YES After renaming modulo { 0->0, 1->1, 2->2 }, it remains to prove termination of the 30-rule system { 0 0 0 1 0 2 0 2 1 2 0 2 2 -> 0 0 1 0 1 1 0 2 1 0 0 0 1 0 1 1 0 , 0 0 0 1 1 2 1 2 1 1 0 0 0 -> 1 0 0 2 2 2 2 1 1 2 0 2 0 0 2 1 0 , 0 1 0 1 0 0 1 0 0 2 1 2 0 -> 0 1 0 2 0 0 2 1 0 0 0 0 0 1 0 0 0 , 0 1 2 0 2 0 1 1 1 1 0 0 2 -> 0 0 0 0 0 2 0 2 2 0 2 2 2 0 0 0 0 , 0 1 2 1 1 0 0 2 2 1 0 2 2 -> 1 0 0 2 1 0 0 2 0 0 0 2 0 2 2 2 2 , 0 1 2 2 0 0 2 0 0 0 2 0 2 -> 2 1 0 0 0 2 1 1 0 2 0 1 0 2 1 0 2 , 0 2 0 1 0 1 1 0 1 2 0 0 1 -> 0 1 1 0 0 0 2 1 1 1 0 2 0 0 2 0 1 , 1 0 0 1 0 2 2 0 0 1 2 0 0 -> 0 0 0 0 0 1 0 1 0 1 1 0 1 0 0 2 0 , 1 0 1 1 1 2 2 2 2 1 0 0 0 -> 2 1 0 0 1 0 1 0 2 2 1 1 0 0 2 2 2 , 1 1 0 0 1 0 0 0 0 1 1 1 2 -> 1 1 0 2 1 0 0 2 1 0 1 0 0 2 0 1 2 , 1 1 2 0 1 0 2 1 2 0 1 0 2 -> 1 1 2 1 0 1 0 2 1 1 1 0 1 0 2 0 2 , 1 1 2 2 1 1 2 1 0 0 1 0 2 -> 0 0 2 0 2 0 0 0 2 0 0 2 0 0 2 2 2 , 2 0 0 0 1 1 2 1 0 2 2 0 0 -> 1 1 0 2 0 1 0 2 2 1 1 1 0 2 2 0 0 , 2 0 0 1 1 2 2 1 0 2 2 2 2 -> 1 0 2 2 1 0 1 2 1 0 1 0 0 2 0 2 0 , 2 0 0 2 1 2 1 1 0 1 0 0 2 -> 2 1 1 1 1 0 2 0 1 0 1 0 2 1 0 0 2 , 2 1 1 2 2 0 2 1 0 0 0 1 0 -> 1 1 2 0 0 2 0 0 1 0 0 2 0 0 0 1 0 , 2 1 2 1 1 2 1 0 0 1 0 1 0 -> 2 2 1 1 1 0 0 0 0 1 0 0 2 2 0 1 0 , 2 1 2 2 0 2 1 0 2 0 2 1 0 -> 1 0 1 2 0 0 2 0 0 2 1 0 2 1 0 0 0 , 2 2 0 1 1 1 1 0 1 0 1 2 0 -> 0 1 1 0 1 1 0 0 2 2 0 1 1 0 1 0 0 , 0 0 1 0 1 1 0 1 1 0 2 2 1 ->= 0 0 2 0 1 1 0 0 1 0 1 0 2 0 1 0 1 , 0 1 1 0 2 1 1 1 2 0 2 2 1 ->= 1 0 2 0 0 2 1 0 0 1 0 1 2 1 0 2 1 , 0 2 0 2 1 1 0 1 0 0 1 1 1 ->= 0 1 0 2 1 0 1 0 0 2 1 0 0 0 1 1 1 , 0 2 0 2 2 2 2 2 1 1 1 0 2 ->= 0 1 0 0 1 0 2 2 2 1 0 2 0 2 2 0 0 , 0 2 2 1 1 1 0 1 1 0 0 0 0 ->= 1 1 0 0 0 2 0 0 2 2 2 0 2 1 1 0 0 , 1 2 0 0 0 1 1 0 0 2 2 1 0 ->= 1 0 2 0 1 0 0 2 1 0 2 0 2 0 1 0 0 , 1 2 1 1 1 0 0 2 0 0 1 1 0 ->= 1 2 1 0 2 0 2 0 2 0 1 0 1 0 1 0 2 , 2 0 1 0 0 0 0 0 2 0 1 1 0 ->= 1 0 1 0 2 0 1 0 1 1 0 0 0 1 0 2 0 , 2 0 2 2 0 2 2 0 2 0 1 1 0 ->= 0 1 1 0 0 0 0 2 0 2 2 0 2 0 2 0 0 , 2 2 0 1 1 1 0 0 0 0 2 0 0 ->= 0 1 0 0 0 2 0 0 1 0 0 2 2 2 2 1 0 , 2 2 1 1 0 0 0 0 2 2 1 1 0 ->= 2 2 0 2 0 2 0 2 0 0 1 0 2 0 2 0 0 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 0]->2, [0, 2]->3, [2, 0]->4, [2, 1]->5, [1, 2]->6, [2, 2]->7, [1, 1]->8 }, it remains to prove termination of the 270-rule system { 0 0 0 1 2 3 4 3 5 6 4 3 7 4 -> 0 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 0 , 0 0 0 1 8 6 5 6 5 8 2 0 0 0 -> 1 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 0 , 0 1 2 1 2 0 1 2 0 3 5 6 4 0 -> 0 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 0 , 0 1 6 4 3 4 1 8 8 8 2 0 3 4 -> 0 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 0 , 0 1 6 5 8 2 0 3 7 5 2 3 7 4 -> 1 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 4 , 0 1 6 7 4 0 3 4 0 0 3 4 3 4 -> 3 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 4 , 0 3 4 1 2 1 8 2 1 6 4 0 1 2 -> 0 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 2 , 1 2 0 1 2 3 7 4 0 1 6 4 0 0 -> 0 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 0 , 1 2 1 8 8 6 7 7 7 5 2 0 0 0 -> 3 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 4 , 1 8 2 0 1 2 0 0 0 1 8 8 6 4 -> 1 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 4 , 1 8 6 4 1 2 3 5 6 4 1 2 3 4 -> 1 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 4 , 1 8 6 7 5 8 6 5 2 0 1 2 3 4 -> 0 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 4 , 3 4 0 0 1 8 6 5 2 3 7 4 0 0 -> 1 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 0 , 3 4 0 1 8 6 7 5 2 3 7 7 7 4 -> 1 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 0 , 3 4 0 3 5 6 5 8 2 1 2 0 3 4 -> 3 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 4 , 3 5 8 6 7 4 3 5 2 0 0 1 2 0 -> 1 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 0 , 3 5 6 5 8 6 5 2 0 1 2 1 2 0 -> 3 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 0 , 3 5 6 7 4 3 5 2 3 4 3 5 2 0 -> 1 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 0 , 3 7 4 1 8 8 8 2 1 2 1 6 4 0 -> 0 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 0 , 0 0 1 2 1 8 2 1 8 2 3 7 5 2 ->= 0 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 2 , 0 1 8 2 3 5 8 8 6 4 3 7 5 2 ->= 1 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 2 , 0 3 4 3 5 8 2 1 2 0 1 8 8 2 ->= 0 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 2 , 0 3 4 3 7 7 7 7 5 8 8 2 3 4 ->= 0 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 0 , 0 3 7 5 8 8 2 1 8 2 0 0 0 0 ->= 1 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 0 , 1 6 4 0 0 1 8 2 0 3 7 5 2 0 ->= 1 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 0 , 1 6 5 8 8 2 0 3 4 0 1 8 2 0 ->= 1 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 4 , 3 4 1 2 0 0 0 0 3 4 1 8 2 0 ->= 1 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 0 , 3 4 3 7 4 3 7 4 3 4 1 8 2 0 ->= 0 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 0 , 3 7 4 1 8 8 2 0 0 0 3 4 0 0 ->= 0 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 0 , 3 7 5 8 2 0 0 0 3 7 5 8 2 0 ->= 3 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 0 , 0 0 0 1 2 3 4 3 5 6 4 3 7 5 -> 0 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 1 , 0 0 0 1 8 6 5 6 5 8 2 0 0 1 -> 1 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 1 , 0 1 2 1 2 0 1 2 0 3 5 6 4 1 -> 0 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 1 , 0 1 6 4 3 4 1 8 8 8 2 0 3 5 -> 0 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 1 , 0 1 6 5 8 2 0 3 7 5 2 3 7 5 -> 1 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 5 , 0 1 6 7 4 0 3 4 0 0 3 4 3 5 -> 3 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 5 , 0 3 4 1 2 1 8 2 1 6 4 0 1 8 -> 0 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 8 , 1 2 0 1 2 3 7 4 0 1 6 4 0 1 -> 0 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 1 , 1 2 1 8 8 6 7 7 7 5 2 0 0 1 -> 3 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 5 , 1 8 2 0 1 2 0 0 0 1 8 8 6 5 -> 1 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 5 , 1 8 6 4 1 2 3 5 6 4 1 2 3 5 -> 1 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 5 , 1 8 6 7 5 8 6 5 2 0 1 2 3 5 -> 0 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 5 , 3 4 0 0 1 8 6 5 2 3 7 4 0 1 -> 1 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 1 , 3 4 0 1 8 6 7 5 2 3 7 7 7 5 -> 1 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 1 , 3 4 0 3 5 6 5 8 2 1 2 0 3 5 -> 3 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 5 , 3 5 8 6 7 4 3 5 2 0 0 1 2 1 -> 1 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 1 , 3 5 6 5 8 6 5 2 0 1 2 1 2 1 -> 3 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 1 , 3 5 6 7 4 3 5 2 3 4 3 5 2 1 -> 1 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 1 , 3 7 4 1 8 8 8 2 1 2 1 6 4 1 -> 0 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 1 , 0 0 1 2 1 8 2 1 8 2 3 7 5 8 ->= 0 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 8 , 0 1 8 2 3 5 8 8 6 4 3 7 5 8 ->= 1 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 8 , 0 3 4 3 5 8 2 1 2 0 1 8 8 8 ->= 0 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 8 , 0 3 4 3 7 7 7 7 5 8 8 2 3 5 ->= 0 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 1 , 0 3 7 5 8 8 2 1 8 2 0 0 0 1 ->= 1 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 1 , 1 6 4 0 0 1 8 2 0 3 7 5 2 1 ->= 1 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 1 , 1 6 5 8 8 2 0 3 4 0 1 8 2 1 ->= 1 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 5 , 3 4 1 2 0 0 0 0 3 4 1 8 2 1 ->= 1 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 1 , 3 4 3 7 4 3 7 4 3 4 1 8 2 1 ->= 0 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 1 , 3 7 4 1 8 8 2 0 0 0 3 4 0 1 ->= 0 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 1 , 3 7 5 8 2 0 0 0 3 7 5 8 2 1 ->= 3 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 1 , 0 0 0 1 2 3 4 3 5 6 4 3 7 7 -> 0 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 3 , 0 0 0 1 8 6 5 6 5 8 2 0 0 3 -> 1 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 3 , 0 1 2 1 2 0 1 2 0 3 