YES After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 99-rule system { 0 0 0 0 0 0 0 0 0 1 0 1 1 1 0 0 1 1 1 0 -> 1 0 0 0 0 0 0 0 1 0 0 0 1 1 0 0 1 1 0 0 , 0 0 0 0 0 0 0 1 1 1 1 0 0 1 0 1 0 0 1 0 -> 0 1 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 , 0 0 0 0 0 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 -> 0 0 1 0 1 0 1 0 0 1 0 0 0 0 1 0 0 1 0 1 , 0 0 0 0 0 0 1 1 1 0 1 0 0 1 0 1 1 0 1 0 -> 0 0 0 0 1 0 1 1 0 0 0 1 0 1 0 0 0 1 0 0 , 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 -> 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 , 0 0 0 0 0 1 0 1 1 1 0 1 0 0 0 1 1 1 0 0 -> 1 0 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 0 0 1 , 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 -> 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 , 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 0 1 0 1 0 -> 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 1 0 1 , 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 -> 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 , 0 0 0 0 1 1 0 1 0 1 0 1 1 0 1 0 0 1 0 0 -> 0 0 0 0 0 0 0 0 1 1 0 0 1 0 1 1 1 1 0 0 , 0 0 0 0 1 1 0 1 0 1 1 1 1 0 0 0 0 0 1 0 -> 1 0 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 0 , 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 -> 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 , 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 -> 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 , 0 0 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 -> 0 1 1 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 1 0 , 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 1 0 1 0 0 -> 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 1 , 0 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 1 0 1 0 -> 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 1 0 , 0 0 0 1 0 1 1 0 1 1 0 0 0 1 1 0 1 0 0 0 -> 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 0 1 0 0 1 , 0 0 0 1 1 0 0 0 0 1 0 1 1 1 0 1 1 0 0 0 -> 0 1 0 1 0 1 0 1 0 0 1 1 0 0 1 0 0 0 0 0 , 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 -> 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 , 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 0 0 1 -> 0 1 0 0 0 0 1 0 0 1 0 1 0 0 1 0 1 0 0 0 , 0 0 0 1 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 0 -> 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 1 0 0 0 0 , 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 -> 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 , 0 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 0 1 0 -> 0 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 , 0 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 0 0 1 0 -> 0 1 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 1 , 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 1 0 1 0 0 -> 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 , 0 0 1 0 0 0 1 1 1 0 0 0 1 1 0 0 1 0 1 0 -> 1 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 , 0 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 0 0 1 0 -> 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 1 0 0 0 0 , 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 -> 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 , 0 0 1 0 1 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 -> 0 0 0 1 0 0 0 0 0 1 1 0 0 0 0 0 1 1 1 0 , 0 0 1 0 1 1 0 0 0 1 1 1 1 0 0 0 0 0 0 0 -> 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 0 0 0 1 0 , 0 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 0 0 0 0 -> 0 0 1 1 0 1 0 1 1 0 0 0 0 0 0 0 0 1 1 0 , 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 0 -> 0 0 1 0 0 0 1 0 1 1 1 0 0 0 1 0 0 0 0 1 , 0 0 1 0 1 1 1 1 0 0 0 1 0 0 0 1 1 0 0 0 -> 0 1 0 0 1 0 0 1 0 0 0 1 0 1 0 0 1 0 0 1 , 0 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 -> 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 , 0 0 1 1 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 -> 1 0 1 0 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 0 , 0 0 1 1 0 1 1 1 0 0 0 0 1 0 0 1 0 1 0 0 -> 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 , 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 -> 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 , 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 -> 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 , 0 0 1 1 1 0 0 0 0 0 1 1 1 0 0 0 0 1 1 0 -> 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 , 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 -> 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 , 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 -> 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 , 0 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 1 0 -> 0 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 , 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 0 -> 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 1 0 1 1 , 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 0 1 0 -> 0 0 0 1 0 0 1 0 0 1 1 0 1 0 0 1 0 0 0 0 , 0 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 1 0 0 0 -> 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 1 0 1 0 , 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 -> 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 , 0 1 0 1 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 -> 1 1 0 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 , 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 -> 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 , 0 1 0 1 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 -> 0 0 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 , 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 0 1 0 0 -> 1 1 0 0 0 0 0 0 1 0 0 1 0 1 1 0 0 1 0 0 , 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 1 0 -> 1 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 0 0 1 0 , 0 1 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0 1 0 -> 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 0 1 0 0 0 , 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 1 0 0 1 0 -> 1 1 0 0 1 1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 , 0 1 1 1 1 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 -> 0 0 0 1 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 , 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 -> 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 , 1 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 0 1 1 0 -> 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 , 1 0 0 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 -> 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 1 , 1 0 0 0 0 1 1 0 1 1 0 0 1 0 0 0 1 0 1 0 -> 0 0 0 1 0 0 1 1 0 0 0 0 1 1 1 0 0 0 0 1 , 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 -> 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 , 1 0 0 0 1 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 -> 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 1 1 0 0 , 1 0 0 0 1 0 1 1 0 1 1 1 0 0 0 0 0 1 0 0 -> 0 0 0 1 0 0 0 1 0 1 0 0 0 1 1 0 1 0 0 1 , 1 0 0 0 1 1 0 0 0 1 0 1 0 0 0 1 0 1 1 0 -> 1 0 0 0 0 1 1 0 0 0 0 1 1 0 0 1 0 1 0 0 , 1 0 0 0 1 1 0 0 1 0 1 1 0 0 1 1 0 0 0 0 -> 1 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 , 1 0 0 0 1 1 1 0 0 1 0 0 0 0 0 1 1 0 1 0 -> 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 , 1 0 0 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 0 -> 1 0 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 , 1 0 0 1 0 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 -> 0 1 0 1 1 1 0 0 0 1 0 1 0 0 0 0 1 0 0 0 , 1 0 0 1 0 1 0 0 0 0 1 1 1 0 0 0 1 0 1 0 -> 0 0 0 0 1 0 0 0 0 1 0 1 0 0 0 1 1 0 0 0 , 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 -> 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 , 1 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 0 0 -> 1 0 0 1 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 , 1 0 0 1 0 1 1 1 0 0 0 0 1 0 0 1 1 0 0 0 -> 0 0 1 0 0 1 1 0 0 0 0 0 1 0 1 0 1 0 1 0 , 1 0 0 1 0 1 1 1 0 0 1 0 1 1 0 1 1 0 1 1 -> 1 0 1 0 0 1 0 1 1 0 1 1 1 0 0 1 0 1 0 1 , 1 0 0 1 1 0 0 0 1 1 0 1 0 0 1 1 0 0 0 0 -> 1 0 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1 0 1 0 , 1 0 0 1 1 0 0 1 0 1 0 0 0 0 1 0 0 1 0 0 -> 0 0 0 1 0 1 0 0 1 1 0 0 0 0 0 0 1 0 0 1 , 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 -> 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 , 1 0 1 0 0 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 -> 0 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 0 0 0 0 , 1 0 1 0 0 1 1 0 1 0 0 1 1 0 1 0 0 0 0 0 -> 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1 1 , 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 -> 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 , 1 0 1 1 1 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 -> 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 , 1 1 0 0 0 0 0 1 0 1 1 0 1 1 0 0 0 0 0 0 -> 1 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 , 1 1 0 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 0 -> 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 , 1 1 0 0 0 0 1 1 0 1 1 0 1 0 0 0 0 0 1 0 -> 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 1 , 1 1 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 1 0 -> 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 1 1 1 0 , 1 1 0 0 0 1 0 1 1 0 0 0 1 1 0 0 0 1 0 0 -> 0 0 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 0 0 , 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 -> 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 , 1 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 -> 0 1 0 0 0 0 0 0 0 1 1 1 0 0 0 1 1 0 0 0 , 1 1 0 0 1 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 -> 0 0 1 0 1 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 , 1 1 0 0 1 1 1 0 0 0 0 0 0 1 1 0 0 0 1 0 -> 1 0 1 0 0 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 , 1 1 0 1 0 0 0 0 0 1 0 0 0 1 1 1 0 1 0 0 -> 0 0 0 0 0 0 0 1 0 0 0 0 1 0 1 1 1 0 1 1 , 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 -> 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 , 1 1 0 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 -> 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 1 , 1 1 0 1 0 1 0 0 0 1 1 1 0 0 0 0 1 0 0 0 -> 0 0 0 0 0 1 0 1 0 1 0 0 1 0 0 1 0 0 0 0 , 1 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 -> 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 , 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 -> 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 , 1 1 1 0 1 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 -> 0 0 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 0 , 1 1 1 0 1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 -> 1 0 1 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1 , 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 -> 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 , 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 -> 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 , 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 -> 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 , 1 1 1 1 1 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 -> 1 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 1 } 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 | \ / After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 25-rule system { 0 0 0 0 0 1 0 0 1 0 1 0 1 1 1 1 1 1 1 0 -> 0 0 1 1 1 1 0 1 0 0 0 1 1 1 0 0 0 1 1 0 , 0 0 0 0 1 0 0 0 1 1 1 1 1 0 1 1 0 0 0 1 -> 0 1 1 1 1 0 1 0 0 1 0 1 0 0 0 0 1 0 0 1 , 0 0 0 0 1 1 0 1 0 1 0 0 1 1 0 0 1 1 0 1 -> 0 0 0 1 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 1 , 0 0 0 0 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 0 -> 0 1 1 0 1 0 0 1 1 0 0 1 0 0 1 1 0 1 0 0 , 0 0 0 1 0 0 0 0 0 0 0 1 1 1 0 1 1 1 0 1 -> 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 0 1 0 0 1 , 0 0 0 1 1 0 0 1 1 0 1 1 1 1 1 0 0 0 0 0 -> 0 0 1 0 0 0 1 1 0 1 1 0 1 1 1 0 1 0 0 0 , 0 0 1 0 0 0 0 0 1 1 1 1 1 1 0 1 0 0 0 1 -> 0 1 0 1 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 1 , 0 0 1 0 1 0 0 1 0 0 1 1 1 0 0 0 0 1 1 1 -> 0 1 1 0 1 1 0 1 0 0 1 0 0 0 0 0 1 1 0 1 , 0 0 1 1 0 1 1 1 1 0 0 1 0 0 1 0 0 0 1 0 -> 0 1 1 0 0 0 1 0 0 0 0 1 1 0 1 0 1 1 1 0 , 0 0 1 1 0 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 -> 0 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 1 0 1 0 , 0 0 1 1 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 -> 0 0 1 0 1 0 0 0 0 1 0 1 0 0 0 1 0 1 1 0 , 0 1 0 0 0 0 0 1 0 0 0 1 0 1 1 1 0 0 0 0 -> 0 0 0 0 0 0 1 0 1 0 0 1 0 0 1 0 1 1 0 0 , 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 0 1 0 -> 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0 , 0 1 0 1 1 1 0 0 1 0 0 0 0 0 0 0 1 1 0 1 -> 0 0 0 0 0 1 0 1 0 1 1 1 0 1 0 0 0 1 0 1 , 1 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 1 0 0 -> 0 1 0 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 , 1 0 0 0 0 1 1 1 1 0 0 1 0 0 0 0 0 0 1 1 -> 1 0 0 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 0 1 , 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0 0 1 0 0 1 -> 1 0 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 0 1 , 1 0 0 1 1 1 1 0 0 0 0 1 0 1 0 1 1 0 0 0 -> 1 1 1 0 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 , 1 0 1 1 1 0 0 0 0 0 0 1 0 1 1 1 0 0 1 0 -> 1 0 0 1 0 1 0 1 1 1 0 0 0 0 1 0 1 0 1 0 , 1 1 0 0 0 1 1 0 1 0 0 0 0 1 1 1 0 0 0 1 -> 1 1 0 0 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 , 1 1 0 1 0 0 1 1 1 1 0 1 0 1 1 0 1 0 1 0 -> 1 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 0 1 0 , 1 1 1 0 0 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 -> 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 1 0 1 0 0 , 1 1 1 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 -> 0 1 0 0 1 1 0 0 0 0 1 0 0 1 0 1 1 0 1 0 , 1 1 1 1 1 0 0 0 0 0 0 1 1 1 0 0 0 1 0 0 -> 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 0 1 1 0 , 1 1 1 1 1 0 1 0 0 1 1 0 1 0 0 0 1 0 0 0 -> 1 1 1 1 0 1 0 1 1 0 1 1 0 0 0 1 0 0 0 0 } The system was reversed. After renaming modulo { 0->0, 1->1 }, it remains to prove termination of the 25-rule system { 0 1 1 1 1 1 1 1 0 1 0 1 0 0 1 0 0 0 0 0 -> 0 1 1 0 0 0 1 1 1 0 0 0 1 0 1 1 1 1 0 0 , 1 0 0 0 1 1 0 1 1 1 1 1 0 0 0 1 0 0 0 0 -> 1 0 0 1 0 0 0 0 1 0 1 0 0 1 0 1 1 1 1 0 , 1 0 1 1 0 0 1 1 0 0 1 0 1 0 1 1 0 0 0 0 -> 1 0 1 1 0 1 1 0 1 0 1 0 0 0 0 1 1 0 0 0 , 0 0 0 1 0 1 0 1 1 1 1 0 0 1 1 1 0 0 0 0 -> 0 0 1 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 , 1 0 1 1 1 0 1 1 1 0 0 0 0 0 0 0 1 0 0 0 -> 1 0 0 1 0 0 1 0 0 1 1 0 0 0 1 1 0 0 1 0 , 0 0 0 0 0 1 1 1 1 1 0 1 1 0 0 1 1 0 0 0 -> 0 0 0 1 0 1 1 1 0 1 1 0 1 1 0 0 0 1 0 0 , 1 0 0 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 -> 1 0 0 0 1 1 0 1 0 0 0 0 1 1 0 1 1 0 1 0 , 1 1 1 0 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 -> 1 0 1 1 0 0 0 0 0 1 0 0 1 0 1 1 0 1 1 0 , 0 1 0 0 0 1 0 0 1 0 0 1 1 1 1 0 1 1 0 0 -> 0 1 1 1 0 1 0 1 1 0 0 0 0 1 0 0 0 1 1 0 , 0 0 0 0 0 0 1 0 1 0 1 1 1 1 1 0 1 1 0 0 -> 0 1 0 1 1 0 1 1 0 1 0 1 1 0 0 0 0 1 0 0 , 0 0 0 0 0 0 0 1 0 1 0 1 0 1 0 1 1 1 0 0 -> 0 1 1 0 1 0 0 0 1 0 1 0 0 0 0 1 0 1 0 0 , 0 0 0 0 1 1 1 0 1 0 0 0 1 0 0 0 0 0 1 0 -> 0 0 1 1 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 , 0 1 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 1 0 -> 0 1 1 0 0 1 1 1 1 1 1 0 0 0 1 0 1 0 1 0 , 1 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 1 0 1 0 -> 1 0 1 0 0 0 1 0 1 1 1 0 1 0 1 0 0 0 0 0 , 0 0 1 0 0 0 0 1 1 1 1 0 1 0 0 0 0 0 0 1 -> 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 0 1 0 1 0 , 1 1 0 0 0 0 0 0 1 0 0 1 1 1 1 0 0 0 0 1 -> 1 0 1 0 1 1 0 0 0 0 1 0 1 1 0 0 0 0 0 1 , 1 0 0 1 0 0 1 1 1 0 0 0 1 0 1 0 1 0 0 1 -> 1 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 0 1 0 1 , 0 0 0 1 1 0 1 0 1 0 0 0 0 1 1 1 1 0 0 1 -> 0 1 0 1 0 0 0 1 1 0 0 0 1 0 1 0 0 1 1 1 , 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 1 1 0 1 -> 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 1 0 0 1 , 1 0 0 0 1 1 1 0 0 0 0 1 0 1 1 0 0 0 1 1 -> 1 0 1 0 0 0 1 0 1 0 0 1 0 1 1 0 0 0 1 1 , 0 1 0 1 0 1 1 0 1 0 1 1 1 1 0 0 1 0 1 1 -> 0 1 0 1 0 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 , 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 0 0 1 1 1 -> 0 0 1 0 1 0 1 0 0 0 1 0 1 1 0 0 1 1 0 1 , 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 1 1 1 -> 0 1 0 1 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 , 0 0 1 0 0 0 1 1 1 0 0 0 0 0 0 1 1 1 1 1 -> 0 1 1 0 0 0 1 0 0 1 0 1 0 1 0 0 1 0 1 1 , 0 0 0 1 0 0 0 1 0 1 1 0 0 1 0 1 1 1 1 1 -> 0 0 0 0 1 0 0 0 1 1 0 1 1 0 1 0 1 1 1 1 } Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,1)->2, (1,0)->3, (0,3)->4, (2,0)->5, (2,1)->6, (1,3)->7 }, it remains to prove termination of the 225-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 1 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 0 -> 1 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 0 , 1 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 1 -> 1 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 1 , 1 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 4 -> 1 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 4 , 2 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 0 -> 2 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 0 , 2 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 1 -> 2 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 1 , 2 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 4 -> 2 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 4 , 6 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 0 -> 6 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 0 , 6 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 1 -> 6 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 1 , 6 3 0 0 1 2 3 1 2 2 2 2 3 0 0 1 3 0 0 0 4 -> 6 3 0 1 3 0 0 0 1 3 1 3 0 1 3 1 2 2 2 3 4 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 0 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 0 -> 0 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 0 , 0 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 1 -> 0 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 1 , 0 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 4 -> 0 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 4 , 3 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 0 -> 3 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 0 , 3 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 1 -> 3 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 1 , 3 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 4 -> 3 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 4 , 5 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 0 -> 5 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 0 , 5 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 1 -> 5 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 1 , 5 0 0 1 3 1 3 1 2 2 2 3 0 1 2 2 3 0 0 0 4 -> 5 0 1 3 1 2 3 0 1 3 0 1 2 3 0 1 3 1 2 3 4 , 1 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 0 -> 1 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 0 , 1 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 1 -> 1 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 1 , 1 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 4 -> 1 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 4 , 2 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 0 -> 2 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 0 , 2 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 1 -> 2 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 1 , 2 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 4 -> 2 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 4 , 6 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 0 -> 6 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 0 , 6 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 1 -> 6 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 1 , 6 3 1 2 2 3 1 2 2 3 0 0 0 0 0 0 1 3 0 0 4 -> 6 3 0 1 3 0 1 3 0 1 2 3 0 0 1 2 3 0 1 3 4 , 0 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 0 -> 0 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 0 , 0 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 1 -> 0 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 1 , 0 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 4 -> 0 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 4 , 3 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 0 -> 3 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 0 , 3 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 1 -> 3 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 1 , 3 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 4 -> 3 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 4 , 5 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 0 -> 5 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 0 , 5 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 1 -> 5 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 