YES After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, it remains to prove termination of the 30-rule system { 0 0 0 0 0 1 1 2 0 0 3 1 3 -> 2 3 3 1 1 2 3 1 2 1 1 2 2 1 0 2 3 , 0 0 0 3 1 2 2 3 2 3 1 0 1 -> 3 2 1 3 0 1 3 1 1 2 1 3 3 3 3 1 3 , 0 0 3 0 1 1 2 1 0 1 3 3 3 -> 1 3 3 1 0 2 1 1 2 2 3 2 1 2 1 1 3 , 0 0 3 2 1 3 2 2 3 2 0 0 0 -> 1 2 1 3 2 3 2 2 3 3 1 0 0 2 1 3 3 , 0 3 0 1 3 1 3 2 2 1 2 2 0 -> 2 3 3 0 3 3 3 1 3 2 0 2 2 1 3 1 2 , 0 3 2 2 0 0 3 2 3 1 1 2 1 -> 2 0 3 3 1 2 0 3 1 2 1 2 1 1 0 3 1 , 0 3 3 3 0 1 2 3 1 1 0 0 3 -> 0 2 2 0 1 2 1 2 1 3 1 3 0 3 3 0 3 , 1 0 1 3 1 1 1 1 3 2 0 3 2 -> 3 3 3 1 3 3 0 1 0 1 2 1 2 1 1 0 3 , 1 0 3 2 3 3 0 0 1 2 1 0 1 -> 2 1 1 1 1 3 2 2 2 1 3 3 1 3 2 2 1 , 1 1 0 0 0 2 3 0 1 2 0 1 3 -> 1 2 2 2 1 3 3 2 1 1 2 1 0 2 0 2 3 , 1 1 2 1 0 2 2 0 3 0 0 0 0 -> 2 2 1 3 3 3 1 2 0 1 0 2 3 1 1 0 3 , 1 3 2 3 1 1 2 0 1 2 3 1 0 -> 1 3 2 2 0 2 3 3 0 1 2 1 2 2 1 3 1 , 2 0 3 3 3 2 2 3 2 0 0 3 3 -> 3 3 2 2 0 1 1 2 1 1 2 1 2 2 1 3 3 , 2 1 2 0 2 1 0 1 1 0 1 2 0 -> 0 0 1 1 3 3 1 1 0 0 3 3 3 3 3 3 2 , 2 2 3 1 3 2 2 0 2 2 2 2 0 -> 2 1 3 0 1 3 2 2 1 0 0 2 1 1 3 0 0 , 2 3 0 3 0 2 1 2 0 3 2 0 1 -> 2 1 3 3 0 2 2 1 3 2 0 2 2 2 1 2 1 , 2 3 1 0 1 0 0 1 1 0 1 2 1 -> 1 3 1 3 3 3 3 2 2 1 3 1 2 1 1 0 3 , 2 3 3 1 2 2 3 0 2 2 0 0 1 -> 2 3 1 2 2 1 1 3 1 3 3 3 3 0 3 0 0 , 2 3 3 1 2 2 3 2 3 1 1 0 1 -> 2 2 1 0 2 1 1 1 2 2 1 1 3 3 2 1 3 , 3 0 3 0 2 3 2 3 3 3 1 2 1 -> 2 1 2 1 3 2 1 3 2 1 2 1 3 1 3 3 1 , 3 0 3 0 2 3 3 2 3 2 2 2 1 -> 2 2 2 1 3 3 3 2 1 1 2 1 1 1 1 3 1 , 3 0 3 1 3 2 0 0 1 2 1 0 0 -> 3 1 3 0 3 3 2 2 1 1 2 2 2 1 1 0 2 , 3 1 2 3 1 1 3 1 1 3 0 1 1 -> 3 3 2 1 3 1 2 3 3 3 2 1 1 2 1 0 1 , 3 2 2 1 0 2 0 3 3 3 3 2 1 -> 3 3 3 2 3 1 1 3 3 2 1 2 1 2 1 3 1 , 3 2 3 0 1 1 3 0 0 0 0 2 1 -> 3 3 2 1 1 2 3 2 1 2 0 3 1 3 2 2 1 , 3 2 3 2 3 2 3 0 3 2 0 1 1 -> 2 2 1 1 2 1 3 3 2 0 0 0 0 0 1 3 3 , 3 3 1 3 1 2 3 2 0 2 2 0 0 -> 2 1 2 1 3 0 2 2 0 2 2 1 1 3 3 3 3 , 3 3 2 1 3 1 2 0 0 3 2 3 3 -> 3 2 1 3 2 2 1 3 3 3 1 0 2 1 3 3 3 , 3 1 2 0 1 0 3 2 0 1 2 0 0 ->= 3 1 1 2 1 0 1 1 2 2 1 2 1 3 0 2 3 , 3 3 3 1 2 1 2 2 3 0 0 0 3 ->= 3 3 3 1 2 1 1 2 1 1 0 3 3 2 2 0 3 } The system was reversed. After renaming modulo { 3->0, 1->1, 0->2, 2->3 }, it remains to prove termination of the 30-rule system { 0 1 0 2 2 3 1 1 2 2 2 2 2 -> 0 3 2 1 3 3 1 1 3 1 0 3 1 1 0 0 3 , 1 2 1 0 3 0 3 3 1 0 2 2 2 -> 0 1 0 0 0 0 1 3 1 1 0 1 2 0 1 3 0 , 0 0 0 1 2 1 3 1 1 2 0 2 2 -> 0 1 1 3 1 3 0 3 3 1 1 3 2 1 0 0 1 , 2 2 2 3 0 3 3 0 1 3 0 2 2 -> 0 0 1 3 2 2 1 0 0 3 3 0 3 0 1 3 1 , 2 3 3 1 3 3 0 1 0 1 2 0 2 -> 3 1 0 1 3 3 2 3 0 1 0 0 0 2 0 0 3 , 1 3 1 1 0 3 0 2 2 3 3 0 2 -> 1 0 2 1 1 3 1 3 1 0 2 3 1 0 0 2 3 , 0 2 2 1 1 0 3 1 2 0 0 0 2 -> 0 2 0 0 2 0 1 0 1 3 1 3 1 2 3 3 2 , 3 0 2 3 0 1 1 1 1 0 1 2 1 -> 0 2 1 1 3 1 3 1 2 1 2 0 0 1 0 0 0 , 1 2 1 3 1 2 2 0 0 3 0 2 1 -> 1 3 3 0 1 0 0 1 3 3 3 0 1 1 1 1 3 , 0 1 2 3 1 2 0 3 2 2 2 1 1 -> 0 3 2 3 2 1 3 1 1 3 0 0 1 3 3 3 1 , 2 2 2 2 0 2 3 3 2 1 3 1 1 -> 0 2 1 1 0 3 2 1 2 3 1 0 0 0 1 3 3 , 2 1 0 3 1 2 3 1 1 0 3 0 1 -> 1 0 1 3 3 1 3 1 2 0 0 3 2 3 3 0 1 , 0 0 2 2 3 0 3 3 0 0 0 2 3 -> 0 0 1 3 3 1 3 1 1 3 1 1 2 3 3 0 0 , 2 3 1 2 1 1 2 1 3 2 3 1 3 -> 3 0 0 0 0 0 0 2 2 1 1 0 0 1 1 2 2 , 2 3 3 3 3 2 3 3 0 1 0 3 3 -> 2 2 0 1 1 3 2 2 1 3 3 0 1 2 0 1 3 , 1 2 3 0 2 3 1 3 2 0 2 0 3 -> 1 3 1 3 3 3 2 3 0 1 3 3 2 0 0 1 3 , 1 3 1 2 1 1 2 2 1 2 1 0 3 -> 0 2 1 1 3 1 0 1 3 3 0 0 0 0 1 0 1 , 1 2 2 3 3 2 0 3 3 1 0 0 3 -> 2 2 0 2 0 0 0 0 1 0 1 1 3 3 1 0 3 , 1 2 1 1 0 3 0 3 3 1 0 0 3 -> 0 1 3 0 0 1 1 3 3 1 1 1 3 2 1 3 3 , 1 3 1 0 0 0 3 0 3 2 0 2 0 -> 1 0 0 1 0 1 3 1 3 0 1 3 0 1 3 1 3 , 1 3 3 3 0 3 0 0 3 2 0 2 0 -> 1 0 1 1 1 1 3 1 1 3 0 0 0 1 3 3 3 , 2 2 1 3 1 2 2 3 0 1 0 2 0 -> 3 2 1 1 3 3 3 1 1 3 3 0 0 2 0 1 0 , 1 1 2 0 1 1 0 1 1 0 3 1 0 -> 1 2 1 3 1 1 3 0 0 0 3 1 0 1 3 0 0 , 1 3 0 0 0 0 2 3 2 1 3 3 0 -> 1 0 1 3 1 3 1 3 0 0 1 1 0 3 0 0 0 , 1 3 2 2 2 2 0 1 1 2 0 3 0 -> 1 3 3 0 1 0 2 3 1 3 0 3 1 1 3 0 0 , 1 1 2 3 0 2 0 3 0 3 0 3 0 -> 0 0 1 2 2 2 2 2 3 0 0 1 3 1 1 3 3 , 2 2 3 3 2 3 0 3 1 0 1 0 0 -> 0 0 0 0 1 1 3 3 2 3 3 2 0 1 3 1 3 , 0 0 3 0 2 2 3 1 0 1 3 0 0 -> 0 0 0 1 3 2 1 0 0 0 1 3 3 0 1 3 0 , 2 2 3 1 2 3 0 2 1 2 3 1 0 ->= 0 3 2 0 1 3 1 3 3 1 1 2 1 3 1 1 0 , 0 2 2 2 0 3 3 1 3 1 0 0 0 ->= 0 2 3 3 0 0 