2 0 0 8 7 4 6 0 1 3 , 0 0 0 0 1 2 8 5 6 1 2 1 4 -> 8 7 3 3 3 2 0 0 8 7 4 6 0 1 4 , 0 0 0 0 1 2 8 5 6 1 2 1 12 -> 8 7 3 3 3 2 0 0 8 7 4 6 0 1 12 , 2 0 0 0 1 2 8 5 6 1 2 1 2 -> 4 7 3 3 3 2 0 0 8 7 4 6 0 1 2 , 2 0 0 0 1 2 8 5 6 1 2 1 3 -> 4 7 3 3 3 2 0 0 8 7 4 6 0 1 3 , 2 0 0 0 1 2 8 5 6 1 2 1 4 -> 4 7 3 3 3 2 0 0 8 7 4 6 0 1 4 , 2 0 0 0 1 2 8 5 6 1 2 1 12 -> 4 7 3 3 3 2 0 0 8 7 4 6 0 1 12 , 6 0 0 0 1 2 8 5 6 1 2 1 2 -> 5 7 3 3 3 2 0 0 8 7 4 6 0 1 2 , 6 0 0 0 1 2 8 5 6 1 2 1 3 -> 5 7 3 3 3 2 0 0 8 7 4 6 0 1 3 , 6 0 0 0 1 2 8 5 6 1 2 1 4 -> 5 7 3 3 3 2 0 0 8 7 4 6 0 1 4 , 6 0 0 0 1 2 8 5 6 1 2 1 12 -> 5 7 3 3 3 2 0 0 8 7 4 6 0 1 12 , 11 0 0 0 1 2 8 5 6 1 2 1 2 -> 13 7 3 3 3 2 0 0 8 7 4 6 0 1 2 , 11 0 0 0 1 2 8 5 6 1 2 1 3 -> 13 7 3 3 3 2 0 0 8 7 4 6 0 1 3 , 11 0 0 0 1 2 8 5 6 1 2 1 4 -> 13 7 3 3 3 2 0 0 8 7 4 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3 3 3 3 4 7 3 3 3 3 , 14 2 0 8 5 5 7 2 8 7 4 7 4 -> 13 7 3 2 1 3 3 3 3 3 3 3 4 7 3 3 3 4 , 14 2 0 8 5 5 7 2 8 7 4 7 12 -> 13 7 3 2 1 3 3 3 3 3 3 3 4 7 3 3 3 12 , 1 4 5 6 0 8 5 5 5 5 5 7 2 0 -> 1 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 6 , 1 4 5 6 0 8 5 5 5 5 5 7 2 1 -> 1 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 7 , 1 4 5 6 0 8 5 5 5 5 5 7 2 8 -> 1 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 5 , 1 4 5 6 0 8 5 5 5 5 5 7 2 9 -> 1 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 10 , 3 4 5 6 0 8 5 5 5 5 5 7 2 0 -> 3 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 6 , 3 4 5 6 0 8 5 5 5 5 5 7 2 1 -> 3 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 7 , 3 4 5 6 0 8 5 5 5 5 5 7 2 8 -> 3 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 5 , 3 4 5 6 0 8 5 5 5 5 5 7 2 9 -> 3 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 10 , 7 4 5 6 0 8 5 5 5 5 5 7 2 0 -> 7 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 6 , 7 4 5 6 0 8 5 5 5 5 5 7 2 1 -> 7 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 7 , 7 4 5 6 0 8 5 5 5 5 5 7 2 8 -> 7 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 5 , 7 4 5 6 0 8 5 5 5 5 5 7 2 9 -> 7 4 5 7 3 3 3 3 2 1 2 8 5 6 8 5 10 , 14 4 5 6 0 8 5 5 5 5 5 7 2 0 -> 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4 , 6 0 1 3 4 5 6 1 2 8 6 8 6 9 -> 7 2 8 7 3 3 4 5 5 5 5 6 1 3 3 3 12 , 11 0 1 3 4 5 6 1 2 8 6 8 6 0 -> 14 2 8 7 3 3 4 5 5 5 5 6 1 3 3 3 2 , 11 0 1 3 4 5 6 1 2 8 6 8 6 1 -> 14 2 8 7 3 3 4 5 5 5 5 6 1 3 3 3 3 , 11 0 1 3 4 5 6 1 2 8 6 8 6 8 -> 14 2 8 7 3 3 4 5 5 5 5 6 1 3 3 3 4 , 11 0 1 3 4 5 6 1 2 8 6 8 6 9 -> 14 2 8 7 3 3 4 5 5 5 5 6 1 3 3 3 12 , 8 6 8 7 4 5 5 5 6 0 8 6 8 6 -> 8 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 0 , 8 6 8 7 4 5 5 5 6 0 8 6 8 7 -> 8 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 1 , 8 6 8 7 4 5 5 5 6 0 8 6 8 5 -> 8 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 8 , 8 6 8 7 4 5 5 5 6 0 8 6 8 10 -> 8 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 9 , 4 6 8 7 4 5 5 5 6 0 8 6 8 6 -> 4 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 0 , 4 6 8 7 4 5 5 5 6 0 8 6 8 7 -> 4 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 1 , 4 6 8 7 4 5 5 5 6 0 8 6 8 5 -> 4 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 8 , 4 6 8 7 4 5 5 5 6 0 8 6 8 10 -> 4 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 9 , 5 6 8 7 4 5 5 5 6 0 8 6 8 6 -> 5 7 4 7 3 3 3 3 4 6 0 1 2 8 6 0 0 , 5 6 8 7 4 5 5 5 6 0 8 6 8 7 -> 5 7 4 7 3 3 3 3 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8 7 4 5 6 1 3 4 10 -> 2 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 12 , 5 7 4 5 6 8 7 4 5 6 1 3 4 6 -> 6 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 2 , 5 7 4 5 6 8 7 4 5 6 1 3 4 7 -> 6 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 3 , 5 7 4 5 6 8 7 4 5 6 1 3 4 5 -> 6 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 4 , 5 7 4 5 6 8 7 4 5 6 1 3 4 10 -> 6 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 12 , 13 7 4 5 6 8 7 4 5 6 1 3 4 6 -> 11 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 2 , 13 7 4 5 6 8 7 4 5 6 1 3 4 7 -> 11 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 3 , 13 7 4 5 6 8 7 4 5 6 1 3 4 5 -> 11 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 4 , 13 7 4 5 6 8 7 4 5 6 1 3 4 10 -> 11 8 5 5 7 2 1 3 3 3 3 4 6 1 3 3 12 , 0 0 0 0 1 2 1 2 0 0 8 7 4 6 -> 0 1 3 3 3 3 3 2 0 8 7 2 8 5 6 , 0 0 0 0 1 2 1 2 0 0 8 7 4 7 -> 0 1 3 3 3 3 3 2 0 8 7 2 8 5 7 , 0 0 0 0 1 2 1 2 0 0 8 7 4 5 -> 0 1 3 3 3 3 3 2 0 8 7 2 8 5 5 , 0 0 0 0 1 2 1 2 0 0 8 7 4 10 -> 0 1 3 3 3 3 3 2 0 8 7 2 8 5 10 , 2 0 0 0 1 2 1 2 0 0 8 7 4 6 -> 2 1 3 3 3 3 3 2 0 8 7 2 8 5 6 , 2 0 0 0 1 2 1 2 0 0 8 7 4 7 -> 2 1 3 3 3 3 3 2 0 8 7 2 8 5 7 , 2 0 0 0 1 2 1 2 0 0 8 7 4 5 -> 2 1 3 3 3 3 3 2 0 8 7 2 8 5 5 , 2 0 0 0 1 2 1 2 0 0 8 7 4 10 -> 2 1 3 3 3 3 3 2 0 8 7 2 8 5 10 , 6 0 0 0 1 2 1 2 0 0 8 7 4 6 -> 6 1 3 3 3 3 3 2 0 8 7 2 8 5 6 , 6 0 0 0 1 2 1 2 0 0 8 7 4 7 -> 6 1 3 3 3 3 3 2 0 8 7 2 8 5 7 , 6 0 0 0 1 2 1 2 0 0 8 7 4 5 -> 6 1 3 3 3 3 3 2 0 8 7 2 8 5 5 , 6 0 0 0 1 2 1 2 0 0 8 7 4 10 -> 6 1 3 3 3 3 3 2 0 8 7 2 8 5 10 , 11 0 0 0 1 2 1 2 0 0 8 7 4 6 -> 11 1 3 3 3 3 3 2 0 8 7 2 8 5 6 , 11 0 0 0 1 2 1 2 0 0 8 7 4 7 -> 11 1 3 3 3 3 3 2 0 8 7 2 8 5 7 , 11 0 0 0 1 2 1 2 0 0 8 7 4 5 -> 11 1 3 3 3 3 3 2 0 8 7 2 8 5 5 , 11 0 0 0 1 2 1 2 0 0 8 7 4 10 -> 11 1 3 3 3 3 3 2 0 8 7 2 8 5 10 , 1 3 2 8 7 3 4 7 3 2 8 6 0 0 0 -> 1 3 3 3 2 8 7 4 5 6 8 6 8 7 3 2 , 1 3 2 8 7 3 4 7 3 2 8 6 0 0 1 -> 1 3 3 3 2 8 7 4 5 6 8 6 8 7 3 3 , 1 3 2 8 7 3 4 7 3 2 8 6 0 0 8 -> 1 3 3 3 2 8 7 4 5 6 8 6 8 7 3 4 , 1 3 2 8 7 3 4 7 3 2 8 6 0 0 9 -> 1 3 3 3 2 8 7 4 5 6 8 6 8 7 3 12 , 3 3 2 8 7 3 4 7 3 2 8 6 0 0 0 -> 3 3 3 3 2 8 7 4 5 6 8 6 8 7 3 2 , 3 3 2 8 7 3 4 7 3 2 8 6 0 0 1 -> 3 3 3 3 2 8 7 4 5 6 8 6 8 7 3 3 , 3 3 2 8 7 3 4 7 3 2 8 6 0 0 8 -> 3 3 3 3 2 8 7 4 5 6 8 6 8 7 3 4 , 3 3 2 8 7 3 4 7 3 2 8 6 0 0 9 -> 3 3 3 3 2 8 7 4 5 6 8 6 8 7 3 12 , 7 3 2 8 7 3 4 7 3 2 8 6 0 0 0 -> 7 3 3 3 2 8 7 4 5 6 8 6 8 7 3 2 , 7 3 2 8 7 3 4 7 3 2 8 6 0 0 1 -> 7 3 3 3 2 8 7 4 5 6 8 6 8 7 3 3 , 7 3 2 8 7 3 4 7 3 2 8 6 0 0 8 -> 7 3 3 3 2 8 7 4 5 6 8 6 8 7 3 4 , 7 3 2 8 7 3 4 7 3 2 8 6 0 0 9 -> 7 3 3 3 2 8 7 4 5 6 8 6 8 7 3 12 , 14 3 2 8 7 3 4 7 3 2 8 6 0 0 0 -> 14 3 3 3 2 8 7 4 5 6 8 6 8 7 3 2 , 14 3 2 8 7 3 4 7 3 2 8 6 0 0 1 -> 14 3 3 3 2 8 7 4 5 6 8 6 8 7 3 3 , 14 3 2 8 7 3 4 7 3 2 8 6 0 0 8 -> 14 3 3 3 2 8 7 4 5 6 8 6 8 7 3 4 , 14 3 2 8 7 3 4 7 3 2 8 6 0 0 9 -> 14 3 3 3 2 8 7 4 5 6 8 6 8 7 3 12 , 0 0 1 3 4 7 4 7 4 7 2 8 7 4 6 -> 0 0 1 3 4 7 4 5 7 4 6 8 7 3 2 , 0 0 1 3 4 7 4 7 4 7 2 8 7 4 7 -> 0 0 1 3 4 7 4 5 7 4 6 8 7 3 3 , 0 0 1 3 4 7 4 7 4 7 2 8 7 4 5 -> 0 0 1 3 4 7 4 5 7 4 6 8 7 3 4 , 0 0 1 3 4 7 4 7 4 7 2 8 7 4 10 -> 0 0 1 3 4 7 4 5 7 4 6 8 7 3 12 , 2 0 1 3 4 7 4 7 4 7 2 8 7 4 6 -> 2 0 1 3 4 7 4 5 7 4 6 8 7 3 2 , 2 0 1 3 4 7 4 7 4 7 2 8 7 4 7 -> 2 0 1 3 4 7 4 5 7 4 6 8 7 3 3 , 2 0 1 3 4 7 4 7 4 7 2 8 7 4 5 -> 2 0 1 3 4 7 4 5 7 4 6 8 7 3 4 , 2 0 1 3 4 7 4 7 4 7 2 8 7 4 10 -> 2 0 1 3 4 7 4 5 7 4 6 8 7 3 12 , 6 0 1 3 4 7 4 7 4 7 2 8 7 4 6 -> 6 0 1 3 4 7 4 5 7 4 6 8 7 3 2 , 6 0 1 3 4 7 4 7 4 7 2 8 7 4 7 -> 6 0 1 3 4 7 4 5 7 4 6 8 7 3 3 , 6 0 1 3 4 7 4 7 4 7 2 8 7 4 5 -> 6 0 1 3 4 7 4 5 7 4 6 8 7 3 4 , 6 0 1 3 4 7 4 7 4 7 2 8 7 4 10 -> 6 0 1 3 4 7 4 5 7 4 6 8 7 3 12 , 11 0 1 3 4 7 4 7 4 7 2 8 7 4 6 -> 11 0 1 3 4 7 4 5 7 4 6 8 7 3 2 , 11 0 1 3 4 7 4 7 4 7 2 8 7 4 7 -> 11 0 1 3 4 7 4 5 7 4 6 8 7 3 3 , 11 0 1 3 4 7 4 7 4 7 2 8 7 4 5 -> 11 0 1 3 4 7 4 5 7 4 6 8 7 3 4 , 11 0 1 3 4 7 4 7 4 7 2 8 7 4 10 -> 11 0 1 3 4 7 4 5 7 4 6 8 7 3 12 , 8 6 0 0 0 0 8 5 7 2 0 1 2 8 7 2 -> 0 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 2 , 8 6 0 0 0 0 8 5 7 2 0 1 2 8 7 3 -> 0 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 3 , 8 6 0 0 0 0 8 5 7 2 0 1 2 8 7 4 -> 0 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 4 , 8 6 0 0 0 0 8 5 7 2 0 1 2 8 7 12 -> 0 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 12 , 4 6 0 0 0 0 8 5 7 2 0 1 2 8 7 2 -> 2 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 2 , 4 6 0 0 0 0 8 5 7 2 0 1 2 8 7 3 -> 2 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 3 , 4 6 0 0 0 0 8 5 7 2 0 1 2 8 7 4 -> 2 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 4 , 4 6 0 0 0 0 8 5 7 2 0 1 2 8 7 12 -> 2 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 12 , 5 6 0 0 0 0 8 5 7 2 0 1 2 8 7 2 -> 6 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 2 , 5 6 0 0 0 0 8 5 7 2 0 1 2 8 7 3 -> 6 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 3 , 5 6 0 0 0 0 8 5 7 2 0 1 2 8 7 4 -> 6 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 4 , 5 6 0 0 0 0 8 5 7 2 0 1 2 8 7 12 -> 6 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 12 , 13 6 0 0 0 0 8 5 7 2 0 1 2 8 7 2 -> 11 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 2 , 13 6 0 0 0 0 8 5 7 2 0 1 2 8 7 3 -> 11 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 3 , 13 6 0 0 0 0 8 5 7 2 0 1 2 8 7 4 -> 11 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 4 , 13 6 0 0 0 0 8 5 7 2 0 1 2 8 7 12 -> 11 0 0 1 3 4 5 7 3 3 3 2 1 4 7 3 3 12 , 1 4 7 4 5 7 2 1 2 0 0 0 1 3 4 6 -> 8 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 6 , 1 4 7 4 5 7 2 1 2 0 0 0 1 3 4 7 -> 8 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 7 , 1 4 7 4 5 7 2 1 2 0 0 0 1 3 4 5 -> 8 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 5 , 1 4 7 4 5 7 2 1 2 0 0 0 1 3 4 10 -> 8 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 10 , 3 4 7 4 5 7 2 1 2 0 0 0 1 3 4 6 -> 4 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 6 , 3 4 7 4 5 7 2 1 2 0 0 0 1 3 4 7 -> 4 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 7 , 3 4 7 4 5 7 2 1 2 0 0 0 1 3 4 5 -> 4 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 5 , 3 4 7 4 5 7 2 1 2 0 0 0 1 3 4 10 -> 4 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 10 , 7 4 7 4 5 7 2 1 2 0 0 0 1 3 4 6 -> 5 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 6 , 7 4 7 4 5 7 2 1 2 0 0 0 1 3 4 7 -> 5 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 7 , 7 4 7 4 5 7 2 1 2 0 0 0 1 3 4 5 -> 5 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 5 , 7 4 7 4 5 7 2 1 2 0 0 0 1 3 4 10 -> 5 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 10 , 14 4 7 4 5 7 2 1 2 0 0 0 1 3 4 6 -> 13 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 6 , 14 4 7 4 5 7 2 1 2 0 0 0 1 3 4 7 -> 13 7 3 3 4 5 7 3 4 5 7 3 3 3 2 8 7 , 14 4 7 4 5 7 2 1 2 0 0 0 1 3 4 5 -> 13 7 3 3 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1 2 1 2 1 2 0 -> 13 6 0 0 0 1 2 1 2 8 7 3 3 3 2 0 0 , 13 6 0 0 1 3 4 6 1 2 1 2 1 2 1 2 1 -> 13 6 0 0 0 1 2 1 2 8 7 3 3 3 2 0 1 , 13 6 0 0 1 3 4 6 1 2 1 2 1 2 1 2 8 -> 13 6 0 0 0 1 2 1 2 8 7 3 3 3 2 0 8 , 13 6 0 0 1 3 4 6 1 2 1 2 1 2 1 2 9 -> 13 6 0 0 0 1 2 1 2 8 7 3 3 3 2 0 9 , 0 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 2 -> 8 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 2 , 0 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 3 -> 8 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 3 , 0 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 4 -> 8 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 4 , 0 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 12 -> 8 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 12 , 2 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 2 -> 4 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 2 , 2 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 3 -> 4 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 3 , 2 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 4 -> 4 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 4 , 2 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 12 -> 4 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 12 , 6 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 2 -> 5 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 2 , 6 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 3 -> 5 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 3 , 6 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 4 -> 5 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 4 , 6 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 12 -> 5 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 12 , 11 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 2 -> 13 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 2 , 11 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 3 -> 13 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 3 , 11 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 4 -> 13 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 4 , 11 0 8 7 4 5 7 3 2 1 2 1 4 5 6 1 12 -> 13 6 8 5 5 5 5 7 4 7 3 3 3 3 3 3 3 3 3 12 , 1 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 6 -> 1 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 6 , 1 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 7 -> 1 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 7 , 1 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 5 -> 1 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 5 , 1 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 10 -> 1 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 10 , 3 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 6 -> 3 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 6 , 3 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 7 -> 3 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 7 , 3 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 5 -> 3 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 5 , 3 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 10 -> 3 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 10 , 7 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 6 -> 7 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 6 , 7 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 7 -> 7 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 7 , 7 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 5 -> 7 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 5 , 7 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 10 -> 7 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 10 , 14 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 6 -> 14 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 6 , 14 