5 6 4 3 -> 0 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 3 , 0 1 6 4 3 4 1 8 8 8 2 0 3 7 -> 0 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 3 , 0 1 6 5 8 2 0 3 7 5 2 3 7 7 -> 1 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 7 , 0 1 6 7 4 0 3 4 0 0 3 4 3 7 -> 3 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 7 , 0 3 4 1 2 1 8 2 1 6 4 0 1 6 -> 0 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 6 , 1 2 0 1 2 3 7 4 0 1 6 4 0 3 -> 0 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 3 , 1 2 1 8 8 6 7 7 7 5 2 0 0 3 -> 3 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 7 , 1 8 2 0 1 2 0 0 0 1 8 8 6 7 -> 1 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 7 , 1 8 6 4 1 2 3 5 6 4 1 2 3 7 -> 1 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 7 , 1 8 6 7 5 8 6 5 2 0 1 2 3 7 -> 0 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 7 , 3 4 0 0 1 8 6 5 2 3 7 4 0 3 -> 1 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 3 , 3 4 0 1 8 6 7 5 2 3 7 7 7 7 -> 1 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 3 , 3 4 0 3 5 6 5 8 2 1 2 0 3 7 -> 3 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 7 , 3 5 8 6 7 4 3 5 2 0 0 1 2 3 -> 1 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 3 , 3 5 6 5 8 6 5 2 0 1 2 1 2 3 -> 3 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 3 , 3 5 6 7 4 3 5 2 3 4 3 5 2 3 -> 1 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 3 , 3 7 4 1 8 8 8 2 1 2 1 6 4 3 -> 0 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 3 , 0 0 1 2 1 8 2 1 8 2 3 7 5 6 ->= 0 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 6 , 0 1 8 2 3 5 8 8 6 4 3 7 5 6 ->= 1 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 6 , 0 3 4 3 5 8 2 1 2 0 1 8 8 6 ->= 0 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 6 , 0 3 4 3 7 7 7 7 5 8 8 2 3 7 ->= 0 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 3 , 0 3 7 5 8 8 2 1 8 2 0 0 0 3 ->= 1 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 3 , 1 6 4 0 0 1 8 2 0 3 7 5 2 3 ->= 1 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 3 , 1 6 5 8 8 2 0 3 4 0 1 8 2 3 ->= 1 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 7 , 3 4 1 2 0 0 0 0 3 4 1 8 2 3 ->= 1 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 3 , 3 4 3 7 4 3 7 4 3 4 1 8 2 3 ->= 0 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 3 , 3 7 4 1 8 8 2 0 0 0 3 4 0 3 ->= 0 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 3 , 3 7 5 8 2 0 0 0 3 7 5 8 2 3 ->= 3 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 3 , 2 0 0 1 2 3 4 3 5 6 4 3 7 4 -> 2 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 0 , 2 0 0 1 8 6 5 6 5 8 2 0 0 0 -> 8 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 0 , 2 1 2 1 2 0 1 2 0 3 5 6 4 0 -> 2 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 0 , 2 1 6 4 3 4 1 8 8 8 2 0 3 4 -> 2 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 0 , 2 1 6 5 8 2 0 3 7 5 2 3 7 4 -> 8 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 4 , 2 1 6 7 4 0 3 4 0 0 3 4 3 4 -> 6 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 4 , 2 3 4 1 2 1 8 2 1 6 4 0 1 2 -> 2 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 2 , 8 2 0 1 2 3 7 4 0 1 6 4 0 0 -> 2 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 0 , 8 2 1 8 8 6 7 7 7 5 2 0 0 0 -> 6 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 4 , 8 8 2 0 1 2 0 0 0 1 8 8 6 4 -> 8 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 4 , 8 8 6 4 1 2 3 5 6 4 1 2 3 4 -> 8 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 4 , 8 8 6 7 5 8 6 5 2 0 1 2 3 4 -> 2 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 4 , 6 4 0 0 1 8 6 5 2 3 7 4 0 0 -> 8 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 0 , 6 4 0 1 8 6 7 5 2 3 7 7 7 4 -> 8 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 0 , 6 4 0 3 5 6 5 8 2 1 2 0 3 4 -> 6 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 4 , 6 5 8 6 7 4 3 5 2 0 0 1 2 0 -> 8 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 0 , 6 5 6 5 8 6 5 2 0 1 2 1 2 0 -> 6 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 0 , 6 5 6 7 4 3 5 2 3 4 3 5 2 0 -> 8 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 0 , 6 7 4 1 8 8 8 2 1 2 1 6 4 0 -> 2 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 0 , 2 0 1 2 1 8 2 1 8 2 3 7 5 2 ->= 2 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 2 , 2 1 8 2 3 5 8 8 6 4 3 7 5 2 ->= 8 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 2 , 2 3 4 3 5 8 2 1 2 0 1 8 8 2 ->= 2 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 2 , 2 3 4 3 7 7 7 7 5 8 8 2 3 4 ->= 2 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 0 , 2 3 7 5 8 8 2 1 8 2 0 0 0 0 ->= 8 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 0 , 8 6 4 0 0 1 8 2 0 3 7 5 2 0 ->= 8 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 0 , 8 6 5 8 8 2 0 3 4 0 1 8 2 0 ->= 8 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 4 , 6 4 1 2 0 0 0 0 3 4 1 8 2 0 ->= 8 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 0 , 6 4 3 7 4 3 7 4 3 4 1 8 2 0 ->= 2 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 0 , 6 7 4 1 8 8 2 0 0 0 3 4 0 0 ->= 2 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 0 , 6 7 5 8 2 0 0 0 3 7 5 8 2 0 ->= 6 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 0 , 2 0 0 1 2 3 4 3 5 6 4 3 7 5 -> 2 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 1 , 2 0 0 1 8 6 5 6 5 8 2 0 0 1 -> 8 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 1 , 2 1 2 1 2 0 1 2 0 3 5 6 4 1 -> 2 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 1 , 2 1 6 4 3 4 1 8 8 8 2 0 3 5 -> 2 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 1 , 2 1 6 5 8 2 0 3 7 5 2 3 7 5 -> 8 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 5 , 2 1 6 7 4 0 3 4 0 0 3 4 3 5 -> 6 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 5 , 2 3 4 1 2 1 8 2 1 6 4 0 1 8 -> 2 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 8 , 8 2 0 1 2 3 7 4 0 1 6 4 0 1 -> 2 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 1 , 8 2 1 8 8 6 7 7 7 5 2 0 0 1 -> 6 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 5 , 8 8 2 0 1 2 0 0 0 1 8 8 6 5 -> 8 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 5 , 8 8 6 4 1 2 3 5 6 4 1 2 3 5 -> 8 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 5 , 8 8 6 7 5 8 6 5 2 0 1 2 3 5 -> 2 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 5 , 6 4 0 0 1 8 6 5 2 3 7 4 0 1 -> 8 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 1 , 6 4 0 1 8 6 7 5 2 3 7 7 7 5 -> 8 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 1 , 6 4 0 3 5 6 5 8 2 1 2 0 3 5 -> 6 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 5 , 6 5 8 6 7 4 3 5 2 0 0 1 2 1 -> 8 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 1 , 6 5 6 5 8 6 5 2 0 1 2 1 2 1 -> 6 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 1 , 6 5 6 7 4 3 5 2 3 4 3 5 2 1 -> 8 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 1 , 6 7 4 1 8 8 8 2 1 2 1 6 4 1 -> 2 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 1 , 2 0 1 2 1 8 2 1 8 2 3 7 5 8 ->= 2 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 8 , 2 1 8 2 3 5 8 8 6 4 3 7 5 8 ->= 8 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 8 , 2 3 4 3 5 8 2 1 2 0 1 8 8 8 ->= 2 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 8 , 2 3 4 3 7 7 7 7 5 8 8 2 3 5 ->= 2 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 1 , 2 3 7 5 8 8 2 1 8 2 0 0 0 1 ->= 8 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 1 , 8 6 4 0 0 1 8 2 0 3 7 5 2 1 ->= 8 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 1 , 8 6 5 8 8 2 0 3 4 0 1 8 2 1 ->= 8 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 5 , 6 4 1 2 0 0 0 0 3 4 1 8 2 1 ->= 8 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 1 , 6 4 3 7 4 3 7 4 3 4 1 8 2 1 ->= 2 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 1 , 6 7 4 1 8 8 2 0 0 0 3 4 0 1 ->= 2 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 1 , 6 7 5 