1 , 5 0 0 0 0 1 2 2 2 2 3 1 2 3 0 1 2 3 0 0 4 -> 5 0 0 1 3 1 2 2 3 1 2 3 1 2 3 0 0 1 3 0 4 , 1 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 0 -> 1 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 0 , 1 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 1 -> 1 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 1 , 1 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 4 -> 1 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 4 , 2 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 0 -> 2 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 0 , 2 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 1 -> 2 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 1 , 2 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 4 -> 2 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 4 , 6 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 0 -> 6 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 0 , 6 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 1 -> 6 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 1 , 6 3 0 0 1 3 1 2 2 2 2 2 3 0 0 0 0 1 3 0 4 -> 6 3 0 0 1 2 3 1 3 0 0 0 1 2 3 1 2 3 1 3 4 , 1 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 0 -> 1 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 0 , 1 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 1 -> 1 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 1 , 1 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 4 -> 1 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 4 , 2 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 0 -> 2 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 0 , 2 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 1 -> 2 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 1 , 2 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 4 -> 2 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 4 , 6 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 0 -> 6 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 0 , 6 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 1 -> 6 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 1 , 6 2 2 3 0 0 0 1 2 2 3 0 1 3 0 1 3 1 3 0 4 -> 6 3 1 2 3 0 0 0 0 1 3 0 1 3 1 2 3 1 2 3 4 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 0 -> 0 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 0 , 0 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 1 -> 0 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 , 0 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 4 -> 0 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 4 , 3 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 0 -> 3 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 0 , 3 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 1 -> 3 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 , 3 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 4 -> 3 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 4 , 5 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 0 -> 5 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 0 , 5 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 1 -> 5 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 1 , 5 0 0 0 0 0 1 3 1 3 1 2 2 2 2 3 1 2 3 0 4 -> 5 1 3 1 2 3 1 2 3 1 3 1 2 3 0 0 0 1 3 0 4 , 0 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 0 -> 0 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 0 , 0 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 1 -> 0 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 1 , 0 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 4 -> 0 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 4 , 3 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 0 -> 3 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 0 , 3 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 1 -> 3 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 1 , 3 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 4 -> 3 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 4 , 5 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 0 -> 5 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 0 , 5 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 1 -> 5 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 1 , 5 0 0 0 0 0 0 1 3 1 3 1 3 1 3 1 2 2 3 0 4 -> 5 1 2 3 1 3 0 0 1 3 1 3 0 0 0 1 3 1 3 0 4 , 0 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 0 -> 0 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 0 , 0 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 1 -> 0 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 1 , 0 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 4 -> 0 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 4 , 3 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 0 -> 3 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 0 , 3 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 1 -> 3 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 1 , 3 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 4 -> 3 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 4 , 5 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 0 -> 5 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 0 , 5 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 1 -> 5 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 1 , 5 0 0 0 1 2 2 3 1 3 0 0 1 3 0 0 0 0 1 3 4 -> 5 0 1 2 3 1 3 0 1 3 0 1 3 1 3 0 0 0 0 0 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 0 -> 1 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 0 , 1 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 1 -> 1 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 1 , 1 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 4 -> 1 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 4 , 2 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 0 -> 2 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 0 , 2 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 1 -> 2 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 1 , 2 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 4 -> 2 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 4 , 6 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 0 -> 6 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 0 , 6 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 1 -> 6 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 1 , 6 3 1 2 3 0 0 0 0 0 0 1 3 0 1 2 2 3 1 3 4 -> 6 3 1 3 0 0 1 3 1 2 2 3 1 3 1 3 0 0 0 0 4 , 0 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 3 -> 0 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 0 , 0 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 2 -> 0 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 1 , 0 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 7 -> 0 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 4 , 3 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 3 -> 3 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 0 , 3 