YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 72-rule system { 0 0 0 0 1 2 1 2 2 1 1 2 0 -> 0 0 0 0 1 2 2 2 2 2 2 2 2 2 1 2 0 , 0 0 0 2 1 0 2 1 1 2 0 2 1 -> 0 0 0 1 0 1 2 2 2 2 2 2 2 2 1 2 2 , 0 0 0 2 2 1 0 2 2 0 1 1 0 -> 0 1 2 0 0 0 0 0 0 0 0 0 0 0 2 1 1 , 0 0 1 0 1 0 0 2 0 2 1 0 1 -> 0 0 0 0 0 1 2 1 0 0 0 0 1 2 2 2 0 , 0 0 1 1 1 0 2 1 2 0 2 1 2 -> 0 0 0 1 0 0 0 0 0 1 2 2 0 2 1 2 1 , 0 0 2 0 1 1 0 2 1 1 0 2 2 -> 0 0 0 2 0 2 2 2 2 2 2 1 0 2 2 0 2 , 0 0 2 1 1 2 1 0 2 2 1 0 0 -> 1 0 0 0 0 0 1 2 2 2 0 2 2 2 2 2 0 , 0 0 2 2 0 0 2 2 1 0 2 0 0 -> 2 0 1 0 0 0 0 0 0 0 0 0 1 2 2 0 0 , 0 1 0 0 1 1 1 1 2 1 0 1 1 -> 0 1 0 1 1 0 0 0 2 2 0 2 2 2 2 0 0 , 0 1 0 1 0 1 1 1 1 0 0 1 2 -> 0 0 2 2 2 2 2 0 2 1 0 0 0 1 2 2 2 , 0 1 0 1 1 0 2 0 2 2 1 0 2 -> 0 2 2 0 2 2 2 2 0 2 2 2 2 0 2 2 2 , 0 1 0 1 1 1 2 2 2 1 1 0 2 -> 0 0 1 0 0 0 0 2 1 0 0 0 0 0 0 1 0 , 0 1 1 0 1 2 2 0 1 1 0 1 0 -> 0 0 0 0 0 0 1 2 2 1 0 0 0 1 2 0 0 , 0 1 1 0 2 1 0 0 1 2 1 1 2 -> 1 0 0 1 0 1 2 0 2 2 2 2 2 2 2 2 2 , 0 1 1 2 2 2 1 1 2 2 2 2 1 -> 1 2 2 2 2 0 2 2 2 0 2 2 2 2 2 0 2 , 0 1 2 0 0 1 0 0 1 2 1 2 1 -> 0 0 1 2 0 2 2 2 2 2 2 2 0 1 0 0 2 , 0 1 2 0 1 2 2 2 1 1 2 0 2 -> 0 0 0 0 0 0 0 0 0 1 2 0 2 0 0 2 2 , 0 1 2 2 0 2 0 2 1 0 1 1 1 -> 0 0 1 2 2 0 2 0 0 0 0 0 0 0 0 0 1 , 0 2 0 1 0 2 2 1 0 0 2 2 0 -> 0 0 0 0 1 2 0 0 0 0 0 0 0 0 1 2 0 , 0 2 0 1 1 0 2 2 1 0 2 2 0 -> 2 0 0 0 2 2 2 2 2 2 2 2 1 0 0 0 1 , 0 2 0 1 1 1 2 1 0 2 0 1 1 -> 0 2 0 2 2 2 0 1 0 0 1 0 0 0 0 1 0 , 0 2 1 0 1 2 0 1 0 0 0 1 1 -> 2 1 2 2 2 2 2 2 2 2 0 2 2 0 2 1 0 , 0 2 1 0 2 1 2 2 2 1 0 0 2 -> 0 0 0 0 0 0 0 0 0 0 0 1 0 2 0 1 2 , 0 2 1 2 1 2 2 0 2 0 1 1 0 -> 2 0 1 0 0 0 1 2 0 0 0 0 0 0 0 2 0 , 1 0 0 0 1 1 1 1 0 1 0 0 1 -> 2 2 0 1 0 0 0 0 0 0 0 0 0 0 1 2 0 , 1 0 0 1 0 2 1 2 1 0 1 2 0 -> 0 0 2 0 0 0 0 0 1 0 0 0 0 0 2 2 0 , 1 0 0 2 0 0 2 2 1 2 1 1 1 -> 0 1 0 2 1 0 0 0 0 0 0 1 2 0 2 0 0 , 1 0 0 2 0 1 2 2 1 0 0 1 2 -> 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 , 1 0 0 2 1 1 0 1 2 0 0 2 1 -> 1 0 0 2 0 0 0 1 2 2 2 0 2 2 2 0 1 , 1 0 0 2 2 0 0 1 1 0 2 1 1 -> 1 2 0 2 2 2 2 2 2 0 2 2 0 2 0 0 1 , 1 0 1 2 1 2 0 2 0 1 2 1 0 -> 2 0 0 1 0 0 0 0 0 1 2 2 2 2 1 2 0 , 1 0 2 0 1 1 1 0 0 0 1 0 1 -> 1 0 0 0 0 1 0 0 0 0 0 1 2 2 1 2 0 , 1 0 2 0 2 0 1 0 1 1 1 1 1 -> 1 1 0 2 2 2 2 2 2 0 2 0 2 1 0 0 1 , 1 0 2 1 1 0 0 2 1 0 2 0 1 -> 0 1 0 0 0 0 0 0 0 0 1 1 2 2 1 1 1 , 1 0 2 1 2 1 0 1 0 0 2 1 0 -> 2 1 0 0 0 0 0 1 2 2 2 1 0 0 2 0 0 , 1 0 2 1 2 1 1 1 0 2 0 1 2 -> 1 1 0 0 0 0 1 0 0 0 0 2 0 0 2 0 2 , 1 0 2 1 2 2 0 0 0 1 2 2 0 -> 0 0 2 2 2 2 2 2 2 2 2 2 2 0 1 0 2 , 1 1 0 0 1 0 1 1 2 1 0 1 2 -> 1 0 0 0 0 0 0 1 2 2 0 0 1 0 2 0 2 , 1 1 0 1 1 0 2 2 1 0 2 0 0 -> 0 1 0 0 0 0 1 2 2 2 2 1 2 0 0 0 1 , 1 1 0 2 0 1 0 2 1 0 2 1 2 -> 1 2 2 2 2 2 2 1 1 2 2 2 2 2 2 1 2 , 1 1 0 2 0 1 1 0 0 2 2 1 2 -> 0 2 1 0 0 0 0 0 1 2 2 0 0 0 0 0 2 , 1 1 1 0 0 0 1 1 0 1 1 0 2 -> 0 0 0 2 2 2 2 2 0 2 2 0 2 2 2 1 2 , 1 1 1 0 0 2 0 2 1 0 2 0 2 -> 1 0 2 0 1 2 2 2 2 0 2 2 0 2 2 2 2 , 1 1 1 2 2 2 2 1 0 0 2 1 2 -> 0 0 0 0 0 0 1 0 0 0 0 1 2 2 1 1 2 , 1 1 2 0 2 0 2 0 1 0 0 2 0 -> 2 0 1 0 0 0 0 1 2 2 2 0 2 2 2 2 1 , 1 1 2 1 0 0 0 1 0 2 0 2 2 -> 1 0 2 1 0 0 0 0 0 0 0 1 2 2 2 2 2 , 1 1 2 2 0 0 2 0 1 1 1 1 0 -> 2 0 0 0 0 1 2 1 0 1 2 2 2 2 1 0 0 , 1 2 0 0 1 1 2 2 1 2 2 0 0 -> 1 0 2 0 2 0 0 0 0 0 0 0 0 0 1 2 2 , 1 2 0 0 2 1 0 2 2 2 0 0 1 -> 0 0 0 0 0 1 2 2 2 0 2 0 2 2 1 0 1 , 1 2 0 1 0 0 1 1 1 1 0 1 1 -> 0 0 0 0 2 0 1 0 0 0 0 0 1 2 1 1 0 , 1 2 0 1 2 1 2 2 1 0 1 0 0 -> 1 0 0 0 1 2 0 2 2 2 2 2 1 0 1 0 0 , 1 2 1 1 2 0 0 2 2 1 0 0 1 -> 1 1 0 0 0 0 0 0 1 0 0 1 2 2 2 2 0 , 1 2 2 0 0 1 2 0 2 1 0 0 1 -> 0 1 0 2 2 2 