8 2 0 0 0 3 7 5 8 2 1 ->= 6 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 1 , 2 0 0 1 2 3 4 3 5 6 4 3 7 7 -> 2 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 3 , 2 0 0 1 8 6 5 6 5 8 2 0 0 3 -> 8 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 3 , 2 1 2 1 2 0 1 2 0 3 5 6 4 3 -> 2 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 3 , 2 1 6 4 3 4 1 8 8 8 2 0 3 7 -> 2 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 3 , 2 1 6 5 8 2 0 3 7 5 2 3 7 7 -> 8 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 7 , 2 1 6 7 4 0 3 4 0 0 3 4 3 7 -> 6 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 7 , 2 3 4 1 2 1 8 2 1 6 4 0 1 6 -> 2 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 6 , 8 2 0 1 2 3 7 4 0 1 6 4 0 3 -> 2 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 3 , 8 2 1 8 8 6 7 7 7 5 2 0 0 3 -> 6 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 7 , 8 8 2 0 1 2 0 0 0 1 8 8 6 7 -> 8 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 7 , 8 8 6 4 1 2 3 5 6 4 1 2 3 7 -> 8 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 7 , 8 8 6 7 5 8 6 5 2 0 1 2 3 7 -> 2 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 7 , 6 4 0 0 1 8 6 5 2 3 7 4 0 3 -> 8 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 3 , 6 4 0 1 8 6 7 5 2 3 7 7 7 7 -> 8 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 3 , 6 4 0 3 5 6 5 8 2 1 2 0 3 7 -> 6 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 7 , 6 5 8 6 7 4 3 5 2 0 0 1 2 3 -> 8 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 3 , 6 5 6 5 8 6 5 2 0 1 2 1 2 3 -> 6 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 3 , 6 5 6 7 4 3 5 2 3 4 3 5 2 3 -> 8 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 3 , 6 7 4 1 8 8 8 2 1 2 1 6 4 3 -> 2 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 3 , 2 0 1 2 1 8 2 1 8 2 3 7 5 6 ->= 2 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 6 , 2 1 8 2 3 5 8 8 6 4 3 7 5 6 ->= 8 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 6 , 2 3 4 3 5 8 2 1 2 0 1 8 8 6 ->= 2 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 6 , 2 3 4 3 7 7 7 7 5 8 8 2 3 7 ->= 2 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 3 , 2 3 7 5 8 8 2 1 8 2 0 0 0 3 ->= 8 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 3 , 8 6 4 0 0 1 8 2 0 3 7 5 2 3 ->= 8 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 3 , 8 6 5 8 8 2 0 3 4 0 1 8 2 3 ->= 8 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 7 , 6 4 1 2 0 0 0 0 3 4 1 8 2 3 ->= 8 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 3 , 6 4 3 7 4 3 7 4 3 4 1 8 2 3 ->= 2 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 3 , 6 7 4 1 8 8 2 0 0 0 3 4 0 3 ->= 2 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 3 , 6 7 5 8 2 0 0 0 3 7 5 8 2 3 ->= 6 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 3 , 4 0 0 1 2 3 4 3 5 6 4 3 7 4 -> 4 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 0 , 4 0 0 1 8 6 5 6 5 8 2 0 0 0 -> 5 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 0 , 4 1 2 1 2 0 1 2 0 3 5 6 4 0 -> 4 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 0 , 4 1 6 4 3 4 1 8 8 8 2 0 3 4 -> 4 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 0 , 4 1 6 5 8 2 0 3 7 5 2 3 7 4 -> 5 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 4 , 4 1 6 7 4 0 3 4 0 0 3 4 3 4 -> 7 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 4 , 4 3 4 1 2 1 8 2 1 6 4 0 1 2 -> 4 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 2 , 5 2 0 1 2 3 7 4 0 1 6 4 0 0 -> 4 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 0 , 5 2 1 8 8 6 7 7 7 5 2 0 0 0 -> 7 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 4 , 5 8 2 0 1 2 0 0 0 1 8 8 6 4 -> 5 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 4 , 5 8 6 4 1 2 3 5 6 4 1 2 3 4 -> 5 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 4 , 5 8 6 7 5 8 6 5 2 0 1 2 3 4 -> 4 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 4 , 7 4 0 0 1 8 6 5 2 3 7 4 0 0 -> 5 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 0 , 7 4 0 1 8 6 7 5 2 3 7 7 7 4 -> 5 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 0 , 7 4 0 3 5 6 5 8 2 1 2 0 3 4 -> 7 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 4 , 7 5 8 6 7 4 3 5 2 0 0 1 2 0 -> 5 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 0 , 7 5 6 5 8 6 5 2 0 1 2 1 2 0 -> 7 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 0 , 7 5 6 7 4 3 5 2 3 4 3 5 2 0 -> 5 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 0 , 7 7 4 1 8 8 8 2 1 2 1 6 4 0 -> 4 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 0 , 4 0 1 2 1 8 2 1 8 2 3 7 5 2 ->= 4 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 2 , 4 1 8 2 3 5 8 8 6 4 3 7 5 2 ->= 5 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 2 , 4 3 4 3 5 8 2 1 2 0 1 8 8 2 ->= 4 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 2 , 4 3 4 3 7 7 7 7 5 8 8 2 3 4 ->= 4 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 0 , 4 3 7 5 8 8 2 1 8 2 0 0 0 0 ->= 5 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 0 , 5 6 4 0 0 1 8 2 0 3 7 5 2 0 ->= 5 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 0 , 5 6 5 8 8 2 0 3 4 0 1 8 2 0 ->= 5 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 4 , 7 4 1 2 0 0 0 0 3 4 1 8 2 0 ->= 5 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 0 , 7 4 3 7 4 3 7 4 3 4 1 8 2 0 ->= 4 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 0 , 7 7 4 1 8 8 2 0 0 0 3 4 0 0 ->= 4 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 0 , 7 7 5 8 2 0 0 0 3 7 5 8 2 0 ->= 7 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 0 , 4 0 0 1 2 3 4 3 5 6 4 3 7 5 -> 4 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 1 , 4 0 0 1 8 6 5 6 5 8 2 0 0 1 -> 5 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 1 , 4 1 2 1 2 0 1 2 0 3 5 6 4 1 -> 4 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 1 , 4 1 6 4 3 4 1 8 8 8 2 0 3 5 -> 4 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 1 , 4 1 6 5 8 2 0 3 7 5 2 3 7 5 -> 5 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 5 , 4 1 6 7 4 0 3 4 0 0 3 4 3 5 -> 7 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 5 , 4 3 4 1 2 1 8 2 1 6 4 0 1 8 -> 4 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 8 , 5 2 0 1 2 3 7 4 0 1 6 4 0 1 -> 4 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 1 , 5 2 1 8 8 6 7 7 7 5 2 0 0 1 -> 7 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 5 , 5 8 2 0 1 2 0 0 0 1 8 8 6 5 -> 5 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 5 , 5 8 6 4 1 2 3 5 6 4 1 2 3 5 -> 5 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 5 , 5 8 6 7 5 8 6 5 2 0 1 2 3 5 -> 4 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 5 , 7 4 0 0 1 8 6 5 2 3 7 4 0 1 -> 5 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 1 , 7 4 0 1 8 6 7 5 2 3 7 7 7 5 -> 5 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 1 , 7 4 0 3 5 6 5 8 2 1 2 0 3 5 -> 7 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 5 , 7 5 8 6 7 4 3 5 2 0 0 1 2 1 -> 5 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 1 , 7 5 6 5 8 6 5 2 0 1 2 1 2 1 -> 7 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 1 , 7 5 6 7 4 3 5 2 3 4 3 5 2 1 -> 5 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 1 , 7 7 4 1 8 8 8 2 1 2 1 6 4 1 -> 4 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 1 , 4 0 1 2 1 8 2 1 8 2 3 7 5 8 ->= 4 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 8 , 4 1 8 2 3 5 8 8 6 4 3 7 5 8 ->= 5 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 8 , 4 3 4 3 5 8 2 1 2 0 1 8 8 8 ->= 4 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 8 , 4 3 4 3 7 7 7 7 5 8 8 2 3 5 ->= 4 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 1 , 4 3 7 5 8 8 2 1 8 2 0 0 0 1 ->= 5 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 1 , 5 6 4 0 0 1 8 2 0 3 7 5 2 1 ->= 5 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 1 , 5 6 5 8 8 2 0 3 4 0 1 8 2 1 ->= 5 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 