YES After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 32-rule system { 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 , 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 0 1 0 0 1 0 1 1 1 1 1 1 1 1 0 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 , 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 , 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 0 , 0 0 1 0 1 0 1 1 0 0 0 0 1 1 1 1 0 1 1 1 0 1 1 1 1 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 1 0 0 1 0 0 1 0 1 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1 1 1 0 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 1 0 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 0 1 0 1 0 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 -> 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 0 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 0 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 0 0 1 0 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 0 0 1 0 0 1 1 0 0 1 1 0 0 0 1 1 0 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 1 0 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 0 1 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 0 1 0 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 0 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 , 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 0 0 1 0 0 0 1 1 0 1 1 0 1 0 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 -> 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 0 1 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 1 1 0 0 -> 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 1 0 1 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 0 1 0 0 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 1 0 0 0 1 1 1 0 1 0 1 1 0 1 0 0 1 0 0 1 1 0 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 1 1 0 -> 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 0 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 0 1 1 1 0 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 0 0 , 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 1 0 0 0 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 1 0 0 1 1 1 0 1 0 1 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 , 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 0 1 1 0 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 1 0 1 1 1 0 0 1 1 0 1 1 , 1 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1 1 0 0 1 1 1 1 1 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 1 1 1 0 1 1 0 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 0 0 0 0 , 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 1 0 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 , 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 0 0 0 1 0 0 0 0 1 , 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 -> 1 1 0 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 1 1 1 0 0 0 1 1 0 1 0 0 0 0 0 1 1 0 1 1 0 1 1 1 0 0 0 0 0 1 1 1 0 0 1 1 0 0 0 1 1 0 1 0 1 1 1 , 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 0 -> 0 0 1 1 1 1 1 0 1 1 1 1 0 1 0 1 1 0 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 1 1 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 , 1 1 0 0 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 0 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 1 0 0 0 0 1 1 0 1 1 0 0 0 1 1 1 0 0 1 1 1 1 1 1 -> 0 0 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 0 1 0 0 1 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 1 1 1 1 1 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 } The system was reversed. After renaming modulo { 1->0, 0->1 }, it remains to prove termination of the 32-rule system { 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 -> 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 1 0 0 0 0 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 -> 1 0 0 1 1 1 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 -> 0 1 1 0 1 0 1 0 1 1 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 -> 1 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 0 0 1 0 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 1 1 1 1 0 0 0 0 1 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1 0 1 0 1 1 -> 1 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 1 0 1 0 1 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 , 1 1 1 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 1 1 0 1 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 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1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 0 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 0 1 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 -> 1 0 1 0 0 1 0 0 1 1 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 0 1 0 1 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 0 1 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 , 1 1 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 , 1 1 0 1 0 0 1 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 0 1 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 1 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 1 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 1 0 0 1 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 , 1 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 1 1 1 0 1 1 1 0 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 0 0 0 1 0 1 0 0 0 1 1 0 1 0 1 0 1 0 1 1 0 1 1 1 0 0 1 0 1 1 1 1 0 1 0 0 0 1 0 0 1 1 1 0 0 0 0 1 0 1 1 1 0 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 -> 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 1 1 0 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 1 0 1 0 1 1 0 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 -> 0 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 0 1 0 0 0 0 0 0 0 1 1 0 0 1 0 0 1 0 1 0 0 1 0 0 0 0 1 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 0 1 1 0 -> 1 1 1 1 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 0 1 0 0 1 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 1 1 1 0 1 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 1 0 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 -> 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 -> 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 1 1 , 0 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 -> 0 0 0 1 0 1 0 0 1 1 1 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1 1 1 1 1 0 1 0 0 1 1 1 0 0 0 1 0 0 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 0 1 0 0 1 1 0 0 0 1 1 1 0 0 , 1 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 -> 0 1 1 1 1 1 1 0 0 0 1 1 1 1 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 0 0 1 1 0 1 1 1 0 0 0 1 0 1 0 0 1 1 0 0 0 0 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 1 1 , 0 0 0 0 0 0 1 1 0 0 0 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 1 1 1 1 1 