2 1 1 3 1 1 3 1 0 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, 2]->4, [2, 3]->5, [3, 1]->6, [1, 1]->7, [1, 2]->8, [2, 0]->9, [0, 3]->10, [3, 2]->11, [2, 1]->12, [1, 3]->13, [3, 3]->14, [3, 0]->15 }, it remains to prove termination of the 480-rule system { 0 1 2 3 4 5 6 7 8 4 4 4 4 9 -> 0 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 15 , 1 8 12 2 10 15 10 14 6 2 3 4 4 9 -> 0 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 0 , 0 0 0 1 8 12 13 6 7 8 9 3 4 9 -> 0 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 2 , 3 4 4 5 15 10 14 15 1 13 15 3 4 9 -> 0 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 2 , 3 5 14 6 13 14 15 1 2 1 8 9 3 9 -> 10 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 15 , 1 13 6 7 2 10 15 3 4 5 14 15 3 9 -> 1 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 15 , 0 3 4 12 7 2 10 6 8 9 0 0 3 9 -> 0 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 9 , 10 15 3 5 15 1 7 7 7 2 1 8 12 2 -> 0 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 0 , 1 8 12 13 6 8 4 9 0 10 15 3 12 2 -> 1 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 15 , 0 1 8 5 6 8 9 10 11 4 4 12 7 2 -> 0 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 2 , 3 4 4 4 9 3 5 14 11 12 13 6 7 2 -> 0 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 15 , 3 12 2 10 6 8 5 6 7 2 10 15 1 2 -> 1 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 2 , 0 0 3 4 5 15 10 14 15 0 0 3 5 15 -> 0 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 0 , 3 5 6 8 12 7 8 12 13 11 5 6 13 15 -> 10 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 9 , 3 5 14 14 14 11 5 14 15 1 2 10 14 15 -> 3 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 15 , 1 8 5 15 3 5 6 13 11 9 3 9 10 15 -> 1 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 15 , 1 13 6 8 12 7 8 4 12 8 12 2 10 15 -> 0 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 2 , 1 8 4 5 14 11 9 10 14 6 2 0 10 15 -> 3 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 15 , 1 8 12 7 2 10 15 10 14 6 2 0 10 15 -> 0 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 15 , 1 13 6 2 0 0 10 15 10 11 9 3 9 0 -> 1 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 15 , 1 13 14 14 15 10 15 0 10 11 9 3 9 0 -> 1 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 15 , 3 4 12 13 6 8 4 5 15 1 2 3 9 0 -> 10 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 0 , 1 7 8 9 1 7 2 1 7 2 10 6 2 0 -> 1 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 0 , 1 13 15 0 0 0 3 5 11 12 13 14 15 0 -> 1 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 0 , 1 13 11 4 4 4 9 1 7 8 9 10 15 0 -> 1 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 0 , 1 7 8 5 15 3 9 10 15 10 15 10 15 0 -> 0 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 15 , 3 4 5 14 11 5 15 10 6 2 1 2 0 0 -> 0 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 15 , 0 0 10 15 3 4 5 6 2 1 13 15 0 0 -> 0 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 0 , 3 4 5 6 8 5 15 3 12 8 5 6 2 0 ->= 0 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 0 , 0 3 4 4 9 10 14 6 13 6 2 0 0 0 ->= 0 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 0 , 0 1 2 3 4 5 6 7 8 4 4 4 4 12 -> 0 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 6 , 1 8 12 2 10 15 10 14 6 2 3 4 4 12 -> 0 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 1 , 0 0 0 1 8 12 13 6 7 8 9 3 4 12 -> 0 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 7 , 3 4 4 5 15 10 14 15 1 13 15 3 4 12 -> 0 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 7 , 3 5 14 6 13 14 15 1 2 1 8 9 3 12 -> 10 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 6 , 1 13 6 7 2 10 15 3 4 5 14 15 3 12 -> 1 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 6 , 0 3 4 12 7 2 10 6 8 9 0 0 3 12 -> 0 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 12 , 10 15 3 5 15 1 7 7 7 2 1 8 12 7 -> 0 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 1 , 1 8 12 13 6 8 4 9 0 10 15 3 12 7 -> 1 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 6 , 0 1 8 5 6 8 9 10 11 4 4 12 7 7 -> 0 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 7 , 3 4 4 4 9 3 5 14 11 12 13 