2 2 0 2 2 2 2 2 2 2 2 , 1 2 2 0 1 2 2 2 0 1 2 1 1 -> 0 0 0 2 2 2 2 2 0 2 2 1 2 0 0 0 1 , 2 0 0 0 0 1 1 2 0 0 1 0 2 -> 0 1 0 0 0 1 2 2 2 2 0 2 0 2 2 2 2 , 2 0 0 2 1 2 1 0 1 0 1 1 1 -> 1 0 0 0 0 0 0 0 1 1 2 2 2 0 2 0 0 , 2 0 1 0 1 0 0 0 2 0 1 2 1 -> 2 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 , 2 0 2 0 1 1 0 0 2 1 1 0 2 -> 2 2 0 0 0 1 0 0 0 0 1 0 0 0 1 0 2 , 2 0 2 2 0 2 2 0 2 1 2 0 1 -> 2 2 2 2 0 0 0 0 0 0 0 0 0 1 2 2 0 , 2 1 0 2 1 2 1 2 1 2 2 2 1 -> 2 1 0 0 0 1 2 0 2 0 0 0 0 0 1 2 1 , 2 1 1 2 1 1 2 0 1 0 1 0 2 -> 2 2 0 2 0 0 1 2 0 2 2 2 2 2 2 1 2 , 2 1 1 2 2 0 2 0 0 2 0 1 0 -> 2 0 1 0 1 2 2 2 2 2 2 2 0 2 2 0 0 , 2 1 2 0 0 2 2 0 2 0 1 2 2 -> 2 0 0 0 0 2 0 0 1 2 2 2 2 2 2 0 2 , 2 1 2 0 2 2 2 1 1 0 0 1 2 -> 1 2 2 0 0 2 2 2 2 2 0 2 2 2 2 2 2 , 2 1 2 1 0 1 0 0 2 1 2 2 0 -> 2 2 1 1 0 0 0 0 0 0 1 2 1 0 0 0 1 , 2 1 2 2 1 2 2 2 2 1 2 1 0 -> 2 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 , 2 2 0 0 1 2 1 0 2 2 1 0 0 -> 2 2 2 2 2 2 2 0 2 2 0 2 2 0 2 2 0 , 2 2 0 0 2 1 2 1 2 0 1 2 0 -> 2 2 2 2 2 2 0 1 0 0 0 0 1 0 0 2 1 , 2 2 0 2 2 0 1 1 2 1 0 1 0 -> 2 2 2 2 2 2 2 2 2 2 1 0 0 2 0 0 1 , 2 2 0 2 2 1 2 1 2 2 0 2 0 -> 2 2 2 2 0 2 2 2 0 2 2 0 1 0 0 0 1 , 2 2 1 0 2 1 1 2 2 0 1 0 1 -> 2 2 2 2 0 1 0 0 0 1 0 0 0 0 0 1 2 , 2 2 1 1 2 1 0 1 1 2 0 0 2 -> 2 2 2 0 0 0 0 1 2 0 0 0 2 2 2 2 2 } The system was reversed. After renaming modulo { 0->0, 2->1, 1->2 }, it remains to prove termination of the 72-rule system { 0 1 2 2 1 1 2 1 2 0 0 0 0 -> 0 1 2 1 1 1 1 1 1 1 1 1 2 0 0 0 0 , 2 1 0 1 2 2 1 0 2 1 0 0 0 -> 1 1 2 1 1 1 1 1 1 1 1 2 0 2 0 0 0 , 0 2 2 0 1 1 0 2 1 1 0 0 0 -> 2 2 1 0 0 0 0 0 0 0 0 0 0 0 1 2 0 , 2 0 2 1 0 1 0 0 2 0 2 0 0 -> 0 1 1 1 2 0 0 0 0 2 1 2 0 0 0 0 0 , 1 2 1 0 1 2 1 0 2 2 2 0 0 -> 2 1 2 1 0 1 1 2 0 0 0 0 0 2 0 0 0 , 1 1 0 2 2 1 0 2 2 0 1 0 0 -> 1 0 1 1 0 2 1 1 1 1 1 1 0 1 0 0 0 , 0 0 2 1 1 0 2 1 2 2 1 0 0 -> 0 1 1 1 1 1 0 1 1 1 2 0 0 0 0 0 2 , 0 0 1 0 2 1 1 0 0 1 1 0 0 -> 0 0 1 1 2 0 0 0 0 0 0 0 0 0 2 0 1 , 2 2 0 2 1 2 2 2 2 0 0 2 0 -> 0 0 1 1 1 1 0 1 1 0 0 0 2 2 0 2 0 , 1 2 0 0 2 2 2 2 0 2 0 2 0 -> 1 1 1 2 0 0 0 2 1 0 1 1 1 1 1 0 0 , 1 0 2 1 1 0 1 0 2 2 0 2 0 -> 1 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 0 , 1 0 2 2 1 1 1 2 2 2 0 2 0 -> 0 2 0 0 0 0 0 0 2 1 0 0 0 0 2 0 0 , 0 2 0 2 2 0 1 1 2 0 2 2 0 -> 0 0 1 2 0 0 0 2 1 1 2 0 0 0 0 0 0 , 1 2 2 1 2 0 0 2 1 0 2 2 0 -> 1 1 1 1 1 1 1 1 1 0 1 2 0 2 0 0 2 , 2 1 1 1 1 2 2 1 1 1 2 2 0 -> 1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 1 2 , 2 1 2 1 2 0 0 2 0 0 1 2 0 -> 1 0 0 2 0 1 1 1 1 1 1 1 0 1 2 0 0 , 1 0 1 2 2 1 1 1 2 0 1 2 0 -> 1 1 0 0 1 0 1 2 0 0 0 0 0 0 0 0 0 , 2 2 2 0 2 1 0 1 0 1 1 2 0 -> 2 0 0 0 0 0 0 0 0 0 1 0 1 1 2 0 0 , 0 1 1 0 0 2 1 1 0 2 0 1 0 -> 0 1 2 0 0 0 0 0 0 0 0 1 2 0 0 0 0 , 0 1 1 0 2 1 1 0 2 2 0 1 0 -> 2 0 0 0 2 1 1 1 1 1 1 1 1 0 0 0 1 , 2 2 0 1 0 2 1 2 2 2 0 1 0 -> 0 2 0 0 0 0 2 0 0 2 0 1 1 1 0 1 0 , 2 2 0 0 0 2 0 1 2 0 2 1 0 -> 0 2 1 0 1 1 0 1 1 1 1 1 1 1 1 2 1 , 1 0 0 2 1 1 1 2 1 0 2 1 0 -> 1 2 0 1 0 2 0 0 0 0 0 0 0 0 0 0 0 , 0 2 2 0 1 0 1 1 2 1 2 1 0 -> 0 1 0 0 0 0 0 0 0 1 2 0 0 0 2 0 1 , 2 0 0 2 0 2 2 2 2 0 0 0 2 -> 0 1 2 0 0 0 0 0 0 0 0 0 0 2 0 1 1 , 0 1 2 0 2 1 2 1 0 2 0 0 2 -> 0 1 1 0 0 0 0 0 2 0 0 0 0 0 1 0 0 , 2 2 2 1 2 1 1 0 0 1 0 0 2 -> 0 0 1 0 1 2 0 0 0 0 0 0 2 1 0 2 0 , 1 2 0 0 2 1 1 2 0 1 0 0 2 -> 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 , 2 1 0 0 1 2 0 2 2 1 0 0 2 -> 2 0 1 1 1 0 1 1 1 2 0 0 0 1 0 0 2 , 2 2 1 0 2 2 0 0 1 1 0 0 2 -> 2 0 0 1 0 1 1 0 1 1 1 1 1 1 0 1 2 , 0 2 1 2 0 1 0 1 2 1 2 0 2 -> 0 1 2 1 1 1 1 2 0 0 0 0 0 2 0 0 1 , 