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 7 -> 14 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 7 , 14 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 5 -> 14 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 5 , 14 3 4 5 6 1 2 1 4 6 8 5 6 0 0 8 10 -> 14 3 3 4 6 8 7 4 7 3 2 0 0 1 3 3 3 4 10 , 0 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 6 -> 8 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 2 , 0 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 7 -> 8 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 3 , 0 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 5 -> 8 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 4 , 0 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 10 -> 8 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 12 , 2 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 6 -> 4 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 2 , 2 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 7 -> 4 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 3 , 2 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 5 -> 4 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 4 , 2 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 10 -> 4 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 12 , 6 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 6 -> 5 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 2 , 6 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 7 -> 5 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 3 , 6 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 5 -> 5 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 4 , 6 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 10 -> 5 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 12 , 11 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 6 -> 13 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 2 , 11 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 7 -> 13 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 3 , 11 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 5 -> 13 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 4 , 11 8 6 1 2 0 8 6 8 7 2 8 7 4 7 4 10 -> 13 7 3 3 4 5 5 7 2 1 4 5 7 2 1 3 3 12 , 8 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 6 -> 1 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 2 , 8 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 7 -> 1 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 3 , 8 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 5 -> 1 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 4 , 8 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 10 -> 1 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 12 , 4 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 6 -> 3 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 2 , 4 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 7 -> 3 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 3 , 4 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 5 -> 3 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 4 , 4 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 10 -> 3 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 12 , 5 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 6 -> 7 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 2 , 5 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 7 -> 7 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 3 , 5 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 5 -> 7 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 4 , 5 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 10 -> 7 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 12 , 13 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 6 -> 14 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 2 , 13 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 7 -> 14 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 3 , 13 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 5 -> 14 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 4 , 13 5 6 1 4 6 8 7 4 5 6 8 5 6 8 5 10 -> 14 3 3 4 5 7 3 3 4 5 7 2 8 5 7 3 3 4 7 12 , 8 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 0 -> 8 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 0 , 8 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 1 -> 8 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 1 , 8 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 8 -> 8 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 8 , 8 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 9 -> 8 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 9 , 4 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 0 -> 4 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 0 , 4 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 1 -> 4 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 1 , 4 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 8 -> 4 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 8 , 4 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 9 -> 4 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 9 , 5 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 0 -> 5 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 0 , 5 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 1 -> 5 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 1 , 5 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 8 -> 5 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 8 , 5 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 9 -> 5 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 9 , 13 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 0 -> 13 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 0 , 13 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 1 -> 13 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 1 , 13 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 8 -> 13 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 8 , 13 6 0 0 0 1 4 6 8 5 7 4 6 0 8 5 6 9 -> 13 5 7 3 3 3 2 8 5 7 4 7 4 5 7 4 6 1 2 9 , 8 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 2 -> 0 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 2 , 8 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 3 -> 0 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 3 , 8 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 4 -> 0 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 4 , 8 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 12 -> 0 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 12 , 4 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 2 -> 2 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 2 , 4 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 3 -> 2 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 3 , 4 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 4 -> 2 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 4 , 4 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 12 -> 2 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 12 , 5 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 2 -> 6 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 2 , 5 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 3 -> 6 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 3 , 5 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 4 -> 6 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 4 , 5 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 12 -> 6 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 12 , 13 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 2 -> 11 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 2 , 13 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 3 -> 11 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 3 , 13 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 4 -> 11 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 4 , 13 5 7 4 6 0 1 3 2 0 8 6 0 0 8 7 3 12 -> 11 1 3 2 0 0 1 4 7 3 4 5 7 3 3 3 4 7 3 12 , 0 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 6 -> 1 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 0 , 0 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 7 -> 1 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 1 , 0 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 5 -> 1 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 8 , 0 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 10 -> 1 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 9 , 2 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 6 -> 3 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 0 , 2 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 7 -> 3 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 1 , 2 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 5 -> 3 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 8 , 2 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 10 -> 3 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 9 , 6 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 6 -> 7 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 0 , 6 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 7 -> 7 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 1 , 6 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 5 -> 7 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 8 , 6 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 10 -> 7 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 9 , 11 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 6 -> 14 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 0 , 11 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 7 -> 14 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 1 , 11 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 5 -> 14 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 8 , 11 0 0 0 0 0 8 6 8 5 6 1 2 8 5 5 5 10 -> 14 4 5 7 3 3 3 2 0 0 1 2 8 5 7 4 7 2 9 , 8 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 0 -> 8 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 0 , 8 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 1 -> 8 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 1 , 8 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 8 -> 8 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 8 , 8 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 9 -> 8 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 9 , 4 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 0 -> 4 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 0 , 4 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 1 -> 4 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 1 , 4 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 8 -> 4 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 8 , 4 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 9 -> 4 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 9 , 5 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 0 -> 5 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 0 , 5 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 1 -> 5 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 1 , 5 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 8 -> 5 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 8 , 5 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 9 -> 5 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 9 , 13 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 0 -> 13 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 0 , 13 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 1 -> 13 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 1 , 13 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 8 -> 13 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 8 , 13 7 3 4 5 6 1 3 3 2 0 8 6 8 5 5 5 6 9 -> 13 5 7 4 7 3 3 4 5 6 1 3 3 3 3 3 4 6 1 2 9 , 8 7 4 6 1 2 8 7 4 7 2 0 8 5 6 8 5 7 2 -> 0 0 8 6 1 3 3 3 2 8 7 3 4 6 1 4 5 6 0 1 2 , 8 7 4 6 1 2 8 7 4 7 2 0 8 5 6 8 5 7 3 -> 0 0 8 6 1 3 3 3 2 8 7 3 4 6 1 4 5 6 0 1 3 , 8 7 4 6 1 2 8 7 4 7 2 0 8 5 6 8 5 7 4 -> 0 0 8 6 1 3 3 3 2 8 7 3 4 6 1 4 5 6 0 1 4 , 8 7 4 6 1 2 8 7 4 7 2 0 8 5 6 8 5 7 12 -> 0 0 8 6 1 3 3 3 2 8 7 3 4 6 1 4 5 6 0 1 12 , 4 7 4 6 1 2 8 7 4 7 2 0 8 5 6 8 5 7 2 -> 2 0 8 6 1 3 3 3 2 8 7 3 4 6 1 4 5 6 0 1 2 , 4 7 4 6 1 2 8 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2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 10 -> 3 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 9 , 7 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 6 -> 7 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 0 , 7 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 7 -> 7 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 1 , 7 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 5 -> 7 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 8 , 7 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 10 -> 7 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 9 , 14 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 6 -> 14 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 0 , 14 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 7 -> 14 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 1 , 14 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 5 -> 14 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 8 , 14 4 6 1 3 2 0 8 7 3 2 0 0 1 2 0 8 6 0 8 10 -> 14 4 7 3 3 3 2 8 6 1 4 5 7 3 3 4 5 6 1 3 2 9 , 0 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 6 -> 8 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 2 , 0 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 7 -> 8 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 3 , 0 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 5 -> 8 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 4 , 0 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 10 -> 8 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 12 , 2 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 6 -> 4 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 2 , 2 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 7 -> 4 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 3 , 2 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 5 -> 4 