6 7 7 -> 0 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 6 , 3 12 2 10 6 8 5 6 7 2 10 15 1 7 -> 1 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 7 , 0 0 3 4 5 15 10 14 15 0 0 3 5 6 -> 0 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 1 , 3 5 6 8 12 7 8 12 13 11 5 6 13 6 -> 10 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 12 , 3 5 14 14 14 11 5 14 15 1 2 10 14 6 -> 3 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 6 , 1 8 5 15 3 5 6 13 11 9 3 9 10 6 -> 1 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 6 , 1 13 6 8 12 7 8 4 12 8 12 2 10 6 -> 0 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 7 , 1 8 4 5 14 11 9 10 14 6 2 0 10 6 -> 3 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 6 , 1 8 12 7 2 10 15 10 14 6 2 0 10 6 -> 0 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 6 , 1 13 6 2 0 0 10 15 10 11 9 3 9 1 -> 1 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 6 , 1 13 14 14 15 10 15 0 10 11 9 3 9 1 -> 1 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 6 , 3 4 12 13 6 8 4 5 15 1 2 3 9 1 -> 10 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 1 , 1 7 8 9 1 7 2 1 7 2 10 6 2 1 -> 1 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 1 , 1 13 15 0 0 0 3 5 11 12 13 14 15 1 -> 1 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 1 , 1 13 11 4 4 4 9 1 7 8 9 10 15 1 -> 1 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 1 , 1 7 8 5 15 3 9 10 15 10 15 10 15 1 -> 0 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 6 , 3 4 5 14 11 5 15 10 6 2 1 2 0 1 -> 0 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 6 , 0 0 10 15 3 4 5 6 2 1 13 15 0 1 -> 0 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 1 , 3 4 5 6 8 5 15 3 12 8 5 6 2 1 ->= 0 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 1 , 0 3 4 4 9 10 14 6 13 6 2 0 0 1 ->= 0 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 1 , 0 1 2 3 4 5 6 7 8 4 4 4 4 4 -> 0 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 11 , 1 8 12 2 10 15 10 14 6 2 3 4 4 4 -> 0 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 3 , 0 0 0 1 8 12 13 6 7 8 9 3 4 4 -> 0 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 8 , 3 4 4 5 15 10 14 15 1 13 15 3 4 4 -> 0 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 8 , 3 5 14 6 13 14 15 1 2 1 8 9 3 4 -> 10 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 11 , 1 13 6 7 2 10 15 3 4 5 14 15 3 4 -> 1 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 11 , 0 3 4 12 7 2 10 6 8 9 0 0 3 4 -> 0 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 4 , 10 15 3 5 15 1 7 7 7 2 1 8 12 8 -> 0 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 3 , 1 8 12 13 6 8 4 9 0 10 15 3 12 8 -> 1 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 11 , 0 1 8 5 6 8 9 10 11 4 4 12 7 8 -> 0 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 8 , 3 4 4 4 9 3 5 14 11 12 13 6 7 8 -> 0 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 11 , 3 12 2 10 6 8 5 6 7 2 10 15 1 8 -> 1 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 8 , 0 0 3 4 5 15 10 14 15 0 0 3 5 11 -> 0 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 3 , 3 5 6 8 12 7 8 12 13 11 5 6 13 11 -> 10 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 4 , 3 5 14 14 14 11 5 14 15 1 2 10 14 11 -> 3 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 11 , 1 8 5 15 3 5 6 13 11 9 3 9 10 11 -> 1 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 11 , 1 13 6 8 12 7 8 4 12 8 12 2 10 11 -> 0 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 8 , 1 8 4 5 14 11 9 10 14 6 2 0 10 11 -> 3 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 11 , 1 8 12 7 2 10 15 10 14 6 2 0 10 11 -> 0 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 11 , 1 13 6 2 0 0 10 15 10 11 9 3 9 3 -> 1 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 11 , 1 13 14 14 15 10 15 0 10 11 9 3 9 3 -> 1 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 11 , 3 4 12 13 6 8 4 5 15 1 2 3 9 3 -> 10 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 3 , 1 7 8 9 1 7 2 1 7 2 10 6 2 3 -> 1 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 3 , 1 13 15 0 0 0 3 5 11 12 13 