2 0 2 0 0 0 2 2 2 0 1 0 2 -> 0 1 2 1 1 2 0 0 0 0 0 2 0 0 0 0 2 , 2 2 2 2 2 0 2 0 1 0 1 0 2 -> 2 0 0 2 1 0 1 0 1 1 1 1 1 1 0 2 2 , 2 0 1 0 2 1 0 0 2 2 1 0 2 -> 2 2 2 1 1 2 2 0 0 0 0 0 0 0 0 2 0 , 0 2 1 0 0 2 0 2 1 2 1 0 2 -> 0 0 1 0 0 2 1 1 1 2 0 0 0 0 0 2 1 , 1 2 0 1 0 2 2 2 1 2 1 0 2 -> 1 0 1 0 0 1 0 0 0 0 2 0 0 0 0 2 2 , 0 1 1 2 0 0 0 1 1 2 1 0 2 -> 1 0 2 0 1 1 1 1 1 1 1 1 1 1 1 0 0 , 1 2 0 2 1 2 2 0 2 0 0 2 2 -> 1 0 1 0 2 0 0 1 1 2 0 0 0 0 0 0 2 , 0 0 1 0 2 1 1 0 2 2 0 2 2 -> 2 0 0 0 1 2 1 1 1 1 2 0 0 0 0 2 0 , 1 2 1 0 2 1 0 2 0 1 0 2 2 -> 1 2 1 1 1 1 1 1 2 2 1 1 1 1 1 1 2 , 1 2 1 1 0 0 2 2 0 1 0 2 2 -> 1 0 0 0 0 0 1 1 2 0 0 0 0 0 2 1 0 , 1 0 2 2 0 2 2 0 0 0 2 2 2 -> 1 2 1 1 1 0 1 1 0 1 1 1 1 1 0 0 0 , 1 0 1 0 2 1 0 1 0 0 2 2 2 -> 1 1 1 1 0 1 1 0 1 1 1 1 2 0 1 0 2 , 1 2 1 0 0 2 1 1 1 1 2 2 2 -> 1 2 2 1 1 2 0 0 0 0 2 0 0 0 0 0 0 , 0 1 0 0 2 0 1 0 1 0 1 2 2 -> 2 1 1 1 1 0 1 1 1 2 0 0 0 0 2 0 1 , 1 1 0 1 0 2 0 0 0 2 1 2 2 -> 1 1 1 1 1 2 0 0 0 0 0 0 0 2 1 0 2 , 0 2 2 2 2 0 1 0 0 1 1 2 2 -> 0 0 2 1 1 1 1 2 0 2 1 2 0 0 0 0 1 , 0 0 1 1 2 1 1 2 2 0 0 1 2 -> 1 1 2 0 0 0 0 0 0 0 0 0 1 0 1 0 2 , 2 0 0 1 1 1 0 2 1 0 0 1 2 -> 2 0 2 1 1 0 1 0 1 1 1 2 0 0 0 0 0 , 2 2 0 2 2 2 2 0 0 2 0 1 2 -> 0 2 2 1 2 0 0 0 0 0 2 0 1 0 0 0 0 , 0 0 2 0 2 1 1 2 1 2 0 1 2 -> 0 0 2 0 2 1 1 1 1 1 0 1 2 0 0 0 2 , 2 0 0 2 1 1 0 0 1 2 2 1 2 -> 0 1 1 1 1 2 0 0 2 0 0 0 0 0 0 2 2 , 2 0 0 2 1 0 1 2 0 0 1 1 2 -> 1 1 1 1 1 1 1 1 0 1 1 1 1 1 0 2 0 , 2 2 1 2 0 1 1 1 2 0 1 1 2 -> 2 0 0 0 1 2 1 1 0 1 1 1 1 1 0 0 0 , 1 0 2 0 0 1 2 2 0 0 0 0 1 -> 1 1 1 1 0 1 0 1 1 1 1 2 0 0 0 2 0 , 2 2 2 0 2 0 2 1 2 1 0 0 1 -> 0 0 1 0 1 1 1 2 2 0 0 0 0 0 0 0 2 , 2 1 2 0 1 0 0 0 2 0 2 0 1 -> 0 0 0 0 0 0 0 0 2 0 0 2 0 0 2 0 1 , 1 0 2 2 1 0 0 2 2 0 1 0 1 -> 1 0 2 0 0 0 2 0 0 0 0 2 0 0 0 1 1 , 2 0 1 2 1 0 1 1 0 1 1 0 1 -> 0 1 1 2 0 0 0 0 0 0 0 0 0 1 1 1 1 , 2 1 1 1 2 1 2 1 2 1 0 2 1 -> 2 1 2 0 0 0 0 0 1 0 1 2 0 0 0 2 1 , 1 0 2 0 2 0 1 2 2 1 2 2 1 -> 1 2 1 1 1 1 1 1 0 1 2 0 0 1 0 1 1 , 0 2 0 1 0 0 1 0 1 1 2 2 1 -> 0 0 1 1 0 1 1 1 1 1 1 1 2 0 2 0 1 , 1 1 2 0 1 0 1 1 0 0 1 2 1 -> 1 0 1 1 1 1 1 1 2 0 0 1 0 0 0 0 1 , 1 2 0 0 2 2 1 1 1 0 1 2 1 -> 1 1 1 1 1 1 0 1 1 1 1 1 0 0 1 1 2 , 0 1 1 2 1 0 0 2 0 2 1 2 1 -> 2 0 0 0 2 1 2 0 0 0 0 0 0 2 2 1 1 , 0 2 1 2 1 1 1 1 2 1 1 2 1 -> 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 1 , 0 0 2 1 1 0 2 1 2 0 0 1 1 -> 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 1 1 , 0 1 2 0 1 2 1 2 1 0 0 1 1 -> 2 1 0 0 2 0 0 0 0 2 0 1 1 1 1 1 1 , 0 2 0 2 1 2 2 0 1 1 0 1 1 -> 2 0 0 1 0 0 2 1 1 1 1 1 1 1 1 1 1 , 0 1 0 1 1 2 1 2 1 1 0 1 1 -> 2 0 0 0 2 0 1 1 0 1 1 1 0 1 1 1 1 , 2 0 2 0 1 1 2 2 1 0 2 1 1 -> 1 2 0 0 0 0 0 2 0 0 0 2 0 1 1 1 1 , 1 0 0 1 2 2 0 2 1 2 2 1 1 -> 1 1 1 1 1 0 0 0 1 2 0 0 0 0 1 1 1 } Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,2)->3, (2,1)->4, (1,1)->5, (2,0)->6, (0,2)->7, (0,4)->8, (1,0)->9, (3,0)->10, (3,2)->11, (3,1)->12, (2,4)->13, (1,4)->14 }, it remains to prove termination of the 1152-rule system { 0 1 2 3 4 5 2 4 2 6 0 0 0 0 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 0 , 0 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 0 1 2 3 4 5 2 4 2 6 0 0 0 7 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 7 , 0 1 2 3 4 5 2 4 2 6 0 0 0 8 -> 0 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 8 , 9 1 2 3 4 5 2 4 2 6 0 0 0 0 -> 9 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 0 , 9 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 9 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 9 1 2 3 4 5 2 4 2 6 0 0 0 7 -> 9 