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 4 , 2 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 10 -> 4 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 12 , 6 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 6 -> 5 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 2 , 6 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 7 -> 5 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 3 , 6 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 5 -> 5 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 4 , 6 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 10 -> 5 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 12 , 11 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 6 -> 13 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 2 , 11 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 7 -> 13 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 3 , 11 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 5 -> 13 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 4 , 11 0 8 5 6 8 7 2 8 7 2 1 3 4 7 3 2 0 8 5 10 -> 13 5 7 3 3 3 3 2 1 3 2 1 3 3 2 0 0 8 5 5 6 8 7 12 , 0 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 0 -> 1 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 2 , 0 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 1 -> 1 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 3 , 0 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 8 -> 1 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 4 , 0 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 9 -> 1 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 12 , 2 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 0 -> 3 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 2 , 2 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 1 -> 3 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 3 , 2 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 8 -> 3 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 4 , 2 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 9 -> 3 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 12 , 6 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 0 -> 7 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 2 , 6 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 1 -> 7 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 3 , 6 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 8 -> 7 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 4 , 6 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 9 -> 7 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 12 , 11 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 0 -> 14 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 2 , 11 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 1 -> 14 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 3 , 11 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 8 -> 14 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 4 , 11 0 0 8 5 6 1 4 7 4 5 5 7 4 7 2 1 3 2 1 2 9 -> 14 2 0 1 2 1 3 3 3 4 6 0 1 3 3 2 1 2 0 0 8 6 1 12 , 1 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 6 -> 1 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 6 , 1 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 7 -> 1 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 7 , 1 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 5 -> 1 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 5 , 1 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 10 -> 1 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 10 , 3 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 6 -> 3 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 6 , 3 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 7 -> 3 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 7 , 3 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 5 -> 3 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 5 , 3 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 10 -> 3 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 10 , 7 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 6 -> 7 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 6 , 7 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 7 -> 7 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 7 , 7 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 5 -> 7 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 5 , 7 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 10 -> 7 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 10 , 14 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 6 -> 14 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 6 , 14 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 7 -> 14 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 7 , 14 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 5 -> 14 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 5 , 14 2 8 5 7 3 2 1 4 7 3 2 8 6 1 2 1 3 3 2 8 10 -> 14 3 3 3 3 4 6 1 2 8 7 2 8 6 0 0 8 7 3 3 4 10 , 0 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 6 -> 0 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 2 , 0 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 7 -> 0 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 3 , 0 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 5 -> 0 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 4 , 0 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 10 -> 0 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 12 , 2 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 6 -> 2 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 2 , 2 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 7 -> 2 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 3 , 2 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 5 -> 2 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 4 , 2 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 10 -> 2 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 12 , 6 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 6 -> 6 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 2 , 6 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 7 -> 6 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 3 , 6 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 5 -> 6 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 4 , 6 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 10 -> 6 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 12 , 11 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 6 -> 11 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 2 , 11 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 7 -> 11 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 3 , 11 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 5 -> 11 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 4 , 11 8 7 2 8 5 5 5 6 1 2 8 6 1 2 1 2 8 5 6 8 10 -> 11 1 3 3 3 3 3 2 0 1 4 7 3 3 3 4 5 7 4 7 2 0 0 1 4 7 3 3 12 , 0 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 0 -> 0 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 6 , 0 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 1 -> 0 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 7 , 0 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 8 -> 0 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 5 , 0 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 9 -> 0 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 10 , 2 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 0 -> 2 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 6 , 2 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 1 -> 2 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 7 , 2 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 8 -> 2 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 5 , 2 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 9 -> 2 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 10 , 6 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 0 -> 6 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 6 , 6 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 1 -> 6 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 7 , 6 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 8 -> 6 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 5 , 6 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 9 -> 6 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 10 , 11 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 0 -> 11 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 6 , 11 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 1 -> 11 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 7 , 11 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 8 -> 11 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 5 , 11 0 0 1 2 1 4 6 8 7 3 4 6 0 1 2 8 7 4 5 6 0 9 -> 11 0 1 3 2 0 0 1 2 8 7 3 3 3 3 3 3 3 4 5 5 6 1 4 10 , 1 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 0 -> 1 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 2 , 1 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 1 -> 1 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 3 , 1 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 8 -> 1 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 4 , 1 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 9 -> 1 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 12 , 3 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 0 -> 3 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 2 , 3 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 1 -> 3 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 3 , 3 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 8 -> 3 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 4 , 3 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 9 -> 3 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 12 , 7 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 0 -> 7 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 2 , 7 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 1 -> 7 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 3 , 7 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 8 -> 7 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 4 , 7 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 9 -> 7 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 12 , 14 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 0 -> 14 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 2 , 14 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 1 -> 14 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 3 , 14 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 8 -> 14 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 4 , 14 4 7 4 6 8 7 2 8 7 3 2 8 5 7 4 7 3 4 6 1 2 9 -> 14 3 3 3 2 8 7 2 8 7 3 4 6 1 4 7 2 0 0 1 3 4 7 12 , 0 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 0 -> 1 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 0 , 0 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 1 -> 1 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 1 , 0 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 8 -> 1 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 8 , 0 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 9 -> 1 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 9 , 2 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 0 -> 3 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 0 , 2 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 1 -> 3 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 1 , 2 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 8 -> 3 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 8 , 2 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 9 -> 3 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 9 , 6 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 0 -> 7 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 0 , 6 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 1 -> 7 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 1 , 6 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 8 -> 7 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 8 , 6 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 9 -> 7 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 9 , 11 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 0 -> 14 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 0 , 11 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 1 -> 14 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 1 , 11 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 8 -> 14 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 8 , 11 1 4 5 6 1 2 0 0 8 6 8 7 4 7 2 0 8 6 8 5 6 9 -> 14 2 1 2 8 6 1 3 3 3 4 7 2 8 7 2 8 5 7 3 3 2 0 9 , 8 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 2 -> 1 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 2 , 8 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 3 -> 1 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 3 , 8 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 4 -> 1 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 4 , 8 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 12 -> 1 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 12 , 4 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 2 -> 3 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 2 , 4 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 3 -> 3 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 3 , 4 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 4 -> 3 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 4 , 4 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 12 -> 3 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 12 , 5 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 2 -> 7 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 2 , 5 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 3 -> 7 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 3 , 5 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 4 -> 7 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 4 , 5 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 12 -> 7 