14 15 3 -> 1 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 3 , 1 13 11 4 4 4 9 1 7 8 9 10 15 3 -> 1 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 3 , 1 7 8 5 15 3 9 10 15 10 15 10 15 3 -> 0 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 11 , 3 4 5 14 11 5 15 10 6 2 1 2 0 3 -> 0 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 11 , 0 0 10 15 3 4 5 6 2 1 13 15 0 3 -> 0 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 3 , 3 4 5 6 8 5 15 3 12 8 5 6 2 3 ->= 0 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 3 , 0 3 4 4 9 10 14 6 13 6 2 0 0 3 ->= 0 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 3 , 0 1 2 3 4 5 6 7 8 4 4 4 4 5 -> 0 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 14 , 1 8 12 2 10 15 10 14 6 2 3 4 4 5 -> 0 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 10 , 0 0 0 1 8 12 13 6 7 8 9 3 4 5 -> 0 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 13 , 3 4 4 5 15 10 14 15 1 13 15 3 4 5 -> 0 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 13 , 3 5 14 6 13 14 15 1 2 1 8 9 3 5 -> 10 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 14 , 1 13 6 7 2 10 15 3 4 5 14 15 3 5 -> 1 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 14 , 0 3 4 12 7 2 10 6 8 9 0 0 3 5 -> 0 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 5 , 10 15 3 5 15 1 7 7 7 2 1 8 12 13 -> 0 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 10 , 1 8 12 13 6 8 4 9 0 10 15 3 12 13 -> 1 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 14 , 0 1 8 5 6 8 9 10 11 4 4 12 7 13 -> 0 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 13 , 3 4 4 4 9 3 5 14 11 12 13 6 7 13 -> 0 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 14 , 3 12 2 10 6 8 5 6 7 2 10 15 1 13 -> 1 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 13 , 0 0 3 4 5 15 10 14 15 0 0 3 5 14 -> 0 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 10 , 3 5 6 8 12 7 8 12 13 11 5 6 13 14 -> 10 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 5 , 3 5 14 14 14 11 5 14 15 1 2 10 14 14 -> 3 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 14 , 1 8 5 15 3 5 6 13 11 9 3 9 10 14 -> 1 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 14 , 1 13 6 8 12 7 8 4 12 8 12 2 10 14 -> 0 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 13 , 1 8 4 5 14 11 9 10 14 6 2 0 10 14 -> 3 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 14 , 1 8 12 7 2 10 15 10 14 6 2 0 10 14 -> 0 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 14 , 1 13 6 2 0 0 10 15 10 11 9 3 9 10 -> 1 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 14 , 1 13 14 14 15 10 15 0 10 11 9 3 9 10 -> 1 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 14 , 3 4 12 13 6 8 4 5 15 1 2 3 9 10 -> 10 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 10 , 1 7 8 9 1 7 2 1 7 2 10 6 2 10 -> 1 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 10 , 1 13 15 0 0 0 3 5 11 12 13 14 15 10 -> 1 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 10 , 1 13 11 4 4 4 9 1 7 8 9 10 15 10 -> 1 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 10 , 1 7 8 5 15 3 9 10 15 10 15 10 15 10 -> 0 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 14 , 3 4 5 14 11 5 15 10 6 2 1 2 0 10 -> 0 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 14 , 0 0 10 15 3 4 5 6 2 1 13 15 0 10 -> 0 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 10 , 3 4 5 6 8 5 15 3 12 8 5 6 2 10 ->= 0 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 10 , 0 3 4 4 9 10 14 6 13 6 2 0 0 10 ->= 0 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 10 , 2 1 2 3 4 5 6 7 8 4 4 4 4 9 -> 2 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 15 , 7 8 12 2 10 15 10 14 6 2 3 4 4 9 -> 2 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 0 , 2 0 0 1 8 12 13 6 7 8 9 3 4 9 -> 2 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 2 , 8 4 4 5 15 10 14 15 1 13 15 3 4 9 -> 2 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 2 , 8 5 14 6 13 14 15 1 2 1 8 9 3 9 -> 13 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 15 , 7 13 6 7 2 10 15 3 4 5 14 15 3 9 -> 7 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 15 , 