5 , 7 4 1 2 0 0 0 0 3 4 1 8 2 1 ->= 5 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 1 , 7 4 3 7 4 3 7 4 3 4 1 8 2 1 ->= 4 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 1 , 7 7 4 1 8 8 2 0 0 0 3 4 0 1 ->= 4 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 1 , 7 7 5 8 2 0 0 0 3 7 5 8 2 1 ->= 7 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 1 , 4 0 0 1 2 3 4 3 5 6 4 3 7 7 -> 4 0 1 2 1 8 2 3 5 2 0 0 1 2 1 8 2 3 , 4 0 0 1 8 6 5 6 5 8 2 0 0 3 -> 5 2 0 3 7 7 7 5 8 6 4 3 4 0 3 5 2 3 , 4 1 2 1 2 0 1 2 0 3 5 6 4 3 -> 4 1 2 3 4 0 3 5 2 0 0 0 0 1 2 0 0 3 , 4 1 6 4 3 4 1 8 8 8 2 0 3 7 -> 4 0 0 0 0 3 4 3 7 4 3 7 7 4 0 0 0 3 , 4 1 6 5 8 2 0 3 7 5 2 3 7 7 -> 5 2 0 3 5 2 0 3 4 0 0 3 4 3 7 7 7 7 , 4 1 6 7 4 0 3 4 0 0 3 4 3 7 -> 7 5 2 0 0 3 5 8 2 3 4 1 2 3 5 2 3 7 , 4 3 4 1 2 1 8 2 1 6 4 0 1 6 -> 4 1 8 2 0 0 3 5 8 8 2 3 4 0 3 4 1 6 , 5 2 0 1 2 3 7 4 0 1 6 4 0 3 -> 4 0 0 0 0 1 2 1 2 1 8 2 1 2 0 3 4 3 , 5 2 1 8 8 6 7 7 7 5 2 0 0 3 -> 7 5 2 0 1 2 1 2 3 7 5 8 2 0 3 7 7 7 , 5 8 2 0 1 2 0 0 0 1 8 8 6 7 -> 5 8 2 3 5 2 0 3 5 2 1 2 0 3 4 1 6 7 , 5 8 6 4 1 2 3 5 6 4 1 2 3 7 -> 5 8 6 5 2 1 2 3 5 8 8 2 1 2 3 4 3 7 , 5 8 6 7 5 8 6 5 2 0 1 2 3 7 -> 4 0 3 4 3 4 0 0 3 4 0 3 4 0 3 7 7 7 , 7 4 0 0 1 8 6 5 2 3 7 4 0 3 -> 5 8 2 3 4 1 2 3 7 5 8 8 2 3 7 4 0 3 , 7 4 0 1 8 6 7 5 2 3 7 7 7 7 -> 5 2 3 7 5 2 1 6 5 2 1 2 0 3 4 3 4 3 , 7 4 0 3 5 6 5 8 2 1 2 0 3 7 -> 7 5 8 8 8 2 3 4 1 2 1 2 3 5 2 0 3 7 , 7 5 8 6 7 4 3 5 2 0 0 1 2 3 -> 5 8 6 4 0 3 4 0 1 2 0 3 4 0 0 1 2 3 , 7 5 6 5 8 6 5 2 0 1 2 1 2 3 -> 7 7 5 8 8 2 0 0 0 1 2 0 3 7 4 1 2 3 , 7 5 6 7 4 3 5 2 3 4 3 5 2 3 -> 5 2 1 6 4 0 3 4 0 3 5 2 3 5 2 0 0 3 , 7 7 4 1 8 8 8 2 1 2 1 6 4 3 -> 4 1 8 2 1 8 2 0 3 7 4 1 8 2 1 2 0 3 , 4 0 1 2 1 8 2 1 8 2 3 7 5 6 ->= 4 0 3 4 1 8 2 0 1 2 1 2 3 4 1 2 1 6 , 4 1 8 2 3 5 8 8 6 4 3 7 5 6 ->= 5 2 3 4 0 3 5 2 0 1 2 1 6 5 2 3 5 6 , 4 3 4 3 5 8 2 1 2 0 1 8 8 6 ->= 4 1 2 3 5 2 1 2 0 3 5 2 0 0 1 8 8 6 , 4 3 4 3 7 7 7 7 5 8 8 2 3 7 ->= 4 1 2 0 1 2 3 7 7 5 2 3 4 3 7 4 0 3 , 4 3 7 5 8 8 2 1 8 2 0 0 0 3 ->= 5 8 2 0 0 3 4 0 3 7 7 4 3 5 8 2 0 3 , 5 6 4 0 0 1 8 2 0 3 7 5 2 3 ->= 5 2 3 4 1 2 0 3 5 2 3 4 3 4 1 2 0 3 , 5 6 5 8 8 2 0 3 4 0 1 8 2 3 ->= 5 6 5 2 3 4 3 4 3 4 1 2 1 2 1 2 3 7 , 7 4 1 2 0 0 0 0 3 4 1 8 2 3 ->= 5 2 1 2 3 4 1 2 1 8 2 0 0 1 2 3 4 3 , 7 4 3 7 4 3 7 4 3 4 1 8 2 3 ->= 4 1 8 2 0 0 0 3 4 3 7 4 3 4 3 4 0 3 , 7 7 4 1 8 8 2 0 0 0 3 4 0 3 ->= 4 1 2 0 0 3 4 0 1 2 0 3 7 7 7 5 2 3 , 7 7 5 8 2 0 0 0 3 7 5 8 2 3 ->= 7 7 4 3 4 3 4 3 4 0 1 2 3 4 3 4 0 3 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 1->0, 8->1, 2->2, 0->3, 6->4, 4->5, 3->6, 5->7, 7->8 }, it remains to prove termination of the 114-rule system { 0 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 6 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 6 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 6 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 3 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 3 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 3 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 3 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 3 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 0 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 6 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 6 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 6 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 6 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 0 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 6 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 6 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 6 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 3 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 3 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 3 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 3 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 3 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 0 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 6 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 6 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 6 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 6 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 0 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 6 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 6 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 6 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 3 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 3 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 3 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 3 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 3 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 0 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 6 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 6 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 6 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 6 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 2 0 4 8 5 3 6 5 3 3 6 5 6 5 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 5 , 1 2 0 1 1 4 8 8 8 7 2 3 3 3 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 5 , 1 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 2 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 2 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 2 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 2 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 2 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 1 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 4 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 2 0 4 8 5 3 6 5 3 3 6 5 6 7 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 7 , 1 2 0 1 1 4 8 8 8 7 2 3 3 0 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 7 , 1 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 2 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 2 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 2 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 2 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 2 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 1 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 4 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 2 0 4 8 5 3 6 5 3 3 6 5 6 8 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 8 , 1 2 0 1 1 4 8 8 8 7 2 3 3 6 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 8 , 1 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 2 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 2 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 2 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 2 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 2 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 1 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 4 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 7 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 8 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 8 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 8 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 5 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 5 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 5 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 5 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 5 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 7 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 8 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 8 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 8 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 8 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 7 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 8 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 8 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 8 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 5 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 5 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 