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 12 , 13 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 2 -> 14 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 2 , 13 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 3 -> 14 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 3 , 13 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 4 -> 14 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 4 , 13 7 4 6 8 5 6 1 3 2 8 5 5 5 5 7 3 2 1 4 7 3 12 -> 14 4 7 3 2 0 8 5 7 2 0 8 6 1 2 1 2 8 6 1 3 3 3 12 , 8 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 6 -> 1 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 2 , 8 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 7 -> 1 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 3 , 8 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 5 -> 1 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 4 , 8 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 10 -> 1 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 12 , 4 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 6 -> 3 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 2 , 4 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 7 -> 3 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 3 , 4 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 5 -> 3 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 4 , 4 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 10 -> 3 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 12 , 5 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 6 -> 7 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 2 , 5 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 7 -> 7 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 3 , 5 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 5 -> 7 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 4 , 5 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 10 -> 7 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 12 , 13 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 6 -> 14 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 2 , 13 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 7 -> 14 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 3 , 13 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 5 -> 14 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 4 , 13 5 5 6 8 7 2 0 0 0 8 6 1 2 1 2 8 5 7 3 3 4 10 -> 14 2 0 0 1 3 4 7 4 6 1 3 2 0 1 3 3 3 2 8 7 4 7 12 , 8 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 6 -> 0 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 2 , 8 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 7 -> 0 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 3 , 8 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 5 -> 0 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 4 , 8 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 10 -> 0 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 12 , 4 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 6 -> 2 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 2 , 4 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 7 -> 2 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 3 , 4 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 5 -> 2 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 4 , 4 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 10 -> 2 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 12 , 5 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 6 -> 6 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 2 , 5 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 7 -> 6 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 3 , 5 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 5 -> 6 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 4 , 5 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 10 -> 6 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 12 , 13 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 6 -> 11 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 2 , 13 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 7 -> 11 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 3 , 13 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 5 -> 11 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 4 , 13 7 4 5 5 5 6 1 4 7 2 1 3 2 8 5 7 3 2 8 7 4 10 -> 11 0 1 4 6 8 7 3 2 1 4 5 5 7 3 3 2 8 7 3 3 3 3 12 , 1 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 6 -> 1 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 0 , 1 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 7 -> 1 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 1 , 1 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 5 -> 1 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 8 , 1 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 10 -> 1 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 9 , 3 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 6 -> 3 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 0 , 3 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 7 -> 3 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 1 , 3 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 5 -> 3 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 8 , 3 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 10 -> 3 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 9 , 7 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 6 -> 7 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 0 , 7 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 7 -> 7 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 1 , 7 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 5 -> 7 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 8 , 7 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 10 -> 7 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 9 , 14 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 6 -> 14 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 0 , 14 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 7 -> 14 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 1 , 14 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 5 -> 14 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 8 , 14 4 6 0 1 2 0 8 5 6 8 6 8 6 8 7 4 6 8 5 7 4 10 -> 14 3 3 4 7 4 5 5 6 0 0 1 3 4 7 4 6 1 2 0 1 4 6 9 , 8 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 6 -> 1 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 6 , 8 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 7 -> 1 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 7 , 8 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 5 -> 1 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 5 , 8 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 10 -> 1 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 10 , 4 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 6 -> 3 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 6 , 4 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 7 -> 3 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 7 , 4 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 5 -> 3 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 5 , 4 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 10 -> 3 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 10 , 5 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 6 -> 7 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 6 , 5 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 7 -> 7 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 7 , 5 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 5 -> 7 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 5 , 5 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 10 -> 7 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 10 , 13 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 6 -> 14 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 6 , 13 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 7 -> 14 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 7 , 13 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 5 -> 14 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 5 , 13 6 1 3 2 0 8 6 0 1 3 4 6 1 2 8 6 1 4 5 7 4 10 -> 14 3 3 3 4 6 8 6 8 6 8 6 0 8 7 2 0 0 8 6 8 5 5 10 , 8 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 0 -> 1 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 6 , 8 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 1 -> 1 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 7 , 8 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 8 -> 1 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 5 , 8 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 9 -> 1 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 10 , 4 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 0 -> 3 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 6 , 4 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 1 -> 3 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 7 , 4 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 8 -> 3 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 5 , 4 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 9 -> 3 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 10 , 5 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 0 -> 7 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 6 , 5 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 1 -> 7 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 7 , 5 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 8 -> 7 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 5 , 5 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 9 -> 7 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 10 , 13 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 0 -> 14 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 6 , 13 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 1 -> 14 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 7 , 13 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 8 -> 14 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 5 , 13 7 2 0 1 4 6 0 8 5 6 1 3 2 8 7 4 7 4 5 7 2 0 9 -> 14 3 3 4 5 6 1 3 3 3 2 8 7 3 4 6 8 5 7 2 1 3 2 8 10 , 8 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 0 -> 8 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 0 , 8 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 1 -> 8 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 1 , 8 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 8 -> 8 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 8 , 8 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 9 -> 8 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 9 , 4 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 0 -> 4 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 0 , 4 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 1 -> 4 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 1 , 4 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 8 -> 4 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 8 , 4 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 9 -> 4 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 9 , 5 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 0 -> 5 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 0 , 5 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 1 -> 5 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 1 , 5 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 8 -> 5 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 8 , 5 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 9 -> 5 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 9 , 13 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 0 -> 13 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 0 , 13 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 1 -> 13 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 1 , 13 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 8 -> 13 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 8 , 13 6 8 6 0 0 0 0 1 4 5 7 2 1 3 4 6 1 3 2 0 8 6 9 -> 13 6 0 0 0 0 1 2 8 7 4 6 1 2 0 8 5 5 6 1 3 3 2 9 , 1 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 0 -> 0 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 6 , 1 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 1 -> 0 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 7 , 1 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 8 -> 0 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 5 , 1 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 9 -> 0 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 10 , 3 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 0 -> 2 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 6 , 3 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 1 -> 2 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 7 , 3 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 8 -> 2 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 5 , 3 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 9 -> 2 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 10 , 7 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 0 -> 6 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 6 , 7 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 1 -> 6 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 7 , 7 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 8 -> 6 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 5 , 7 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 9 -> 6 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 10 , 14 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 0 -> 11 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 6 , 14 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 1 -> 11 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 7 , 14 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 8 -> 11 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 5 , 14 4 6 8 6 8 5 7 3 3 2 1 2 8 7 4 6 1 4 7 4 5 6 9 -> 11 1 3 4 5 5 6 8 6 1 3 3 4 5 6 8 7 3 3 3 3 3 3 2 8 10 , 1 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 2 -> 1 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 