0 0 0 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 1 0 0 -> 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 1 1 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 1 1 1 1 0 0 1 0 0 1 1 0 0 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, (1,3)->4, (2,0)->5, (2,1)->6, (0,3)->7 }, it remains to prove termination of the 288-rule system { 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 0 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 0 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 0 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 2 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 2 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 2 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 5 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 5 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 5 1 3 3 3 3 3 2 1 2 0 0 1 3 3 3 2 0 1 2 1 2 1 2 0 0 0 1 2 1 2 1 3 2 1 3 2 0 1 3 2 1 2 1 2 1 2 0 1 3 3 3 2 1 3 2 1 2 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 1 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 1 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 1 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 3 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 3 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 3 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 6 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 6 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 1 2 0 0 0 0 0 0 0 1 2 1 3 2 1 2 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 6 2 0 1 3 3 2 0 1 3 2 0 1 3 2 1 3 2 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 0 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 0 1 3 2 1 2 1 2 1 3 2 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 0 1 3 2 1 2 1 2 1 3 2 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 4 -> 0 1 3 2 1 2 1 2 1 3 2 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 2 -> 2 1 3 2 1 2 1 2 1 3 2 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 1 2 0 0 1 2 0 0 0 1 3 3 3 2 0 1 2 1 2 1 3 3 -> 2 1 3 2 1 2 1 2 1 3 2 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 0 0 0 1 2 0 0 0 1 2 0 1 3 3 2 0 1 2 0 0 0 0 1 2 1 3 2 1 3 2 0 1 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 0 1 3 3 3 3 3 3 2 0 0 0 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2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 1 -> 1 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 7 -> 1 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 0 -> 3 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 1 -> 3 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 7 -> 3 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 0 -> 6 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 1 -> 6 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 0 1 2 0 1 3 3 2 0 1 2 1 3 2 0 1 3 2 1 2 0 0 0 0 0 0 1 3 2 0 1 2 0 1 2 1 2 0 1 2 0 0 0 1 2 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 2 1 3 2 0 1 3 3 3 3 2 0 1 2 0 1 3 2 7 -> 6 3 3 3 3 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 2 1 2 0 1 2 1 3 2 1 3 2 0 1 2 0 0 1 2 1 2 0 1 2 1 3 3 3 2 1 3 3 2 1 3 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 0 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 1 2 0 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 0 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 2 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 5 1 3 3 3 2 1 3 3 2 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 0 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 0 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 , 0 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 0 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 2 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 2 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 , 2 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 2 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 5 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 0 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 5 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 1 , 5 0 1 2 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 5 0 0 1 2 1 2 0 1 3 3 2 0 1 3 2 0 0 1 3 3 3 3 2 0 0 1 2 0 1 2 0 1 3 3 3 3 2 1 2 0 1 3 3 2 0 0 1 2 0 0 0 1 3 3 3 2 1 2 1 2 0 1 3 3 3 3 3 2 1 2 0 1 3 2 0 0 1 3 3 2 0 7 , 1 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 0 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 2 , 1 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 0 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 3 , 1 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 0 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 4 , 3 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 2 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 2 , 3 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 2 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 3 , 3 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 2 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 4 , 6 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 5 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 2 , 6 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 5 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 3 , 6 2 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 5 1 3 3 3 3 3 2 0 0 1 3 3 3 3 2 1 3 2 1 3 3 2 0 1 3 3 3 2 0 0 1 3 2 1 3 3 2 0 0 1 2 1 2 0 1 3 2 0 0 0 1 3 2 1 3 3 2 0 0 0 1 3 2 1 2 0 1 2 1 2 0 0 0 1 2 0 0 0 0 1 3 4 , 0 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 0 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 0 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 0 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 0 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 0 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 2 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 2 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 2 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 2 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 2 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 2 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 , 5 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 0 -> 5 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 2 , 5 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 1 -> 5 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 3 , 5 0 0 0 0 0 1 3 2 0 0 1 3 3 2 0 1 2 0 1 3 3 3 2 0 0 0 1 3 3 2 0 0 0 0 0 0 0 1 3 3 2 0 0 1 2 0 1 3 3 3 3 2 0 0 1 3 2 0 0 0 0 0 1 2 0 1 3 3 2 0 0 1 3 2 1 2 1 3 2 0 7 -> 5 0 0 0 0 0 1 2 0 0 0 1 2 0 0 0 0 1 3 2 1 2 0 0 0 0 1 2 1 2 1 2 0 1 3 3 3 3 3 3 3 2 0 1 3 3 3 3 2 1 3 2 1 3 2 1 2 0 0 1 2 1 2 1 3 2 1 3 3 3 3 2 0 1 2 0 1 3 2 0 1 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.