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 7 , 9 1 2 3 4 5 2 4 2 6 0 0 0 8 -> 9 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 8 , 6 1 2 3 4 5 2 4 2 6 0 0 0 0 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 0 , 6 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 6 1 2 3 4 5 2 4 2 6 0 0 0 7 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 7 , 6 1 2 3 4 5 2 4 2 6 0 0 0 8 -> 6 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 8 , 10 1 2 3 4 5 2 4 2 6 0 0 0 0 -> 10 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 0 , 10 1 2 3 4 5 2 4 2 6 0 0 0 1 -> 10 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 1 , 10 1 2 3 4 5 2 4 2 6 0 0 0 7 -> 10 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 7 , 10 1 2 3 4 5 2 4 2 6 0 0 0 8 -> 10 1 2 4 5 5 5 5 5 5 5 5 2 6 0 0 0 8 , 7 4 9 1 2 3 4 9 7 4 9 0 0 0 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 0 , 7 4 9 1 2 3 4 9 7 4 9 0 0 1 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 7 4 9 1 2 3 4 9 7 4 9 0 0 7 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 7 , 7 4 9 1 2 3 4 9 7 4 9 0 0 8 -> 1 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 8 , 2 4 9 1 2 3 4 9 7 4 9 0 0 0 -> 5 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 0 , 2 4 9 1 2 3 4 9 7 4 9 0 0 1 -> 5 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 2 4 9 1 2 3 4 9 7 4 9 0 0 7 -> 5 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 7 , 2 4 9 1 2 3 4 9 7 4 9 0 0 8 -> 5 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 8 , 3 4 9 1 2 3 4 9 7 4 9 0 0 0 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 0 , 3 4 9 1 2 3 4 9 7 4 9 0 0 1 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 3 4 9 1 2 3 4 9 7 4 9 0 0 7 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 7 , 3 4 9 1 2 3 4 9 7 4 9 0 0 8 -> 4 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 8 , 11 4 9 1 2 3 4 9 7 4 9 0 0 0 -> 12 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 0 , 11 4 9 1 2 3 4 9 7 4 9 0 0 1 -> 12 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 1 , 11 4 9 1 2 3 4 9 7 4 9 0 0 7 -> 12 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 7 , 11 4 9 1 2 3 4 9 7 4 9 0 0 8 -> 12 5 2 4 5 5 5 5 5 5 5 2 6 7 6 0 0 8 , 0 7 3 6 1 5 9 7 4 5 9 0 0 0 -> 7 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 0 , 0 7 3 6 1 5 9 7 4 5 9 0 0 1 -> 7 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 0 7 3 6 1 5 9 7 4 5 9 0 0 7 -> 7 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 7 , 0 7 3 6 1 5 9 7 4 5 9 0 0 8 -> 7 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 8 , 9 7 3 6 1 5 9 7 4 5 9 0 0 0 -> 2 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 0 , 9 7 3 6 1 5 9 7 4 5 9 0 0 1 -> 2 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 9 7 3 6 1 5 9 7 4 5 9 0 0 7 -> 2 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 7 , 9 7 3 6 1 5 9 7 4 5 9 0 0 8 -> 2 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 8 , 6 7 3 6 1 5 9 7 4 5 9 0 0 0 -> 3 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 0 , 6 7 3 6 1 5 9 7 4 5 9 0 0 1 -> 3 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 6 7 3 6 1 5 9 7 4 5 9 0 0 7 -> 3 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 7 , 6 7 3 6 1 5 9 7 4 5 9 0 0 8 -> 3 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 8 , 10 7 3 6 1 5 9 7 4 5 9 0 0 0 -> 11 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 0 , 10 7 3 6 1 5 9 7 4 5 9 0 0 1 -> 11 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 1 , 10 7 3 6 1 5 9 7 4 5 9 0 0 7 -> 11 