2 3 4 12 7 2 10 6 8 9 0 0 3 9 -> 2 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 9 , 13 15 3 5 15 1 7 7 7 2 1 8 12 2 -> 2 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 0 , 7 8 12 13 6 8 4 9 0 10 15 3 12 2 -> 7 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 15 , 2 1 8 5 6 8 9 10 11 4 4 12 7 2 -> 2 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 2 , 8 4 4 4 9 3 5 14 11 12 13 6 7 2 -> 2 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 15 , 8 12 2 10 6 8 5 6 7 2 10 15 1 2 -> 7 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 2 , 2 0 3 4 5 15 10 14 15 0 0 3 5 15 -> 2 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 0 , 8 5 6 8 12 7 8 12 13 11 5 6 13 15 -> 13 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 9 , 8 5 14 14 14 11 5 14 15 1 2 10 14 15 -> 8 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 15 , 7 8 5 15 3 5 6 13 11 9 3 9 10 15 -> 7 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 15 , 7 13 6 8 12 7 8 4 12 8 12 2 10 15 -> 2 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 2 , 7 8 4 5 14 11 9 10 14 6 2 0 10 15 -> 8 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 15 , 7 8 12 7 2 10 15 10 14 6 2 0 10 15 -> 2 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 15 , 7 13 6 2 0 0 10 15 10 11 9 3 9 0 -> 7 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 15 , 7 13 14 14 15 10 15 0 10 11 9 3 9 0 -> 7 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 15 , 8 4 12 13 6 8 4 5 15 1 2 3 9 0 -> 13 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 0 , 7 7 8 9 1 7 2 1 7 2 10 6 2 0 -> 7 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 0 , 7 13 15 0 0 0 3 5 11 12 13 14 15 0 -> 7 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 0 , 7 13 11 4 4 4 9 1 7 8 9 10 15 0 -> 7 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 0 , 7 7 8 5 15 3 9 10 15 10 15 10 15 0 -> 2 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 15 , 8 4 5 14 11 5 15 10 6 2 1 2 0 0 -> 2 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 15 , 2 0 10 15 3 4 5 6 2 1 13 15 0 0 -> 2 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 0 , 8 4 5 6 8 5 15 3 12 8 5 6 2 0 ->= 2 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 0 , 2 3 4 4 9 10 14 6 13 6 2 0 0 0 ->= 2 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 0 , 2 1 2 3 4 5 6 7 8 4 4 4 4 12 -> 2 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 6 , 7 8 12 2 10 15 10 14 6 2 3 4 4 12 -> 2 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 1 , 2 0 0 1 8 12 13 6 7 8 9 3 4 12 -> 2 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 7 , 8 4 4 5 15 10 14 15 1 13 15 3 4 12 -> 2 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 7 , 8 5 14 6 13 14 15 1 2 1 8 9 3 12 -> 13 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 6 , 7 13 6 7 2 10 15 3 4 5 14 15 3 12 -> 7 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 6 , 2 3 4 12 7 2 10 6 8 9 0 0 3 12 -> 2 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 12 , 13 15 3 5 15 1 7 7 7 2 1 8 12 7 -> 2 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 1 , 7 8 12 13 6 8 4 9 0 10 15 3 12 7 -> 7 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 6 , 2 1 8 5 6 8 9 10 11 4 4 12 7 7 -> 2 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 7 , 8 4 4 4 9 3 5 14 11 12 13 6 7 7 -> 2 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 6 , 8 12 2 10 6 8 5 6 7 2 10 15 1 7 -> 7 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 7 , 2 0 3 4 5 15 10 14 15 0 0 3 5 6 -> 2 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 1 , 8 5 6 8 12 7 8 12 13 11 5 6 13 6 -> 13 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 12 , 8 5 14 14 14 11 5 14 15 1 2 10 14 6 -> 8 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 6 , 7 8 5 15 3 5 6 13 11 9 3 9 10 6 -> 7 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 6 , 7 13 6 8 12 7 8 4 12 8 12 2 10 6 -> 2 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 7 , 7 8 4 5 14 11 9 10 14 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12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 10 , 12 13 15 0 0 0 3 5 11 12 13 14 15 10 -> 12 