YES After renaming modulo { 0->0, 1->1, 2->2, 3->3 }, it remains to prove termination of the 29-rule system { 0 0 0 1 1 1 2 3 3 1 3 3 2 -> 0 2 2 1 0 1 2 3 0 0 3 2 2 3 1 2 2 , 0 0 0 3 3 1 1 1 3 3 1 3 2 -> 3 0 2 1 0 3 3 3 1 2 2 2 1 2 1 2 2 , 0 0 2 0 3 1 3 2 1 0 0 2 3 -> 0 2 2 2 1 3 3 3 2 2 0 3 1 3 2 1 2 , 0 1 0 0 3 3 2 1 2 0 1 2 3 -> 3 2 2 1 2 2 0 3 0 2 2 2 1 2 2 3 1 , 0 1 2 0 1 1 0 2 2 1 2 0 2 -> 2 0 3 3 2 2 1 0 3 3 3 3 2 2 2 3 3 , 0 1 2 1 1 1 2 2 0 1 3 2 0 -> 2 3 2 0 1 2 3 0 3 3 2 1 3 3 1 3 3 , 0 2 2 0 0 3 1 0 3 2 1 3 0 -> 3 1 2 2 1 3 3 2 2 3 0 2 2 1 1 1 0 , 0 2 3 3 1 0 3 3 0 2 3 1 1 -> 2 1 3 2 2 2 0 2 2 2 3 3 2 2 2 0 3 , 0 3 0 3 0 2 3 0 0 3 1 2 1 -> 3 1 1 2 2 3 0 1 2 2 2 2 3 2 2 2 0 , 0 3 0 3 1 0 1 2 2 0 3 1 3 -> 2 3 2 2 3 0 3 0 3 3 2 2 1 2 2 0 3 , 1 0 0 1 2 2 2 3 2 3 2 0 1 -> 1 2 1 0 2 2 1 2 1 0 3 3 2 2 2 3 3 , 1 0 2 3 0 3 2 3 2 2 3 2 3 -> 1 3 2 2 1 2 2 2 3 3 2 2 3 1 2 1 2 , 1 3 1 0 1 1 3 2 2 1 1 2 1 -> 1 2 3 2 3 2 1 2 2 2 2 2 2 0 1 2 2 , 2 0 0 1 3 0 3 1 3 0 1 2 1 -> 2 2 3 3 0 1 0 0 3 3 3 1 0 2 2 1 2 , 2 0 0 2 3 0 3 1 0 0 2 1 3 -> 2 0 2 1 2 2 2 2 3 2 3 1 3 3 1 3 1 , 2 1 0 2 2 0 0 1 3 2 0 3 3 -> 2 0 2 2 1 3 2 1 1 1 2 2 1 3 3 3 3 , 2 1 0 3 0 3 0 3 3 0 2 1 1 -> 2 2 0 1 2 1 1 0 2 2 2 3 2 3 0 2 2 , 2 1 1 2 0 1 1 3 0 2 3 0 1 -> 2 2 3 3 3 3 3 2 1 0 1 2 2 3 3 2 2 , 2 1 1 3 3 0 3 2 3 2 1 1 3 -> 2 3 2 3 2 2 3 3 2 1 2 2 3 3 0 1 3 , 2 1 1 3 3 3 0 3 0 3 0 0 2 -> 2 0 2 2 0 2 1 3 3 3 2 3 3 2 3 3 2 , 2 2 0 0 1 0 2 3 0 3 0 1 0 -> 2 2 2 1 0 2 0 1 3 1 3 0 3 3 3 3 2 , 2 2 0 0 3 0 2 2 3 0 1 3 3 -> 2 2 1 1 0 1 2 1 2 0 2 2 2 0 2 2 2 , 2 2 0 3 0 1 0 2 3 2 3 1 2 -> 2 2 0 2 2 2 1 0 0 3 1 3 1 3 3 2 2 , 2 2 1 0 2 1 2 1 1 0 1 2 0 -> 2 2 0 2 0 3 1 2 2 0 1 2 2 2 2 2 2 , 2 3 1 1 0 2 3 1 2 3 3 1 1 -> 2 2 2 1 2 1 1 2 0 2 0 0 3 0 1 3 3 , 2 3 2 0 3 0 1 3 2 2 2 0 2 -> 2 1 2 2 3 0 0 1 3 2 2 3 2 2 3 3 2 , 2 3 2 1 1 1 3 2 3 2 3 2 1 -> 2 2 2 0 3 2 2 0 2 3 2 3 0 2 2 0 2 , 3 0 2 3 0 1 0 3 3 0 0 1 0 -> 3 0 0 1 2 2 3 3 3 2 0 1 2 0 3 3 2 , 1 3 2 0 2 1 2 1 2 2 1 2 0 ->= 3 2 1 2 1 2 2 1 2 2 0 2 2 0 2 2 2 } The system was reversed. After renaming modulo { 2->0, 3->1, 1->2, 0->3 }, it remains to prove termination of the 29-rule system { 0 1 1 2 1 1 0 2 2 2 3 3 3 -> 0 0 2 1 0 0 1 3 3 1 0 2 3 2 0 0 3 , 0 1 2 1 1 2 2 2 1 1 3 3 3 -> 0 0 2 0 2 0 0 0 2 1 1 1 3 2 0 3 1 , 1 0 3 3 2 0 1 2 1 3 0 3 3 -> 0 2 0 1 2 1 3 0 0 1 1 1 2 0 0 0 3 , 1 0 2 3 0 2 0 1 1 3 3 2 3 -> 2 1 0 0 2 0 0 0 3 1 3 0 0 2 0 0 1 , 0 3 0 2 0 0 3 2 2 3 0 2 3 -> 1 1 0 0 0 1 1 1 1 3 2 0 0 1 1 3 0 , 3 0 1 2 3 0 0 2 2 2 0 2 3 -> 1 1 2 1 1 2 0 1 1 3 1 0 2 3 0 1 0 , 3 1 2 0 1 3 2 1 3 3 0 0 3 -> 3 2 2 2 0 