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 2 -> 3 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 1 , 3 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 7 -> 3 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 4 , 5 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 3 -> 5 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 0 , 5 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 2 -> 5 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 1 , 5 0 1 3 0 0 0 1 2 2 2 3 1 3 0 0 0 0 0 1 7 -> 5 1 3 0 1 3 0 0 1 2 3 0 1 3 0 0 1 3 1 3 4 , 1 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 3 -> 1 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 3 , 1 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 2 -> 1 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 2 , 1 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 7 -> 1 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 7 , 2 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 3 -> 2 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 3 , 2 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 2 -> 2 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 2 , 2 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 7 -> 2 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 7 , 6 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 3 -> 6 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 3 , 6 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 2 -> 6 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 2 , 6 2 3 0 0 0 0 0 1 3 0 1 2 2 2 3 0 0 0 1 7 -> 6 3 1 3 1 2 3 0 0 0 1 3 1 2 3 0 0 0 0 1 7 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 3 -> 0 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 3 , 0 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 2 -> 0 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 2 , 0 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 7 -> 0 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 7 , 3 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 3 -> 3 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 3 , 3 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 2 -> 3 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 2 , 3 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 7 -> 3 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 7 , 5 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 3 -> 5 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 3 , 5 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 2 -> 5 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 2 , 5 0 0 1 2 3 1 3 1 3 0 0 0 1 2 2 2 3 0 1 7 -> 5 1 3 1 3 0 0 1 2 3 0 0 1 3 1 3 0 1 2 2 7 , 0 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 3 -> 0 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 3 , 0 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 2 -> 0 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 2 , 0 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 7 -> 0 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 7 , 3 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 3 -> 3 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 3 , 3 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 2 -> 3 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 2 , 3 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 7 -> 3 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 7 , 5 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 3 -> 5 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 3 , 5 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 2 -> 5 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 2 , 5 1 3 0 1 2 2 3 1 3 0 0 0 0 0 1 2 2 3 1 7 -> 5 1 3 1 3 1 3 0 0 0 1 2 2 3 1 3 1 3 0 1 7 , 1 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 3 -> 1 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 3 , 1 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 2 -> 1 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 2 , 1 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 7 -> 1 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 7 , 2 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 3 -> 2 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 3 , 2 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 2 -> 2 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 2 , 2 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 7 -> 2 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 7 , 6 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 3 -> 6 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 3 , 6 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 2 -> 6 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 2 , 6 3 0 0 1 2 2 3 0 0 0 1 3 1 2 3 0 0 1 2 7 -> 6 3 1 3 0 0 1 3 1 3 0 1 3 1 2 3 0 0 1 2 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 3 -> 0 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 3 , 0 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 2 -> 0 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 2 , 0 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 7 -> 0 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 7 , 3 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 3 -> 3 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 3 , 3 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 2 -> 3 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 2 , 3 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 7 -> 3 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 7 , 5 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 3 -> 5 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 3 , 5 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 2 -> 5 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 2 , 5 1 2 3 0 1 2 3 0 1 3 0 0 0 1 3 0 1 2 2 7 -> 5 0 1 3 1 3 1 3 0 0 1 3 1 2 3 0 1 2 3 1 7 , 0 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 3 -> 0 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 0 , 0 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 2 -> 0 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 1 , 0 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 7 -> 0 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 4 , 3 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 3 -> 3 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 0 , 3 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 2 -> 3 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 1 , 3 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 7 -> 3 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 4 , 5 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 3 -> 5 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 0 , 5 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 2 -> 5 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 1 , 5 0 0 0 0 0 0 0 1 3 0 0 1 2 2 2 3 1 2 2 7 -> 5 1 3 1 2 3 1 3 0 1 3 0 0 0 1 2 3 0 1 3 4 , 0 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 