2 , 1 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 3 -> 1 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 3 , 1 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 4 -> 1 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 4 , 1 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 12 -> 1 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 12 , 3 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 2 -> 3 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 2 , 3 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 3 -> 3 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 3 , 3 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 4 -> 3 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 4 , 3 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 12 -> 3 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 12 , 7 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 2 -> 7 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 2 , 7 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 3 -> 7 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 3 , 7 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 4 -> 7 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 4 , 7 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 12 -> 7 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 12 , 14 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 2 -> 14 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 2 , 14 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 3 -> 14 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 3 , 14 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 4 -> 14 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 4 , 14 4 5 5 5 5 6 8 6 0 0 1 2 0 1 3 4 7 4 5 5 6 1 12 -> 14 2 1 3 2 0 1 2 8 7 3 3 4 5 7 3 4 6 1 2 0 8 7 3 3 12 , 1 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 0 -> 1 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 0 , 1 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 1 -> 1 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 1 , 1 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 8 -> 1 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 8 , 1 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 9 -> 1 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 9 , 3 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 0 -> 3 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 0 , 3 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 1 -> 3 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 1 , 3 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 8 -> 3 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 8 , 3 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 9 -> 3 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 9 , 7 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 0 -> 7 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 0 , 7 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 1 -> 7 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 1 , 7 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 8 -> 7 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 8 , 7 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 9 -> 7 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 9 , 14 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 0 -> 14 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 0 , 14 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 1 -> 14 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 1 , 14 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 8 -> 14 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 8 , 14 4 6 1 4 6 1 4 6 0 0 8 7 2 8 5 7 4 6 0 1 4 6 0 9 -> 14 3 2 8 6 0 1 3 3 4 7 2 8 6 1 4 5 7 3 4 5 7 4 7 2 9 , 0 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 0 -> 0 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 6 , 0 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 1 -> 0 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 7 , 0 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 8 -> 0 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 5 , 0 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 9 -> 0 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 10 , 2 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 0 -> 2 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 6 , 2 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 1 -> 2 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 7 , 2 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 8 -> 2 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 5 , 2 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 9 -> 2 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 10 , 6 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 0 -> 6 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 6 , 6 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 1 -> 6 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 7 , 6 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 8 -> 6 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 5 , 6 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 9 -> 6 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 10 , 11 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 0 -> 11 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 6 , 11 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 1 -> 11 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 7 , 11 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 8 -> 11 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 5 , 11 0 0 0 8 7 2 0 0 0 0 0 8 5 5 7 4 7 2 0 8 6 1 2 9 -> 11 0 8 5 5 5 7 3 3 3 4 5 7 3 3 4 5 7 2 1 2 8 6 0 1 4 10 , 8 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 0 -> 8 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 2 , 8 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 1 -> 8 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 3 , 8 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 8 -> 8 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 4 , 8 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 9 -> 8 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 12 , 4 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 0 -> 4 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 2 , 4 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 1 -> 4 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 3 , 4 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 8 -> 4 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 4 , 4 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 9 -> 4 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 12 , 5 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 0 -> 5 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 2 , 5 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 1 -> 5 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 3 , 5 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 8 -> 5 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 4 , 5 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 9 -> 5 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 12 , 13 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 0 -> 13 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 2 , 13 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 1 -> 13 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 3 , 13 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 8 -> 13 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 4 , 13 5 6 1 3 3 2 0 0 1 4 7 4 5 7 3 2 8 6 1 4 6 1 2 9 -> 13 7 4 6 1 2 8 5 5 6 0 8 7 2 8 5 6 0 8 5 7 3 3 3 3 12 , 1 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 0 -> 1 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 0 , 1 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 1 -> 1 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 1 , 1 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 8 -> 1 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 8 , 1 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 9 -> 1 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 9 , 3 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 0 -> 3 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 0 , 3 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 1 -> 3 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 1 , 3 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 8 -> 3 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 8 , 3 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 9 -> 3 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 9 , 7 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 0 -> 7 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 0 , 7 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 1 -> 7 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 1 , 7 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 8 -> 7 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 8 , 7 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 9 -> 7 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 9 , 14 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 0 -> 14 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 0 , 14 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 1 -> 14 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 1 , 14 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 8 -> 14 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 8 , 14 2 0 0 1 2 8 7 3 2 0 0 1 4 7 4 7 3 2 1 3 4 7 2 9 -> 14 3 4 7 3 3 3 4 7 3 2 8 7 4 6 1 4 5 6 1 3 4 5 7 2 9 , 0 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 0 -> 8 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 2 , 0 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 1 -> 8 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 3 , 0 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 8 -> 8 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 4 , 0 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 9 -> 8 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 12 , 2 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 0 -> 4 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 2 , 2 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 1 -> 4 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 3 , 2 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 8 -> 4 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 4 , 2 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 9 -> 4 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 12 , 6 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 0 -> 5 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 2 , 6 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 1 -> 5 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 3 , 6 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 8 -> 5 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 4 , 6 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 9 -> 5 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 12 , 11 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 0 -> 13 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 2 , 11 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 1 -> 13 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 3 , 11 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 8 -> 13 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 4 , 11 8 6 8 6 1 4 5 6 8 6 0 8 6 0 0 1 2 0 1 2 1 4 6 9 -> 13 6 0 1 4 5 6 0 1 3 3 3 4 5 5 5 7 4 5 7 3 2 8 5 6 1 12 , 0 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 2 -> 1 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 2 , 0 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 3 -> 1 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 3 , 0 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 4 -> 1 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 4 , 0 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 12 -> 1 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 12 , 2 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 2 -> 3 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 2 , 2 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 3 -> 3 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 3 , 2 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 4 -> 3 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 4 , 2 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 12 -> 3 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 12 , 6 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 2 -> 7 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 2 , 6 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 3 -> 7 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 3 , 6 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 4 -> 7 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 4 , 6 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 12 -> 7 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 12 , 11 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 2 -> 14 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 2 , 11 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 3 -> 14 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 3 , 11 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 4 -> 14 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 4 , 11 0 8 5 6 0 0 1 4 5 5 6 0 8 7 2 0 0 0 1 3 2 8 7 12 -> 14 2 1 4 6 0 1 3 2 0 0 1 3 3 3 3 3 4 7 4 7 4 5 5 7 2 1 12 , 8 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 2 -> 1 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 2 , 8 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 3 -> 1 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 3 , 8 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 4 -> 1 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 4 , 8 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 12 -> 1 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 12 , 4 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 2 -> 3 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 2 , 4 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 