0 3 1 0 0 1 1 2 0 0 2 1 , 2 2 1 0 3 1 1 3 2 1 1 0 3 -> 1 3 0 0 0 1 1 0 0 0 3 0 0 0 1 2 0 , 2 0 2 1 3 3 1 0 3 1 3 1 3 -> 3 0 0 0 1 0 0 0 0 2 3 1 0 0 2 2 1 , 1 2 1 3 0 0 2 3 2 1 3 1 3 -> 1 3 0 0 2 0 0 1 1 3 1 3 1 0 0 1 0 , 2 3 0 1 0 1 0 0 0 2 3 3 2 -> 1 1 0 0 0 1 1 3 2 0 2 0 0 3 2 0 2 , 1 0 1 0 0 1 0 1 3 1 0 3 2 -> 0 2 0 2 1 0 0 1 1 0 0 0 2 0 0 1 2 , 2 0 2 2 0 0 1 2 2 3 2 1 2 -> 0 0 2 3 0 0 0 0 0 0 2 0 1 0 1 0 2 , 2 0 2 3 1 2 1 3 1 2 3 3 0 -> 0 2 0 0 3 2 1 1 1 3 3 2 3 1 1 0 0 , 1 2 0 3 3 2 1 3 1 0 3 3 0 -> 2 1 2 1 1 2 1 0 1 0 0 0 0 2 0 3 0 , 1 1 3 0 1 2 3 3 0 0 3 2 0 -> 1 1 1 1 2 0 0 2 2 2 0 1 2 0 0 3 0 , 2 2 0 3 1 1 3 1 3 1 3 2 0 -> 0 0 3 1 0 1 0 0 0 3 2 2 0 2 3 0 0 , 2 3 1 0 3 1 2 2 3 0 2 2 0 -> 0 0 1 1 0 0 2 3 2 0 1 1 1 1 1 0 0 , 1 2 2 0 1 0 1 3 1 1 2 2 0 -> 1 2 3 1 1 0 0 2 0 1 1 0 0 1 0 1 0 , 0 3 3 1 3 1 3 1 1 1 2 2 0 -> 0 1 1 0 1 1 0 1 1 1 2 0 3 0 0 3 0 , 3 2 3 1 3 1 0 3 2 3 3 0 0 -> 0 1 1 1 1 3 1 2 1 2 3 0 3 2 0 0 0 , 1 1 2 3 1 0 0 3 1 3 3 0 0 -> 0 0 0 3 0 0 0 3 0 2 0 2 3 2 2 0 0 , 0 2 1 0 1 0 3 2 3 1 3 0 0 -> 0 0 1 1 2 1 2 1 3 3 2 0 0 0 3 0 0 , 3 0 2 3 2 2 0 2 0 3 2 0 0 -> 0 0 0 0 0 0 2 3 0 0 2 1 3 0 3 0 0 , 2 2 1 1 0 2 1 0 3 2 2 1 0 -> 1 1 2 3 1 3 3 0 3 0 2 2 0 2 0 0 0 , 0 3 0 0 0 1 2 3 1 3 0 1 0 -> 0 1 1 0 0 1 0 0 1 2 3 3 1 0 0 2 0 , 2 0 1 0 1 0 1 2 2 2 0 1 0 -> 0 3 0 0 3 1 0 1 0 3 0 0 1 3 0 0 0 , 3 2 3 3 1 1 3 2 3 1 0 3 1 -> 0 1 1 3 0 2 3 0 1 1 1 0 0 2 3 3 1 , 3 0 2 0 0 2 0 2 0 3 0 1 2 ->= 0 0 0 3 0 0 3 0 0 2 0 0 2 0 2 0 1 } 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, 1]->2, [1, 2]->3, [2, 1]->4, [1, 0]->5, [0, 2]->6, [2, 2]->7, [2, 3]->8, [3, 3]->9, [3, 0]->10, [1, 3]->11, [3, 1]->12, [3, 2]->13, [2, 0]->14, [0, 3]->15 }, it remains to prove termination of the 464-rule system { 0 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 0 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 1 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 1 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 0 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 15 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 15 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 6 7 4 5 15 12 2 11 13 4 2 5 15 10 -> 1 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 0 , 6 14 6 4 11 9 12 5 15 12 11 12 11 10 -> 15 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 5 , 1 3 4 11 10 0 6 8 13 4 11 12 11 10 -> 1 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 0 , 6 8 10 1 5 1 5 0 0 6 8 9 13 14 -> 1 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 14 , 1 5 1 5 0 1 5 1 11 12 5 15 13 14 -> 0 