5 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 5 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 5 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 7 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 8 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 8 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 8 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 8 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 7 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 8 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 8 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 8 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 5 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 5 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 5 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 5 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 5 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 7 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 8 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 8 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 8 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 8 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 113-rule system { 0 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 6 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 6 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 6 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 3 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 3 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 3 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 3 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 3 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 0 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 6 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 6 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 6 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 6 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 0 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 6 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 6 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 6 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 3 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 3 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 3 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 3 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 3 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 0 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 6 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 6 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 6 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 6 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 0 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 6 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 6 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 6 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 3 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 3 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 3 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 3 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 3 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 0 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 6 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 6 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 6 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 6 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 2 0 4 8 5 3 6 5 3 3 6 5 6 5 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 5 , 1 2 0 1 1 4 8 8 8 7 2 3 3 3 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 5 , 1 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 2 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 2 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 2 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 2 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 2 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 1 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 4 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 2 0 4 8 5 3 6 5 3 3 6 5 6 7 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 7 , 1 2 0 1 1 4 8 8 8 7 2 3 3 0 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 7 , 1 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 2 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 2 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 2 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 2 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 2 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 1 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 4 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 2 0 4 8 5 3 6 5 3 3 6 5 6 8 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 8 , 1 2 0 1 1 4 8 8 8 7 2 3 3 6 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 8 , 2 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 2 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 2 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 2 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 2 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 1 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 4 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 7 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 8 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 8 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 8 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 5 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 5 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 5 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 5 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 5 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 7 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 8 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 8 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 8 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 8 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 7 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 8 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 8 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 8 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 5 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 5 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 5 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 5 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 5 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 7 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 8 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 8 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 8 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 8 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 7 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 8 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 8 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 8 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 5 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 5 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 5 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 5 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 5 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 7 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 8 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 8 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 8 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 8 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 112-rule system { 0 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 6 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 6 