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 10 , 12 13 11 4 4 4 9 1 7 8 9 10 15 10 -> 12 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 10 , 12 7 8 5 15 3 9 10 15 10 15 10 15 10 -> 9 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 14 , 4 4 5 14 11 5 15 10 6 2 1 2 0 10 -> 9 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 14 , 9 0 10 15 3 4 5 6 2 1 13 15 0 10 -> 9 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 10 , 4 4 5 6 8 5 15 3 12 8 5 6 2 10 ->= 9 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 10 , 9 3 4 4 9 10 14 6 13 6 2 0 0 10 ->= 9 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 10 , 15 1 2 3 4 5 6 7 8 4 4 4 4 9 -> 15 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 15 , 6 8 12 2 10 15 10 14 6 2 3 4 4 9 -> 15 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 0 , 15 0 0 1 8 12 13 6 7 8 9 3 4 9 -> 15 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 2 , 11 4 4 5 15 10 14 15 1 13 15 3 4 9 -> 15 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 2 , 11 5 14 6 13 14 15 1 2 1 8 9 3 9 -> 14 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 15 , 6 13 6 7 2 10 15 3 4 5 14 15 3 9 -> 6 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 15 , 15 3 4 12 7 2 10 6 8 9 0 0 3 9 -> 15 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 9 , 14 15 3 5 15 1 7 7 7 2 1 8 12 2 -> 15 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 0 , 6 8 12 13 6 8 4 9 0 10 15 3 12 2 -> 6 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 15 , 15 1 8 5 6 8 9 10 11 4 4 12 7 2 -> 15 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 2 , 11 4 4 4 9 3 5 14 11 12 13 6 7 2 -> 15 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 15 , 11 12 2 10 6 8 5 6 7 2 10 15 1 2 -> 6 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 2 , 15 0 3 4 5 15 10 14 15 0 0 3 5 15 -> 15 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 0 , 11 5 6 8 12 7 8 12 13 11 5 6 13 15 -> 14 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 9 , 11 5 14 14 14 11 5 14 15 1 2 10 14 15 -> 11 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 15 , 6 8 5 15 3 5 6 13 11 9 3 9 10 15 -> 6 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 15 , 6 13 6 8 12 7 8 4 12 8 12 2 10 15 -> 15 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 2 , 6 8 4 5 14 11 9 10 14 6 2 0 10 15 -> 11 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 15 , 6 8 12 7 2 10 15 10 14 6 2 0 10 15 -> 15 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 15 , 6 13 6 2 0 0 10 15 10 11 9 3 9 0 -> 6 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 15 , 6 13 14 14 15 10 15 0 10 11 9 3 9 0 -> 6 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 15 , 11 4 12 13 6 8 4 5 15 1 2 3 9 0 -> 14 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 0 , 6 7 8 9 1 7 2 1 7 2 10 6 2 0 -> 6 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 0 , 6 13 15 0 0 0 3 5 11 12 13 14 15 0 -> 6 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 0 , 6 13 11 4 4 4 9 1 7 8 9 10 15 0 -> 6 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 0 , 6 7 8 5 15 3 9 10 15 10 15 10 15 0 -> 15 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 15 , 11 4 5 14 11 5 15 10 6 2 1 2 0 0 -> 15 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 15 , 15 0 10 15 3 4 5 6 2 1 13 15 0 0 -> 15 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 0 , 11 4 5 6 8 5 15 3 12 8 5 6 2 0 ->= 15 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 0 , 15 3 4 4 9 10 14 6 13 6 2 0 0 0 ->= 15 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 0 , 15 1 2 3 4 5 6 7 8 4 4 4 4 12 -> 15 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 6 , 6 8 12 2 10 15 10 14 6 2 3 4 4 12 -> 15 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 1 , 15 0 0 1 8 12 13 6 7 8 9 3 4 12 -> 15 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 7 , 11 4 4 5 15 10 14 15 1 13 15 3 4 12 -> 15 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 7 , 11 5 14 6 13 14 15 1 2 1 8 9 3 12 -> 14 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 6 , 6 13 6 7 2 10 15 3 4 5 14 15 3 12 -> 6 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 6 , 15 3 4 12 7 2 10 6 8 9 0 0 3 12 -> 15 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 12 , 14 15 3 5 15 1 7 7 7 2 1 8 12 7 -> 15 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 1 , 6 8 12 13 6 8 4 9 0 10 15 3 12 7 -> 6 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 6 , 15 1 8 5 6 8 9 10 11 4 4 12 7 7 -> 15 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 7 , 11 4 4 4 9 3 5 14 11 12 13 6 7 7 -> 15 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 6 , 11 12 2 10 6 8 5 6 7 2 10 15 1 7 -> 6 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 7 , 15 0 3 4 5 15 10 14 15 0 0 3 5 6 -> 15 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 1 , 11 5 6 8 12 7 8 12 13 11 5 6 13 6 -> 14 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 12 , 11 5 14 14 14 11 5 14 15 1 2 10 14 6 -> 11 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 6 , 6 8 5 15 3 5 6 13 11 9 3 9 10 6 -> 6 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 6 , 6 13 6 8 12 7 8 4 12 8 12 2 10 6 -> 15 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 7 , 6 8 4 5 14 11 9 10 14 6 2 0 10 6 -> 11 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 6 , 6 8 12 7 2 10 15 10 14 6 2 0 10 6 -> 15 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 6 , 6 13 6 2 0 0 10 15 10 11 9 3 9 1 -> 6 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 6 , 6 13 14 14 15 10 15 0 10 11 9 3 9 1 -> 6 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 6 , 11 4 12 13 6 8 4 5 15 1 2 3 9 1 -> 14 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 1 , 6 7 8 9 1 7 2 1 7 2 10 6 2 1 -> 6 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 1 , 6 13 15 0 0 0 3 5 11 12 13 14 15 1 -> 6 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 1 , 6 13 11 4 4 4 9 1 7 8 9 10 15 1 -> 6 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 1 , 6 7 8 5 15 3 9 10 15 10 15 10 15 1 -> 15 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 6 , 11 4 5 14 11 5 15 10 6 2 1 2 0 1 -> 15 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 6 , 15 0 10 15 3 4 5 6 2 1 13 15 0 1 -> 15 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 1 , 11 4 5 6 8 5 15 3 12 8 5 6 2 1 ->= 15 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 1 , 15 3 4 4 9 10 14 6 13 6 2 0 0 1 ->= 15 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 1 , 15 1 2 3 4 5 6 7 8 4 4 4 4 4 -> 15 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 11 , 6 8 12 2 10 15 10 14 6 2 3 4 4 4 -> 15 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 3 , 15 0 0 1 8 12 13 6 7 8 9 3 4 4 -> 15 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 8 , 11 4 4 5 15 10 14 15 1 13 15 3 4 4 -> 15 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 8 , 11 5 14 6 13 14 15 1 2 1 8 9 3 4 -> 14 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 11 , 6 13 6 7 2 10 15 3 4 5 14 15 3 4 -> 6 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 11 , 15 3 4 12 7 2 10 6 8 9 0 0 3 4 -> 15 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 4 , 14 15 3 5 15 1 7 7 7 2 1 8 12 8 -> 15 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 3 , 6 8 12 13 6 8 4 9 0 10 15 3 12 8 -> 6 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 11 , 15 1 8 5 6 8 9 10 11 4 4 12 7 8 -> 15 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 8 , 11 4 4 4 9 3 5 14 11 12 13 6 7 8 -> 15 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 11 , 11 12 2 10 6 8 5 6 7 2 10 15 1 8 -> 6 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 8 , 15 0 3 4 5 15 10 14 15 0 0 3 5 11 -> 15 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 3 , 11 5 6 8 12 7 8 12 13 11 5 6 13 11 -> 14 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 4 , 11 5 14 14 14 11 5 14 15 1 2 10 14 11 -> 11 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 11 , 6 8 5 15 3 5 6 13 11 9 3 9 10 11 -> 6 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 11 , 6 13 6 8 12 7 8 4 12 8 12 2 10 11 -> 15 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 8 , 6 8 4 5 14 11 9 10 14 6 2 0 10 11 -> 11 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 11 , 6 8 12 7 2 10 15 10 14 6 2 0 10 11 -> 15 