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 7 , 10 7 3 6 1 5 9 7 4 5 9 0 0 8 -> 11 3 4 9 0 0 0 0 0 0 0 0 0 0 1 2 6 8 , 7 6 7 4 9 1 9 0 7 6 7 6 0 0 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 0 , 7 6 7 4 9 1 9 0 7 6 7 6 0 1 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 7 6 7 4 9 1 9 0 7 6 7 6 0 7 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 7 , 7 6 7 4 9 1 9 0 7 6 7 6 0 8 -> 0 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 8 , 2 6 7 4 9 1 9 0 7 6 7 6 0 0 -> 9 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 0 , 2 6 7 4 9 1 9 0 7 6 7 6 0 1 -> 9 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 2 6 7 4 9 1 9 0 7 6 7 6 0 7 -> 9 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 7 , 2 6 7 4 9 1 9 0 7 6 7 6 0 8 -> 9 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 8 , 3 6 7 4 9 1 9 0 7 6 7 6 0 0 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 0 , 3 6 7 4 9 1 9 0 7 6 7 6 0 1 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 3 6 7 4 9 1 9 0 7 6 7 6 0 7 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 7 , 3 6 7 4 9 1 9 0 7 6 7 6 0 8 -> 6 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 8 , 11 6 7 4 9 1 9 0 7 6 7 6 0 0 -> 10 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 0 , 11 6 7 4 9 1 9 0 7 6 7 6 0 1 -> 10 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 1 , 11 6 7 4 9 1 9 0 7 6 7 6 0 7 -> 10 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 7 , 11 6 7 4 9 1 9 0 7 6 7 6 0 8 -> 10 1 5 5 2 6 0 0 0 7 4 2 6 0 0 0 0 8 , 1 2 4 9 1 2 4 9 7 3 3 6 0 0 -> 7 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 0 , 1 2 4 9 1 2 4 9 7 3 3 6 0 1 -> 7 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 1 , 1 2 4 9 1 2 4 9 7 3 3 6 0 7 -> 7 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 7 , 1 2 4 9 1 2 4 9 7 3 3 6 0 8 -> 7 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 8 , 5 2 4 9 1 2 4 9 7 3 3 6 0 0 -> 2 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 0 , 5 2 4 9 1 2 4 9 7 3 3 6 0 1 -> 2 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 1 , 5 2 4 9 1 2 4 9 7 3 3 6 0 7 -> 2 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 7 , 5 2 4 9 1 2 4 9 7 3 3 6 0 8 -> 2 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 8 , 4 2 4 9 1 2 4 9 7 3 3 6 0 0 -> 3 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 0 , 4 2 4 9 1 2 4 9 7 3 3 6 0 1 -> 3 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 1 , 4 2 4 9 1 2 4 9 7 3 3 6 0 7 -> 3 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 7 , 4 2 4 9 1 2 4 9 7 3 3 6 0 8 -> 3 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 8 , 12 2 4 9 1 2 4 9 7 3 3 6 0 0 -> 11 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 0 , 12 2 4 9 1 2 4 9 7 3 3 6 0 1 -> 11 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 1 , 12 2 4 9 1 2 4 9 7 3 3 6 0 7 -> 11 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 7 , 12 2 4 9 1 2 4 9 7 3 3 6 0 8 -> 11 4 2 4 9 1 5 2 6 0 0 0 0 7 6 0 0 8 , 1 5 9 7 3 4 9 7 3 6 1 9 0 0 -> 1 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 0 , 1 5 9 7 3 4 9 7 3 6 1 9 0 1 -> 1 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 1 , 1 5 9 7 3 4 9 7 3 6 1 9 0 7 -> 1 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 7 , 1 5 9 7 3 4 9 7 3 6 1 9 0 8 -> 1 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 8 , 5 5 9 7 3 4 9 7 3 6 1 9 0 0 -> 5 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 0 , 5 5 9 7 3 4 9 7 3 6 1 9 0 1 -> 5 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 1 , 5 