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 6 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 3 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 3 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 3 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 3 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 3 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 0 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 6 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 6 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 6 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 6 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 0 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 6 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 6 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 6 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 3 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 3 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 3 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 3 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 3 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 0 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 6 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 6 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 6 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 6 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 0 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 6 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 6 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 6 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 3 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 3 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 3 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 3 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 3 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 0 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 6 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 6 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 6 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 6 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 2 0 4 8 5 3 6 5 3 3 6 5 6 5 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 5 , 1 2 0 1 1 4 8 8 8 7 2 3 3 3 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 5 , 2 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 2 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 2 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 2 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 2 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 1 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 4 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 2 0 4 8 5 3 6 5 3 3 6 5 6 7 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 7 , 1 2 0 1 1 4 8 8 8 7 2 3 3 0 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 7 , 1 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 2 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 2 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 2 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 2 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 2 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 1 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 4 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 2 0 4 8 5 3 6 5 3 3 6 5 6 8 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 8 , 1 2 0 1 1 4 8 8 8 7 2 3 3 6 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 8 , 2 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 2 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 2 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 2 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 2 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 1 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 4 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 7 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 8 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 8 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 8 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 5 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 5 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 5 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 5 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 5 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 7 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 8 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 8 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 8 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 8 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 7 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 8 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 8 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 8 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 5 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 5 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 5 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 5 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 5 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 7 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 8 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 8 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 8 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 8 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 7 1 2 3 0 2 3 3 3 0 1 1 4 8 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 8 , 8 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 8 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 8 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 5 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 5 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 5 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 5 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 5 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 7 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 8 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 8 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 8 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 8 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 110-rule system { 0 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 6 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 6 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 6 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 3 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 3 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 3 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 3 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 3 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 0 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 6 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 6 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 6 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 6 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 0 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 0 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 6 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 6 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 6 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 3 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 3 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 3 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 3 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 3 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 0 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 6 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 6 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 6 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 6 