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 11 , 6 13 6 2 0 0 10 15 10 11 9 3 9 3 -> 6 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 11 , 6 13 14 14 15 10 15 0 10 11 9 3 9 3 -> 6 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 11 , 11 4 12 13 6 8 4 5 15 1 2 3 9 3 -> 14 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 3 , 6 7 8 9 1 7 2 1 7 2 10 6 2 3 -> 6 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 3 , 6 13 15 0 0 0 3 5 11 12 13 14 15 3 -> 6 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 3 , 6 13 11 4 4 4 9 1 7 8 9 10 15 3 -> 6 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 3 , 6 7 8 5 15 3 9 10 15 10 15 10 15 3 -> 15 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 11 , 11 4 5 14 11 5 15 10 6 2 1 2 0 3 -> 15 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 11 , 15 0 10 15 3 4 5 6 2 1 13 15 0 3 -> 15 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 3 , 11 4 5 6 8 5 15 3 12 8 5 6 2 3 ->= 15 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 3 , 15 3 4 4 9 10 14 6 13 6 2 0 0 3 ->= 15 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 3 , 15 1 2 3 4 5 6 7 8 4 4 4 4 5 -> 15 10 11 12 13 14 6 7 13 6 2 10 6 7 2 0 10 14 , 6 8 12 2 10 15 10 14 6 2 3 4 4 5 -> 15 1 2 0 0 0 1 13 6 7 2 1 8 9 1 13 15 10 , 15 0 0 1 8 12 13 6 7 8 9 3 4 5 -> 15 1 7 13 6 13 15 10 14 6 7 13 11 12 2 0 1 13 , 11 4 4 5 15 10 14 15 1 13 15 3 4 5 -> 15 0 1 13 11 4 12 2 0 10 14 15 10 15 1 13 6 13 , 11 5 14 6 13 14 15 1 2 1 8 9 3 5 -> 14 6 2 1 13 14 11 5 15 1 2 0 0 3 9 0 10 14 , 6 13 6 7 2 10 15 3 4 5 14 15 3 5 -> 6 2 3 12 7 13 6 13 6 2 3 5 6 2 0 3 5 14 , 15 3 4 12 7 2 10 6 8 9 0 0 3 5 -> 15 3 9 0 3 9 1 2 1 13 6 13 6 8 5 14 11 5 , 14 15 3 5 15 1 7 7 7 2 1 8 12 13 -> 15 3 12 7 13 6 13 6 8 12 8 9 0 1 2 0 0 10 , 6 8 12 13 6 8 4 9 0 10 15 3 12 13 -> 6 13 14 15 1 2 0 1 13 14 14 15 1 7 7 7 13 14 , 15 1 8 5 6 8 9 10 11 4 4 12 7 13 -> 15 10 11 5 11 12 13 6 7 13 15 0 1 13 14 14 6 13 , 11 4 4 4 9 3 5 14 11 12 13 6 7 13 -> 15 3 12 7 2 10 11 12 8 5 6 2 0 0 1 13 14 14 , 11 12 2 10 6 8 5 6 7 2 10 15 1 13 -> 6 2 1 13 14 6 13 6 8 9 0 10 11 5 14 15 1 13 , 15 0 3 4 5 15 10 14 15 0 0 3 5 14 -> 15 0 1 13 14 6 13 6 7 13 6 7 8 5 14 15 0 10 , 11 5 6 8 12 7 8 12 13 11 5 6 13 14 -> 14 15 0 0 0 0 0 3 4 12 7 2 0 1 7 8 4 5 , 11 5 14 14 14 11 5 14 15 1 2 10 14 14 -> 11 4 9 1 7 13 11 4 12 13 14 15 1 8 9 1 13 14 , 6 8 5 15 3 5 6 13 11 9 3 9 10 14 -> 6 13 6 13 14 14 11 5 15 1 13 14 11 9 0 1 13 14 , 6 13 6 8 12 7 8 4 12 8 12 2 10 14 -> 15 3 12 7 13 6 2 1 13 14 15 0 0 0 1 2 1 13 , 6 8 4 5 14 11 9 10 14 6 2 0 10 14 -> 11 4 9 3 9 0 0 0 1 2 1 7 13 14 6 2 10 14 , 6 8 12 7 2 10 15 10 14 6 2 0 10 14 -> 15 1 13 15 0 1 7 13 14 6 7 7 13 11 12 13 14 14 , 6 13 6 2 0 0 10 15 10 11 9 3 9 10 -> 6 2 0 1 2 1 13 6 13 15 1 13 15 1 13 6 13 14 , 6 13 14 14 15 10 15 0 10 11 9 3 9 10 -> 6 2 1 7 7 7 13 6 7 13 15 0 0 1 13 14 14 14 , 11 4 12 13 6 8 4 5 15 1 2 3 9 10 -> 14 11 12 7 13 14 14 6 7 13 14 15 0 3 9 1 2 10 , 6 7 8 9 1 7 2 1 7 2 10 6 2 10 -> 6 8 12 13 6 7 13 15 0 0 10 6 2 1 13 15 0 10 , 6 13 15 0 0 0 3 5 11 12 13 14 15 10 -> 6 2 1 13 6 13 6 13 15 0 1 7 2 10 15 0 0 10 , 6 13 11 4 4 4 9 1 7 8 9 10 15 10 -> 6 13 14 15 1 2 3 5 6 13 15 10 6 7 13 15 0 10 , 6 7 8 5 15 3 9 10 15 10 15 10 15 10 -> 15 0 1 8 4 4 4 4 5 15 0 1 13 6 7 13 14 14 , 11 4 5 14 11 5 15 10 6 2 1 2 0 10 -> 15 0 0 0 1 7 13 14 11 5 14 11 9 1 13 6 13 14 , 15 0 10 15 3 4 5 6 2 1 13 15 0 10 -> 15 0 0 1 13 11 12 2 0 0 1 13 14 15 1 13 15 10 , 11 4 5 6 8 5 15 3 12 8 5 6 2 10 ->= 15 10 11 9 1 13 6 13 14 6 7 8 12 13 6 7 2 10 , 15 3 4 4 9 10 14 6 13 6 2 0 0 10 ->= 15 3 5 14 15 0 3 12 7 13 6 7 13 6 2 0 0 10 } 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 11 | | 0 1 | \ / 4 is interpreted by / \ | 1 25 | | 0 1 | \ / 5 is interpreted by / \ | 1 42 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 12 | | 0 1 | \ / 8 is interpreted by / \ | 1 44 | | 0 1 | \ / 9 is interpreted by / \ | 1 8 | | 0 1 | \ / 10 is interpreted by / \ | 1 28 | | 0 1 | \ / 11 is interpreted by / \ | 1 6 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 8 | | 0 1 | \ / 15 is interpreted by / \ | 1 8 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.