5 9 7 3 4 9 7 3 6 1 9 0 7 -> 5 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 7 , 5 5 9 7 3 4 9 7 3 6 1 9 0 8 -> 5 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 8 , 4 5 9 7 3 4 9 7 3 6 1 9 0 0 -> 4 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 0 , 4 5 9 7 3 4 9 7 3 6 1 9 0 1 -> 4 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 1 , 4 5 9 7 3 4 9 7 3 6 1 9 0 7 -> 4 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 7 , 4 5 9 7 3 4 9 7 3 6 1 9 0 8 -> 4 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 8 , 12 5 9 7 3 4 9 7 3 6 1 9 0 0 -> 12 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 0 , 12 5 9 7 3 4 9 7 3 6 1 9 0 1 -> 12 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 1 , 12 5 9 7 3 4 9 7 3 6 1 9 0 7 -> 12 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 7 , 12 5 9 7 3 4 9 7 3 6 1 9 0 8 -> 12 9 1 5 9 7 4 5 5 5 5 5 9 1 9 0 0 8 , 0 0 7 4 5 9 7 4 2 3 4 9 0 0 -> 0 1 5 5 5 5 9 1 5 5 2 6 0 0 0 0 7 6 , 0 0 7 4 5 9 7 4 2 3 4 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1 5 9 1 5 9 1 5 5 5 5 5 5 14 , 0 1 2 6 1 2 4 2 4 9 0 1 5 9 -> 7 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 9 , 0 1 2 6 1 2 4 2 4 9 0 1 5 5 -> 7 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 5 , 0 1 2 6 1 2 4 2 4 9 0 1 5 2 -> 7 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 2 , 0 1 2 6 1 2 4 2 4 9 0 1 5 14 -> 7 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 14 , 9 1 2 6 1 2 4 2 4 9 0 1 5 9 -> 2 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 9 , 9 1 2 6 1 2 4 2 4 9 0 1 5 5 -> 2 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 5 , 9 1 2 6 1 2 4 2 4 9 0 1 5 2 -> 2 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 2 , 9 1 2 6 1 2 4 2 4 9 0 1 5 14 -> 2 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 14 , 6 1 2 6 1 2 4 2 4 9 0 1 5 9 -> 3 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 9 , 6 1 2 6 1 2 4 2 4 9 0 1 5 5 -> 3 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 5 , 6 1 2 6 1 2 4 2 4 9 0 1 5 2 -> 3 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 2 , 6 1 2 6 1 2 4 2 4 9 0 1 5 14 -> 3 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 14 , 10 1 2 6 1 2 4 2 4 9 0 1 5 9 -> 11 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 9 , 10 1 2 6 1 2 4 2 4 9 0 1 5 5 -> 11 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 5 , 10 1 2 6 1 2 4 2 4 9 0 1 5 2 -> 11 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 2 , 10 1 2 6 1 2 4 2 4 9 0 1 5 14 -> 11 4 9 0 7 6 0 0 0 7 6 1 5 5 5 5 5 14 , 0 7 6 7 4 2 3 6 1 5 9 1 5 9 -> 7 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 9 , 0 7 6 7 4 2 3 6 1 5 9 1 5 5 -> 7 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 5 , 0 7 6 7 4 2 3 6 1 5 9 1 5 2 -> 7 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 2 , 0 7 6 7 4 2 3 6 1 5 9 1 5 14 -> 7 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 14 , 9 7 6 7 4 2 3 6 1 5 9 1 5 9 -> 2 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 9 , 9 7 6 7 4 2 3 6 1 5 9 1 5 5 -> 2 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 5 , 9 7 6 7 4 2 3 6 1 5 9 1 5 2 -> 2 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 2 , 9 7 6 7 4 2 3 6 1 5 9 1 5 14 -> 2 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 14 , 6 7 6 7 4 2 3 6 1 5 9 1 5 9 -> 3 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 9 , 6 7 6 7 4 2 3 6 1 5 9 1 5 5 -> 3 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 5 , 6 7 6 7 4 2 3 6 1 5 9 1 5 2 -> 3 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 