3 -> 0 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 3 , 0 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 2 -> 0 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 2 , 0 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 7 -> 0 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 7 , 3 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 3 -> 3 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 3 , 3 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 2 -> 3 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 2 , 3 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 7 -> 3 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 7 , 5 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 3 -> 5 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 3 , 5 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 2 -> 5 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 2 , 5 0 1 3 0 0 1 2 2 3 0 0 0 0 0 1 2 2 2 2 7 -> 5 1 2 3 0 0 1 3 0 1 3 1 3 1 3 0 1 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } 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 0 | | 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 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 63-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 62-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 61-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 60-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 59-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 58-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 57-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 56-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 55-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 54-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 53-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 52-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 51-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 50-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 49-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 48-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 47-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 0 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 46-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 45-rule system { 0 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 0 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 3 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 4 -> 3 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 4 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 0 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 0 , 5 1 2 2 2 2 2 2 3 1 3 1 3 0 1 3 0 0 0 0 1 -> 5 1 2 3 0 0 1 2 2 3 0 0 1 3 1 2 2 2 3 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 1 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 1 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 2 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 4 -> 2 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 4 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 0 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 0 , 6 3 1 2 3 0 1 2 3 0 1 3 1 3 1 2 3 0 0 0 1 -> 6 3 1 2 3 1 2 3 1 3 1 3 0 0 0 1 2 3 0 0 1 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 0 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 0 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 3 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 4 -> 3 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 4 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 0 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 0 , 5 1 3 0 0 1 3 0 1 3 0 1 2 2 2 3 1 2 3 0 1 -> 5 1 2 2 3 1 3 1 2 3 0 0 0 1 3 0 0 1 2 3 1 , 0 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 0 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 0 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 0 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 3 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 4 -> 3 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 4 , 5 1 3 0 1 2 2 2 2 3 0 1 2 2 3 0 1 3 1 3 1 -> 5 1 2 3 0 1 2 2 2 2 2 3 0 0 1 3 1 3 1 3 1 , 1 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 1 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 3 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 3 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 2 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 7 -> 2 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 7 , 6 3 0 1 3 0 1 2 2 3 0 0 1 3 1 3 1 3 0 1 2 -> 6 3 1 3 1 2 2 3 1 3 0 0 0 0 1 3 0 1 3 1 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 0 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 0 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 7 -> 3 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 7 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 3 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 3 , 5 1 3 1 3 1 2 3 1 3 1 2 2 2 3 0 1 3 1 2 2 -> 5 1 3 1 3 1 2 2 3 1 3 0 1 3 1 2 2 3 1 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 3 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 3 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 3 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 3 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 2 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 2 , 5 0 0 1 3 0 0 1 3 1 2 3 0 1 3 1 2 2 2 2 7 -> 5 0 0 0 1 3 0 0 1 2 3 1 2 3 1 3 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 3->0, 1->1, 2->2, 0->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 44-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 5 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 5 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 5 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 5 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 6 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 6 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 6 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 6 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 5 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 5 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 5 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 5 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 5 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 5 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 6 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 6 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 5 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 5 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 5 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 5 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 43-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 5 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 5 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 6 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 