3 -> 3 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 3 , 4 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 4 -> 3 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 4 , 4 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 12 -> 3 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 12 , 5 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 2 -> 7 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 2 , 5 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 3 -> 7 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 3 , 5 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 4 -> 7 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 4 , 5 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 12 -> 7 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 12 , 13 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 2 -> 14 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 2 , 13 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 3 -> 14 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 3 , 13 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 4 -> 14 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 4 , 13 5 7 4 7 3 4 5 7 2 1 2 8 6 8 7 2 8 7 2 0 8 5 7 12 -> 14 3 2 0 8 5 7 2 0 0 1 3 3 4 6 8 5 6 0 8 7 3 3 3 3 12 , 0 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 6 -> 1 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 6 , 0 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 7 -> 1 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 7 , 0 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 5 -> 1 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 5 , 0 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 10 -> 1 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 10 , 2 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 6 -> 3 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 6 , 2 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 7 -> 3 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 7 , 2 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 5 -> 3 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 5 , 2 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 10 -> 3 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 10 , 6 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 6 -> 7 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 6 , 6 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 7 -> 7 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 7 , 6 8 6 8 5 6 8 7 2 1 2 1 2 0 8 7 4 7 4 7 4 7 3 4 5 -> 7 3 3 3 2 1 2 8 6 1 2 8 6 8 7 3 4 6 1 4 6 0 0 0 8 5 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1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 0 -> 2 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 2 , 3 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 1 -> 2 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 3 , 3 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 8 -> 2 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 4 , 3 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 9 -> 2 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 12 , 7 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 0 -> 6 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 2 , 7 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 1 -> 6 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 3 , 7 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 8 -> 6 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 4 , 7 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 9 -> 6 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 12 , 14 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 0 -> 11 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 2 , 14 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 1 -> 11 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 3 , 14 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 8 -> 11 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 4 , 14 3 2 1 4 5 7 4 6 0 1 4 6 1 2 0 8 6 0 0 0 0 0 0 0 9 -> 11 0 0 0 1 3 2 8 6 8 6 1 3 3 3 4 5 7 2 1 2 0 1 3 3 3 12 , 0 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 0 -> 8 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 0 , 0 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 1 -> 8 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 1 , 0 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 8 -> 8 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 8 , 0 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 9 -> 8 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 9 , 2 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 0 -> 4 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 0 , 2 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 1 -> 4 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 1 , 2 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 8 -> 4 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 8 , 2 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 9 -> 4 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 9 , 6 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 0 -> 5 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 0 , 6 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 1 -> 5 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 1 , 6 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 8 -> 5 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 8 , 6 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 9 -> 5 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 9 , 11 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 0 -> 13 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 0 , 11 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 1 -> 13 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 1 , 11 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 8 -> 13 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 8 , 11 8 5 6 8 6 0 0 1 2 8 7 4 5 6 1 3 2 8 7 4 6 0 1 2 9 -> 13 5 6 8 7 2 0 1 3 3 3 3 2 0 8 7 4 7 3 4 5 5 6 1 3 4 6 9 , 1 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 0 -> 1 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 2 , 1 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 1 -> 1 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 3 , 1 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 8 -> 1 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 4 , 1 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 9 -> 1 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 12 , 3 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 0 -> 3 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 2 , 3 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 1 -> 3 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 3 , 3 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 8 -> 3 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 4 , 3 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 9 -> 3 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 12 , 7 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 0 -> 7 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 2 , 7 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 1 -> 7 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 3 , 7 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 8 -> 7 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 4 , 7 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 9 -> 7 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 12 , 14 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 0 -> 14 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 2 , 14 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 1 -> 14 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 3 , 14 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 8 -> 14 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 4 , 14 4 7 4 5 6 8 5 5 6 1 2 0 0 8 6 8 5 6 1 2 1 4 5 6 9 -> 14 4 6 0 0 1 3 4 6 8 6 0 8 6 1 4 7 3 3 3 4 5 6 0 0 1 12 , 1 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 0 -> 1 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 6 , 1 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 1 -> 1 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 7 , 1 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 8 -> 1 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 5 , 1 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 9 -> 1 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 10 , 3 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 0 -> 3 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 6 , 3 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 1 -> 3 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 7 , 3 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 8 -> 3 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 5 , 3 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 9 -> 3 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 10 , 7 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 0 -> 7 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 6 , 7 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 1 -> 7 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 7 , 7 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 8 -> 7 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 5 , 7 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 9 -> 7 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 10 , 14 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 0 -> 14 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 6 , 14 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 1 -> 14 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 7 , 14 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 8 -> 14 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 5 , 14 2 1 4 6 0 0 0 8 5 7 4 5 7 2 0 8 6 1 2 8 5 5 5 6 9 -> 14 3 4 5 6 8 5 7 4 6 1 3 4 6 0 1 3 4 6 8 7 4 7 3 3 4 10 , 8 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 2 -> 1 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 2 , 8 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 3 -> 1 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 3 , 8 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 4 -> 1 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 4 , 8 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 12 -> 1 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 12 , 4 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 2 -> 3 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 2 , 4 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 3 -> 3 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 3 , 4 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 4 -> 3 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 4 , 4 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 12 -> 3 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 12 , 5 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 2 -> 7 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 2 , 5 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 3 -> 7 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 3 , 5 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 4 -> 7 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 4 , 5 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 12 -> 7 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 12 , 13 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 2 -> 14 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 2 , 13 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 3 -> 14 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 3 , 13 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 4 -> 14 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 4 , 13 6 8 7 2 8 5 7 2 1 2 0 1 2 8 6 1 2 1 2 8 6 0 0 1 12 -> 14 4 7 3 3 4 6 0 1 3 3 3 2 0 0 8 5 7 4 7 2 1 4 5 6 1 12 , 8 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 2 -> 0 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 2 , 8 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 3 -> 0 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 3 , 8 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 4 -> 0 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 4 , 8 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 12 -> 0 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 12 , 4 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 2 -> 2 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 2 , 4 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 3 -> 2 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 3 , 4 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 4 -> 2 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 4 , 4 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 12 -> 2 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 12 , 5 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 2 -> 6 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 2 , 5 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 3 -> 6 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 3 , 5 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 4 -> 6 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 4 , 5 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 12 -> 6 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 12 , 13 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 2 -> 11 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 2 , 13 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 3 -> 11 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 3 , 13 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 4 -> 11 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 4 , 13 6 8 6 8 6 8 5 5 6 0 0 8 5 6 0 8 7 2 1 2 0 8 7 3 12 -> 11 0 0 1 4 7 2 1 4 6 1 2 0 0 8 7 4 5 6 1 3 4 5 7 3 3 3 12 , 8 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 2 -> 1 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 2 , 8 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 3 -> 1 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 3 , 8 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 4 -> 1 