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 6 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 0 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 6 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 0 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 6 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 0 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 3 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 3 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 3 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 0 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 3 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 3 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 3 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 3 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 3 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 0 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 0 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 0 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 6 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 0 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 6 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 3 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 6 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 3 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 6 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 6 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 2 0 4 8 5 3 6 5 3 3 6 5 6 5 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 5 , 1 2 0 1 1 4 8 8 8 7 2 3 3 3 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 5 , 2 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 2 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 2 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 2 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 2 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 1 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 4 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 2 0 4 8 5 3 6 5 3 3 6 5 6 7 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 7 , 1 2 0 1 1 4 8 8 8 7 2 3 3 0 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 7 , 1 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 1 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 2 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 2 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 2 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 2 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 2 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 1 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 4 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 2 0 4 8 5 3 6 5 3 3 6 5 6 8 -> 4 7 2 3 3 6 7 1 2 6 5 0 2 6 7 2 6 8 , 1 2 0 1 1 4 8 8 8 7 2 3 3 6 -> 4 7 2 3 0 2 0 2 6 8 7 1 2 3 6 8 8 8 , 2 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 2 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 2 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 1 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 2 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 2 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 2 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 2 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 2 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 1 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 1 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 1 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 4 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 4 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 , 7 1 2 3 0 2 3 3 3 0 1 1 4 5 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 5 , 8 5 3 0 1 4 8 7 2 6 8 8 8 5 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 3 , 8 7 1 4 8 5 6 7 2 3 3 0 2 3 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 3 , 8 7 4 8 5 6 7 2 6 5 6 7 2 3 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 3 , 5 3 0 2 0 1 2 0 1 2 6 8 7 2 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 2 , 5 0 1 2 6 7 1 1 4 5 6 8 7 2 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 2 , 5 6 5 6 7 1 2 0 2 3 0 1 1 2 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 2 , 5 6 5 6 8 8 8 8 7 1 1 2 6 5 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 3 , 5 6 8 7 1 1 2 0 1 2 3 3 3 3 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 3 , 7 4 7 1 1 2 3 6 5 3 0 1 2 3 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 5 , 8 5 0 2 3 3 3 3 6 5 0 1 2 3 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 3 , 8 5 6 8 5 6 8 5 6 5 0 1 2 3 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 3 , 8 8 5 0 1 1 2 3 3 3 6 5 3 3 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 3 , 8 8 7 1 2 3 3 3 6 8 7 1 2 3 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 3 , 7 1 2 3 0 2 3 3 3 0 1 1 4 7 -> 7 1 2 6 7 2 3 6 7 2 0 2 3 6 5 0 4 7 , 8 5 3 0 1 4 8 7 2 6 8 8 8 7 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 0 , 8 7 1 4 8 5 6 7 2 3 3 0 2 0 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 0 , 8 7 4 8 5 6 7 2 6 5 6 7 2 0 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 0 , 5 3 0 2 0 1 2 0 1 2 6 8 7 1 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 1 , 5 0 1 2 6 7 1 1 4 5 6 8 7 1 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 1 , 5 6 5 6 7 1 2 0 2 3 0 1 1 1 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 1 , 5 6 5 6 8 8 8 8 7 1 1 2 6 7 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 0 , 5 6 8 7 1 1 2 0 1 2 3 3 3 0 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 0 , 7 4 7 1 1 2 3 6 5 3 0 1 2 0 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 7 , 8 5 0 2 3 3 3 3 6 5 0 1 2 0 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 0 , 8 5 6 8 5 6 8 5 6 5 0 1 2 0 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 0 , 8 8 5 0 1 1 2 3 3 3 6 5 3 0 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 0 , 8 8 7 1 2 3 3 3 6 8 7 1 2 0 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 0 , 8 5 3 0 1 4 8 7 2 6 8 8 8 8 -> 7 2 6 8 7 2 0 4 7 2 0 2 3 6 5 6 5 6 , 8 7 1 4 8 5 6 7 2 3 3 0 2 6 -> 7 1 4 5 3 6 5 3 0 2 3 6 5 3 3 0 2 6 , 8 7 4 8 5 6 7 2 6 5 6 7 2 6 -> 7 2 0 4 5 3 6 5 3 6 7 2 6 7 2 3 3 6 , 5 3 0 2 0 1 2 0 1 2 6 8 7 4 ->= 5 3 6 5 0 1 2 3 0 2 0 2 6 5 0 2 0 4 , 5 0 1 2 6 7 1 1 4 5 6 8 7 4 ->= 7 2 6 5 3 6 7 2 3 0 2 0 4 7 2 6 7 4 , 5 6 5 6 7 1 2 0 2 3 0 1 1 4 ->= 5 0 2 6 7 2 0 2 3 6 7 2 3 3 0 1 1 4 , 5 6 5 6 8 8 8 8 7 1 1 2 6 8 ->= 5 0 2 3 0 2 6 8 8 7 2 6 5 6 8 5 3 6 , 5 6 8 7 1 1 2 0 1 2 3 3 3 6 ->= 7 1 2 3 3 6 5 3 6 8 8 5 6 7 1 2 3 6 , 7 4 7 1 1 2 3 6 5 3 0 1 2 6 ->= 7 4 7 2 6 5 6 5 6 5 0 2 0 2 0 2 6 8 , 8 5 0 2 3 3 3 3 6 5 0 1 2 6 ->= 7 2 0 2 6 5 0 2 0 1 2 3 3 0 2 6 5 6 , 8 5 6 8 5 6 8 5 6 5 0 1 2 6 ->= 5 0 1 2 3 3 3 6 5 6 8 5 6 5 6 5 3 6 , 8 8 5 0 1 1 2 3 3 3 6 5 3 6 ->= 5 0 2 3 3 6 5 3 0 2 3 6 8 8 8 7 2 6 , 8 8 7 1 2 3 3 3 6 8 7 1 2 6 ->= 8 8 5 6 5 6 5 6 5 3 0 2 6 5 6 5 3 6 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 / \ | 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 6->0, 7->1, 1->2, 4->3, 8->4, 5->5, 2->6, 3->7, 0->8 }, it remains to prove termination of the 21-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 1 2 3 4 5 0 1 6 7 7 8 6 0 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 0 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 6 0 4 1 2 2 6 8 2 6 7 7 7 0 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 0 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 0 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 0 , 4 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 4 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 20-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 6 0 4 1 2 2 6 8 2 6 7 7 7 0 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 0 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 0 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 0 , 