6 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 6 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 6 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 5 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 5 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 5 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 5 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 5 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 5 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 6 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 6 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 5 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 5 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 5 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 5 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 5 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 5 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 6->5, 5->6, 7->7 }, it remains to prove termination of the 42-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 6 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 6 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 41-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 6 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 6 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 40-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 6 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 6 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 39-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 6 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 6 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 , 6 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 6 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 38-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 6 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 6 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 37-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 3 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 3 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 36-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 1 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 1 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 35-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 42: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 34-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 5 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 5 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 33-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 32-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 3 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 31-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 30-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 4 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 4 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 29-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 4 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 4 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 28-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 1 2 2 2 2 0 3 1 2 2 0 3 1 0 1 0 1 -> 0 1 2 0 3 1 2 2 2 2 2 0 3 3 1 0 1 0 1 0 1 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 27-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 7 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 7 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 25-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 24-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 1 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 1 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 23-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 3 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 3 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 22-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 1 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 1 , 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 21-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 3 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 42: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 20-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 6 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 6 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 7 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 7 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 42: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 6->7 }, it remains to prove termination of the 19-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 0 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 0 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 6 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 6 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 7 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 7 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 6 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 18-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 0 1 0 3 3 1 0 3 1 0 3 1 2 2 2 0 1 2 0 3 3 -> 0 1 2 2 0 1 0 1 2 0 3 3 3 1 0 3 3 1 2 0 3 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 6 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 6 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 7 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 7 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 6 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 42: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 17-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 2 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 2 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 6 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 6 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 7 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 7 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 6 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 16-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 6 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 6 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 7 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 7 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 6 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 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/ \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 15-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 3 1 0 3 1 2 2 0 3 3 1 0 1 0 1 0 3 1 6 -> 2 0 1 0 1 2 2 0 1 0 3 3 3 3 1 0 3 1 0 1 6 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 7 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 7 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 6 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 6->7 }, it remains to prove termination of the 