2 , 6 7 6 7 4 2 3 6 1 5 9 1 5 14 -> 3 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 14 , 10 7 6 7 4 2 3 6 1 5 9 1 5 9 -> 11 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 9 , 10 7 6 7 4 2 3 6 1 5 9 1 5 5 -> 11 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 5 , 10 7 6 7 4 2 3 6 1 5 9 1 5 2 -> 11 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 2 , 10 7 6 7 4 2 3 6 1 5 9 1 5 14 -> 11 6 0 1 9 0 7 4 5 5 5 5 5 5 5 5 5 14 , 0 1 9 1 5 2 4 2 4 5 9 1 5 9 -> 7 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 9 , 0 1 9 1 5 2 4 2 4 5 9 1 5 5 -> 7 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 5 , 0 1 9 1 5 2 4 2 4 5 9 1 5 2 -> 7 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 2 , 0 1 9 1 5 2 4 2 4 5 9 1 5 14 -> 7 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 14 , 9 1 9 1 5 2 4 2 4 5 9 1 5 9 -> 2 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 9 , 9 1 9 1 5 2 4 2 4 5 9 1 5 5 -> 2 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 5 , 9 1 9 1 5 2 4 2 4 5 9 1 5 2 -> 2 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 2 , 9 1 9 1 5 2 4 2 4 5 9 1 5 14 -> 2 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 14 , 6 1 9 1 5 2 4 2 4 5 9 1 5 9 -> 3 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 9 , 6 1 9 1 5 2 4 2 4 5 9 1 5 5 -> 3 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 5 , 6 1 9 1 5 2 4 2 4 5 9 1 5 2 -> 3 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 2 , 6 1 9 1 5 2 4 2 4 5 9 1 5 14 -> 3 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 14 , 10 1 9 1 5 2 4 2 4 5 9 1 5 9 -> 11 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 9 , 10 1 9 1 5 2 4 2 4 5 9 1 5 5 -> 11 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 5 , 10 1 9 1 5 2 4 2 4 5 9 1 5 2 -> 11 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 2 , 10 1 9 1 5 2 4 2 4 5 9 1 5 14 -> 11 6 0 0 7 6 1 5 9 1 5 5 9 1 5 5 5 14 , 7 6 7 6 1 5 2 3 4 9 7 4 5 9 -> 1 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 9 , 7 6 7 6 1 5 2 3 4 9 7 4 5 5 -> 1 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 5 , 7 6 7 6 1 5 2 3 4 9 7 4 5 2 -> 1 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 2 , 7 6 7 6 1 5 2 3 4 9 7 4 5 14 -> 1 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 14 , 2 6 7 6 1 5 2 3 4 9 7 4 5 9 -> 5 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 9 , 2 6 7 6 1 5 2 3 4 9 7 4 5 5 -> 5 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 5 , 2 6 7 6 1 5 2 3 4 9 7 4 5 2 -> 5 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 2 , 2 6 7 6 1 5 2 3 4 9 7 4 5 14 -> 5 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 14 , 3 6 7 6 1 5 2 3 4 9 7 4 5 9 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 9 , 3 6 7 6 1 5 2 3 4 9 7 4 5 5 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 5 , 3 6 7 6 1 5 2 3 4 9 7 4 5 2 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 2 , 3 6 7 6 1 5 2 3 4 9 7 4 5 14 -> 4 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 14 , 11 6 7 6 1 5 2 3 4 9 7 4 5 9 -> 12 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 9 , 11 6 7 6 1 5 2 3 4 9 7 4 5 5 -> 12 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 5 , 11 6 7 6 1 5 2 3 4 9 7 4 5 2 -> 12 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 2 , 11 6 7 6 1 5 2 3 4 9 7 4 5 14 -> 12 2 6 0 0 0 0 7 6 0 0 7 6 1 5 5 5 14 , 1 9 0 1 2 3 6 7 4 2 3 4 5 9 -> 1 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 9 , 1 9 0 1 2 3 6 7 4 2 3 4 5 5 -> 1 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 