4 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 4 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 19-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 0 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 0 , 4 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 4 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 18-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 4 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 17-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 16-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 0 5 0 4 5 0 4 5 0 5 8 2 6 0 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 15-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 0 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 0 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 0 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 7 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 0 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 0 , 6 0 4 1 2 2 6 8 2 6 7 7 7 7 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 7 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 7 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 7 , 4 5 8 6 7 7 7 7 0 5 8 2 6 7 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 7 , 4 5 0 4 5 0 4 5 0 5 8 2 6 7 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 7 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 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, 5->1, 8->2, 6->3, 7->4, 2->5, 4->6, 1->7, 3->8 }, it remains to prove termination of the 14-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 0 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 2 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 0 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 0 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 0 , 3 0 6 7 5 5 3 2 5 3 4 4 4 4 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 4 , 3 0 6 7 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 2 , 6 7 5 8 6 1 0 7 3 4 4 2 3 4 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 4 , 6 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 6 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 6 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 6 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 13-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 0 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 2 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 0 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 , 3 0 6 7 5 5 3 2 5 3 4 4 4 4 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 4 , 3 0 6 7 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 2 , 6 7 5 8 6 1 0 7 3 4 4 2 3 4 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 4 , 6 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 6 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 6 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 6 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 12-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 0 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 2 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 0 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 , 3 0 6 7 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 2 , 6 7 5 8 6 1 0 7 3 4 4 2 3 4 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 4 , 6 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 6 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 6 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 6 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 11-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 0 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 2 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 0 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 , 3 0 6 7 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 6 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 6 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 6 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 10-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 4 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 0 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 2 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 3 0 6 7 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 6 6 1 0 7 5 3 4 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 6 1 0 6 1 0 6 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 4 , 6 7 5 8 6 1 0 7 3 4 4 2 3 2 -> 7 5 8 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 6 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 7 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 6 1 0 6 1 0 6 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 6 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 7->6, 8->7, 6->8 }, it remains to prove termination of the 9-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 2 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 3 0 8 6 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 8 8 1 0 6 5 3 4 2 , 8 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 6 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 8 1 0 8 1 0 8 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 8 1 0 1 0 1 4 4 , 8 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 6 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 8 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 6 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 8 1 0 8 1 0 8 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 8 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 8-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 2 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 3 0 8 6 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 8 8 1 0 6 5 3 4 2 , 8 1 0 8 1 0 8 1 0 1 2 5 3 4 ->= 1 2 5 3 4 4 4 0 1 0 8 1 0 1 0 1 4 4 , 8 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 6 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 8 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 6 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 8 1 0 8 1 0 8 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 8 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 7-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 4 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 4 , 0 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 2 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 3 0 8 6 5 5 3 2 5 3 4 4 4 2 ->= 5 5 3 4 4 0 1 4 0 8 8 1 0 6 5 3 4 2 , 8 6 5 7 8 1 0 6 3 4 4 2 3 2 -> 6 5 7 1 4 0 1 4 2 3 4 0 1 4 4 2 3 2 , 8 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 6 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 , 8 1 0 8 1 0 8 1 0 1 2 5 3 2 ->= 1 2 5 3 4 4 4 0 1 0 8 1 0 1 0 1 4 2 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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, 6->1, 5->2, 7->3, 8->4, 1->5, 3->6, 4->7, 2->8 }, it remains to prove termination of the 6-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 6 0 4 1 2 2 6 8 2 6 7 7 7 8 ->= 2 2 6 7 7 0 5 7 0 4 4 5 0 1 2 6 7 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 15: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8 }, it remains to prove termination of the 5-rule system { 0 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 8 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 0 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 8 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 1 2 3 4 5 0 1 6 7 7 8 6 8 -> 1 2 3 5 7 0 5 7 8 6 7 0 5 7 7 8 6 8 , 4 5 8 6 7 7 7 7 0 5 8 2 6 8 ->= 1 6 8 6 0 5 8 6 8 2 6 7 7 8 6 0 5 8 , 4 5 0 4 5 0 4 5 0 5 8 2 6 8 ->= 5 8 2 6 7 7 7 0 5 0 4 5 0 5 0 5 7 8 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 5->1, 8->2, 6->3, 7->4, 2->5 }, it remains to prove termination of the 1-rule system { 0 1 2 3 4 4 4 4 0 1 2 5 3 2 ->= 2 3 2 3 0 1 2 3 2 5 3 4 4 2 3 0 1 2 } The system is trivially terminating.