14-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 13-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 2 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 2 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 12-rule system { 0 1 2 2 2 2 2 2 0 1 0 1 0 3 1 0 3 3 3 3 4 -> 0 1 2 0 3 3 1 2 2 0 3 3 1 0 1 2 2 2 0 3 4 , 1 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 1 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 3 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 3 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 2 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 4 -> 2 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 4 , 5 0 1 2 0 3 1 2 0 3 1 0 1 0 1 2 0 3 3 3 1 -> 5 0 1 2 0 1 2 0 1 0 1 0 3 3 3 1 2 0 3 3 1 , 3 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 3 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 0 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 6 1 0 1 0 1 2 0 1 0 1 2 2 2 0 3 1 0 1 2 0 -> 6 1 0 1 0 1 2 2 0 1 0 3 1 0 1 2 2 0 1 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 0 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 0 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 2 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 2 , 0 3 3 1 0 3 3 1 0 1 2 0 3 1 0 1 2 2 2 2 7 -> 0 3 3 3 1 0 3 3 1 2 0 1 2 0 1 0 1 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 { 1->0, 0->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 11-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 3 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 3 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 4 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 4 , 5 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 5 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 3 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 3 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 1 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 1 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 6 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 6 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 7 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 10-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 3 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 3 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 4 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 4 , 5 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 5 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 1 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 1 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 6 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 6 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 7 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7 }, it remains to prove termination of the 9-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 3 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 3 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 4 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 4 , 5 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 5 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 6 0 1 0 1 0 2 1 0 1 0 2 2 2 1 3 0 1 0 2 1 -> 6 0 1 0 1 0 2 2 1 0 1 3 0 1 0 2 2 1 0 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 7 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 7 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6 }, it remains to prove termination of the 8-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 3 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 3 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 4 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 4 , 5 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 5 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 6 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6 }, it remains to prove termination of the 7-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 4 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 4 , 5 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 5 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 6 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 5->4, 6->5 }, it remains to prove termination of the 6-rule system { 0 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 0 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 2 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 2 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 4 1 0 2 1 3 0 2 1 3 0 1 0 1 0 2 1 3 3 3 0 -> 4 1 0 2 1 0 2 1 0 1 0 1 3 3 3 0 2 1 3 3 0 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 1 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 1 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 2 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 2 , 1 3 3 0 1 3 3 0 1 0 2 1 3 0 1 0 2 2 2 2 5 -> 1 3 3 3 0 1 3 3 0 2 1 0 2 1 0 1 0 2 2 2 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 { 2->0, 1->1, 0->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 5-rule system { 0 1 2 0 1 3 2 0 1 3 2 1 2 1 2 0 1 3 3 3 2 -> 0 1 2 0 1 2 0 1 2 1 2 1 3 3 3 2 0 1 3 3 2 , 4 1 2 0 1 3 2 0 1 3 2 1 2 1 2 0 1 3 3 3 2 -> 4 1 2 0 1 2 0 1 2 1 2 1 3 3 3 2 0 1 3 3 2 , 1 3 3 2 1 3 3 2 1 2 0 1 3 2 1 2 0 0 0 0 1 -> 1 3 3 3 2 1 3 3 2 0 1 2 0 1 2 1 2 0 0 0 1 , 1 3 3 2 1 3 3 2 1 2 0 1 3 2 1 2 0 0 0 0 0 -> 1 3 3 3 2 1 3 3 2 0 1 2 0 1 2 1 2 0 0 0 0 , 1 3 3 2 1 3 3 2 1 2 0 1 3 2 1 2 0 0 0 0 5 -> 1 3 3 3 2 1 3 3 2 0 1 2 0 1 2 1 2 0 0 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 4-rule system { 0 1 2 0 1 3 2 0 1 3 2 1 2 1 2 0 1 3 3 3 2 -> 0 1 2 0 1 2 0 1 2 1 2 1 3 3 3 2 0 1 3 3 2 , 4 1 2 0 1 3 2 0 1 3 2 1 2 1 2 0 1 3 3 3 2 -> 4 1 2 0 1 2 0 1 2 1 2 1 3 3 3 2 0 1 3 3 2 , 1 3 3 2 1 3 3 2 1 2 0 1 3 2 1 2 0 0 0 0 0 -> 1 3 3 3 2 1 3 3 2 0 1 2 0 1 2 1 2 0 0 0 0 , 1 3 3 2 1 3 3 2 1 2 0 1 3 2 1 2 0 0 0 0 5 -> 1 3 3 3 2 1 3 3 2 0 1 2 0 1 2 1 2 0 0 0 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 { 4->0, 1->1, 2->2, 0->3, 3->4, 5->5 }, it remains to prove termination of the 3-rule system { 0 1 2 3 1 4 2 3 1 4 2 1 2 1 2 3 1 4 4 4 2 -> 0 1 2 3 1 2 3 1 2 1 2 1 4 4 4 2 3 1 4 4 2 , 1 4 4 2 1 4 4 2 1 2 3 1 4 2 1 2 3 3 3 3 3 -> 1 4 4 4 2 1 4 4 2 3 1 2 3 1 2 1 2 3 3 3 3 , 1 4 4 2 1 4 4 2 1 2 3 1 4 2 1 2 3 3 3 3 5 -> 1 4 4 4 2 1 4 4 2 3 1 2 3 1 2 1 2 3 3 3 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 2-rule system { 0 1 2 3 1 4 2 3 1 4 2 1 2 1 2 3 1 4 4 4 2 -> 0 1 2 3 1 2 3 1 2 1 2 1 4 4 4 2 3 1 4 4 2 , 1 4 4 2 1 4 4 2 1 2 3 1 4 2 1 2 3 3 3 3 5 -> 1 4 4 4 2 1 4 4 2 3 1 2 3 1 2 1 2 3 3 3 5 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 { 1->0, 4->1, 2->2, 3->3, 5->4 }, it remains to prove termination of the 1-rule system { 0 1 1 2 0 1 1 2 0 2 3 0 1 2 0 2 3 3 3 3 4 -> 0 1 1 1 2 0 1 1 2 3 0 2 3 0 2 0 2 3 3 3 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 22: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 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.