5 , 1 9 0 1 2 3 6 7 4 2 3 4 5 2 -> 1 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 2 , 1 9 0 1 2 3 6 7 4 2 3 4 5 14 -> 1 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 14 , 5 9 0 1 2 3 6 7 4 2 3 4 5 9 -> 5 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 9 , 5 9 0 1 2 3 6 7 4 2 3 4 5 5 -> 5 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 5 , 5 9 0 1 2 3 6 7 4 2 3 4 5 2 -> 5 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 2 , 5 9 0 1 2 3 6 7 4 2 3 4 5 14 -> 5 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 14 , 4 9 0 1 2 3 6 7 4 2 3 4 5 9 -> 4 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 9 , 4 9 0 1 2 3 6 7 4 2 3 4 5 5 -> 4 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 5 , 4 9 0 1 2 3 6 7 4 2 3 4 5 2 -> 4 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 2 , 4 9 0 1 2 3 6 7 4 2 3 4 5 14 -> 4 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 14 , 12 9 0 1 2 3 6 7 4 2 3 4 5 9 -> 12 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 9 , 12 9 0 1 2 3 6 7 4 2 3 4 5 5 -> 12 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 5 , 12 9 0 1 2 3 6 7 4 2 3 4 5 2 -> 12 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 2 , 12 9 0 1 2 3 6 7 4 2 3 4 5 14 -> 12 5 5 5 5 9 0 0 1 2 6 0 0 0 1 5 5 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 4 | | 0 1 | \ / 3 is interpreted by / \ | 1 6 | | 0 1 | \ / 4 is interpreted by / \ | 1 5 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 4 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 3 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 2 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 7->0, 6->1, 0->2, 1->3, 5->4, 9->5, 4->6, 2->7, 3->8, 11->9 }, it remains to prove termination of the 4-rule system { 0 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 0 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 , 7 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 7 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 , 8 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 8 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 , 9 1 2 3 4 4 5 0 6 5 2 3 7 1 -> 9 1 0 6 4 5 3 5 3 4 4 7 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 { 7->0, 1->1, 2->2, 3->3, 4->4, 5->5, 0->6, 6->7, 8->8, 9->9 }, it remains to prove termination of the 3-rule system { 0 1 2 3 4 4 5 6 7 5 2 3 0 1 -> 0 1 6 7 4 5 3 5 3 4 4 0 1 2 2 2 2 2 , 8 1 2 3 4 4 5 6 7 5 2 3 0 1 -> 8 1 6 7 4 5 3 5 3 4 4 0 1 2 2 2 2 2 , 9 1 2 3 4 4 5 6 7 5 2 3 0 1 -> 9 1 6 7 4 5 3 5 3 4 4 0 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 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 1 | | 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 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 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 { 8->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 0->8, 9->9 }, it remains to prove termination of the 2-rule system { 0 1 2 3 4 4 5 6 7 5 2 3 8 1 -> 0 1 6 7 4 5 3 5 3 4 4 8 1 2 2 2 2 2 , 9 1 2 3 4 4 5 6 7 5 2 3 8 1 -> 9 1 6 7 4 5 3 5 3 4 4 8 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 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 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 { 9->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 1-rule system { 0 1 2 3 4 4 5 6 7 5 2 3 8 1 -> 0 1 6 7 4 5 3 5 3 4 4 8 1 2 2 2 2 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 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 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.