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 4 , 8 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 12 -> 1 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 12 , 4 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 2 -> 3 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 2 , 4 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 3 -> 3 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 3 , 4 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 4 -> 3 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 4 , 4 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 12 -> 3 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 12 , 5 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 2 -> 7 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 2 , 5 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 3 -> 7 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 3 , 5 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 4 -> 7 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 4 , 5 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 12 -> 7 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 12 , 13 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 2 -> 14 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 2 , 13 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 3 -> 14 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 3 , 13 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 4 -> 14 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 4 , 13 6 8 5 7 4 6 0 1 2 1 2 1 2 0 0 8 7 3 2 0 1 3 4 7 12 -> 14 2 0 8 7 3 3 2 0 1 3 3 4 7 3 2 1 2 0 8 5 5 5 7 3 3 12 , 0 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 2 -> 1 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 2 , 0 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 3 -> 1 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 3 , 0 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 4 -> 1 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 4 , 0 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 12 -> 1 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 12 , 2 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 2 -> 3 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 2 , 2 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 3 -> 3 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 3 , 2 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 4 -> 3 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 4 , 2 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 12 -> 3 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 12 , 6 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 2 -> 7 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 2 , 6 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 3 -> 7 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 3 , 6 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 4 -> 7 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 4 , 6 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 12 -> 7 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 12 , 11 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 2 -> 14 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 2 , 11 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 3 -> 14 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 3 , 11 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 4 -> 14 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 4 , 11 8 7 4 7 3 4 7 4 7 2 8 7 2 0 1 3 4 5 5 6 0 8 5 7 12 -> 14 3 3 4 5 6 0 8 6 1 4 6 1 4 5 5 7 3 4 6 8 6 1 4 7 12 , 1 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 6 -> 1 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 2 , 1 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 7 -> 1 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 3 , 1 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 5 -> 1 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 4 , 1 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 10 -> 1 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 12 , 3 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 6 -> 3 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 2 , 3 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 7 -> 3 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 3 , 3 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 5 -> 3 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 4 , 3 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 10 -> 3 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 12 , 7 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 6 -> 7 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 2 1 3 3 4 7 2 8 6 1 2 , 7 4 6 8 6 1 4 6 0 0 0 1 2 0 1 2 0 1 2 8 6 0 0 0 8 7 -> 7 2 1 3 3 4 5 5 5 6 1 2 8 5 5 6 1 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2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 10 -> 0 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 10 , 2 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 6 -> 2 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 6 , 2 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 7 -> 2 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 7 , 2 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 5 -> 2 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 5 , 2 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 10 -> 2 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 10 , 6 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 6 -> 6 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 6 , 6 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 7 -> 6 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 7 , 6 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 5 -> 6 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 5 , 6 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 10 -> 6 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 10 , 11 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 6 -> 11 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 6 , 11 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 7 -> 11 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 7 , 11 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 5 -> 11 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 5 , 11 8 5 7 2 0 1 2 0 1 4 6 8 6 0 1 2 1 4 5 5 6 0 1 4 5 7 2 8 10 -> 11 8 5 6 1 4 7 3 3 2 0 8 5 7 3 4 6 0 1 2 1 4 5 6 8 5 7 2 0 8 10 , 8 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 6 -> 0 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 6 , 8 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 7 -> 0 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 7 , 8 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 5 -> 0 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 5 , 8 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 10 -> 0 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 10 , 4 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 6 -> 2 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 6 , 4 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 7 -> 2 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 7 , 4 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 5 -> 2 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 5 , 4 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 10 -> 2 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 10 , 5 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 6 -> 6 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 6 , 5 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 7 -> 6 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 7 , 5 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 5 -> 6 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 5 , 5 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 10 -> 6 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 10 , 13 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 6 -> 11 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 6 , 13 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 7 -> 11 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 7 , 13 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 5 -> 11 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 5 , 13 6 0 1 4 6 0 0 8 5 5 7 4 5 6 0 1 2 0 8 7 4 7 2 1 2 1 4 5 10 -> 11 8 7 3 2 8 5 5 7 3 2 8 5 6 0 1 4 6 8 6 1 3 4 5 7 3 3 4 6 8 10 , 1 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 2 -> 1 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 2 , 1 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 3 -> 1 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 3 , 1 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 4 -> 1 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 4 , 1 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 12 -> 1 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 12 , 3 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 2 -> 3 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 2 , 3 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 3 -> 3 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 3 , 3 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 4 -> 3 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 4 , 3 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 12 -> 3 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 12 , 7 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 2 -> 7 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 2 , 7 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 3 -> 7 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 3 , 7 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 4 -> 7 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 4 , 7 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 12 -> 7 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 12 , 14 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 2 -> 14 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 2 , 14 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 3 -> 14 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 3 , 14 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 4 -> 14 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 4 , 14 3 2 8 5 5 6 0 8 5 7 4 7 4 6 0 0 8 7 2 0 8 5 6 8 7 3 2 1 3 12 -> 14 3 2 8 5 5 6 8 6 0 0 8 6 8 6 0 8 6 0 1 3 4 5 7 4 7 3 4 7 3 12 } 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 0 | | 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 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 1->0, 4->1, 7->2, 3->3, 2->4, 8->5, 0->6, 5->7, 6->8, 14->9, 12->10, 13->11, 10->12, 9->13 }, it remains to prove termination of the 102-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 9 1 2 3 4 5 2 4 5 -> 9 4 0 3 1 7 8 0 1 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 11 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 9 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 11 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 9 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 11 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 9 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 11 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 9 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 11 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 9 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 11 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 9 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 11 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 9 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 11 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 9 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 12 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 12 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 12 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 12 , 11 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 9 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 11 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 9 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 11 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 9 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 11 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 12 -> 9 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 12 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 13 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 13 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 13 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 13 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 13 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 13 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 13 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 13 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 11 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 9 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 11 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 9 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 13 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 13 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 13 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 13 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 13 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 13 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 13 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 13 } 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 0 | | 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 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 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, 12->11, 13->12, 11->13 }, it remains to prove termination of the 88-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 9 1 2 3 4 5 2 4 5 -> 9 4 0 3 1 7 8 0 1 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 87-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 86-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 85-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 84-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 83-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 82-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 81-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 80-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 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| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 79-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 78-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 77-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 29: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 76-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 75-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 74-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 73-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 72-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 0 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 0 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 71-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 44: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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70-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 10 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 10 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 44: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 69-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 11 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 11 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 12 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 12 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 13 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 13 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 13 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 13 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 12 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 12 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 13 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 13 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 46: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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, 12->11, 13->12 }, it remains to prove termination of the 68-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 67-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 9 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 9 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 66-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 65-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 47: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 64-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 47: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 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0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 63-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 5 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 51: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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| 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 62-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 10 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 10 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 11 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 11 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 12 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 12 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 12 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 12 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 11 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 11 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 12 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 12 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 11->10, 12->11, 10->12 }, it remains to prove termination of the 61-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 53: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 60-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 53: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 59-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 5 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 5 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type 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0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 58-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 11 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 11 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 57-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 5 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 0 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 29: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 56-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 55-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 47: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 54-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 53-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 9 1 2 3 4 5 2 4 6 -> 9 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 10 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 10 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 11 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 11 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 12 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 12 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 10 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 10 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 11 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 11 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 10->9, 11->10, 12->11 }, it remains to prove termination of the 52-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 51-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 50-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 16: 0 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 49-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 2 1 2 3 4 5 2 4 5 -> 2 4 0 3 1 7 8 0 1 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 30: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 48-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 0 1 2 3 4 5 2 4 5 -> 0 4 0 3 1 7 8 0 1 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 18: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 47-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 9 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 9 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 46-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 5 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 5 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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| | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 45-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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| | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 44-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 5 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 5 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 43-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 9 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 9 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 10 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 10 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 11 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 11 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 10 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 10 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 10->9, 11->10 }, it remains to prove termination of the 42-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 6 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 6 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 41-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 5 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 1 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 48: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 40-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 10 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 10 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 29: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 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0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 39-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 38-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 44: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 37-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 3 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 3 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 44: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 36-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 35-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 8 6 0 4 0 4 5 2 3 4 0 4 6 6 5 7 2 1 8 5 7 7 7 8 0 4 6 -> 2 1 8 5 2 1 7 8 0 1 2 1 2 1 8 0 4 6 6 6 5 7 7 8 5 2 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 51: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 34-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 8 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 8 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 33-rule system { 0 1 2 3 4 5 2 4 6 -> 0 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 6 -> 3 4 0 3 1 7 8 0 4 , 3 1 2 3 4 5 2 4 5 -> 3 4 0 3 1 7 8 0 1 , 2 1 2 3 4 5 2 4 6 -> 2 4 0 3 1 7 8 0 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 3 3 4 5 2 3 1 2 3 4 5 8 6 6 5 -> 3 3 3 3 4 5 2 1 7 8 5 8 5 2 3 1 , 2 3 4 5 2 3 1 2 3 4 5 8 6 6 6 -> 2 3 3 3 4 5 2 1 7 8 5 8 5 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 5 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 0 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 4 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 4 , 7 8 5 7 7 8 5 8 5 2 3 3 4 5 7 2 3 1 8 0 1 -> 2 4 6 6 0 1 8 5 7 2 3 3 3 1 7 2 1 2 1 2 3 1 , 5 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 0 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 4 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 4 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 3 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 3 , 7 2 1 8 5 7 8 0 3 4 5 7 7 7 7 2 3 4 0 1 2 3 1 -> 2 1 2 3 4 6 5 7 2 4 6 5 8 0 4 0 4 5 8 0 3 3 3 1 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 5 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 0 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 2 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 2 , 7 8 0 3 4 6 5 8 6 0 3 1 8 0 4 5 8 0 1 7 2 1 7 -> 2 3 3 3 1 8 5 8 5 8 5 8 6 5 2 4 6 6 5 8 5 7 7 7 , 5 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 5 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 1 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 7 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 7 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 9 8 5 8 6 6 6 6 0 1 7 2 4 0 3 1 8 0 3 4 6 5 8 0 -> 9 8 6 6 6 6 0 4 5 2 1 8 0 4 6 5 7 7 8 0 3 3 4 0 , 1 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 1 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 7 7 8 0 3 3 4 6 6 0 1 2 1 7 2 3 4 5 8 0 1 8 0 4 6 -> 7 2 1 8 0 4 5 7 7 8 6 5 2 4 5 7 8 6 5 7 2 3 3 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 4 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 4 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 3 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 3 , 3 1 2 3 1 2 1 2 3 1 8 6 6 5 2 4 5 8 0 3 4 0 1 7 7 8 0 1 -> 1 7 8 6 6 0 3 3 1 7 7 7 2 4 6 0 4 5 7 7 2 3 1 2 4 0 3 3 1 , 5 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 5 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 6 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 6 , 1 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 1 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 7 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 7 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 , 9 8 5 8 5 7 8 6 6 6 0 4 0 1 2 4 5 7 2 4 5 8 5 8 6 6 0 4 6 0 -> 9 7 2 1 8 6 5 8 6 6 6 6 6 6 0 4 5 7 2 4 5 7 2 4 6 5 8 0 4 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 3->0, 1->1, 2->2, 4->3, 5->4, 6->5, 0->6, 7->7, 8->8, 9->9 }, it remains to prove termination of the 15-rule system { 0 1 2 0 3 4 2 3 5 -> 0 3 6 0 1 7 8 6 3 , 0 1 2 0 3 4 2 3 4 -> 0 3 6 0 1 7 8 6 1 , 0 0 3 4 2 0 1 2 0 3 4 8 5 5 5 -> 0 0 0 0 3 4 2 1 7 8 4 8 4 2 0 3 , 2 0 3 4 2 0 1 2 0 3 4 8 5 5 5 -> 2 0 0 0 3 4 2 1 7 8 4 8 4 2 0 3 , 7 8 4 7 7 8 4 8 4 2 0 0 3 4 7 2 0 1 8 6 3 -> 2 3 5 5 6 1 8 4 7 2 0 0 0 1 7 2 1 2 1 2 0 3 , 4 8 4 8 5 5 5 5 6 1 7 2 3 6 0 1 8 6 0 3 5 4 8 6 -> 4 8 5 5 5 5 6 3 4 2 1 8 6 3 5 4 7 7 8 6 0 0 3 6 , 1 8 4 8 5 5 5 5 6 1 7 2 3 6 0 1 8 6 0 3 5 4 8 6 -> 1 8 5 5 5 5 6 3 4 2 1 8 6 3 5 4 7 7 8 6 0 0 3 6 , 7 8 4 8 5 5 5 5 6 1 7 2 3 6 0 1 8 6 0 3 5 4 8 6 -> 7 8 5 5 5 5 6 3 4 2 1 8 6 3 5 4 7 7 8 6 0 0 3 6 , 9 8 4 8 5 5 5 5 6 1 7 2 3 6 0 1 8 6 0 3 5 4 8 6 -> 9 8 5 5 5 5 6 3 4 2 1 8 6 3 5 4 7 7 8 6 0 0 3 6 , 0 1 2 0 1 2 1 2 0 1 8 5 5 4 2 3 4 8 6 0 3 6 1 7 7 8 6 3 -> 1 7 8 5 5 6 0 0 1 7 7 7 2 3 5 6 3 4 7 7 2 0 1 2 3 6 0 0 3 , 4 8 4 8 4 7 8 5 5 5 6 3 6 1 2 3 4 7 2 3 4 8 4 8 5 5 6 3 5 6 -> 4 7 2 1 8 5 4 8 5 5 5 5 5 5 6 3 4 7 2 3 4 7 2 3 5 4 8 6 3 6 , 1 8 4 8 4 7 8 5 5 5 6 3 6 1 2 3 4 7 2 3 4 8 4 8 5 5 6 3 5 5 -> 1 7 2 1 8 5 4 8 5 5 5 5 5 5 6 3 4 7 2 3 4 7 2 3 5 4 8 6 3 5 , 1 8 4 8 4 7 8 5 5 5 6 3 6 1 2 3 4 7 2 3 4 8 4 8 5 5 6 3 5 6 -> 1 7 2 1 8 5 4 8 5 5 5 5 5 5 6 3 4 7 2 3 4 7 2 3 5 4 8 6 3 6 , 7 8 4 8 4 7 8 5 5 5 6 3 6 1 2 3 4 7 2 3 4 8 4 8 5 5 6 3 5 6 -> 7 7 2 1 8 5 4 8 5 5 5 5 5 5 6 3 4 7 2 3 4 7 2 3 5 4 8 6 3 6 , 9 8 4 8 4 7 8 5 5 5 6 3 6 1 2 3 4 7 2 3 4 8 4 8 5 5 6 3 5 6 -> 9 7 2 1 8 5 4 8 5 5 5 5 5 5 6 3 4 7 2 3 4 7 2 3 5 4 8 6 3 6 } 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 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.