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 14 , 6 14 6 7 14 0 1 3 7 8 13 4 3 14 -> 0 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 14 , 6 14 6 8 12 3 4 11 12 3 8 9 10 0 -> 0 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 0 , 1 3 14 15 9 13 4 11 12 5 15 9 10 0 -> 6 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 0 , 1 2 11 10 1 3 8 9 10 0 15 13 14 0 -> 1 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 0 , 6 7 14 15 12 2 11 12 11 12 11 13 14 0 -> 0 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 0 , 6 8 12 5 15 12 3 7 8 10 6 7 14 0 -> 0 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 0 , 1 3 7 14 1 5 1 11 12 2 3 7 14 0 -> 1 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 0 , 0 15 9 12 11 12 11 12 2 2 3 7 14 0 -> 0 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 0 , 15 13 8 12 11 12 5 15 13 8 9 10 0 0 -> 0 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 0 , 1 2 3 8 12 5 0 15 12 11 9 10 0 0 -> 0 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 0 , 0 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 15 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 6 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 0 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 6 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 15 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 15 10 6 14 0 6 14 6 14 15 10 1 3 14 ->= 0 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 5 , 0 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 0 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 1 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 1 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 0 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 15 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 15 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 6 7 4 5 15 12 2 11 13 4 2 5 15 12 -> 1 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 1 , 6 14 6 4 11 9 12 5 15 12 11 12 11 12 -> 15 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 2 , 1 3 4 11 10 0 6 8 13 4 11 12 11 12 -> 1 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 1 , 6 8 10 1 5 1 5 0 0 6 8 9 13 4 -> 1 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 4 , 1 5 1 5 0 1 5 1 11 12 5 15 13 4 -> 0 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 4 , 6 14 6 7 14 0 1 3 7 8 13 4 3 4 -> 0 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 4 , 6 14 6 8 12 3 4 11 12 3 8 9 10 1 -> 0 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 1 , 1 3 14 15 9 13 4 11 12 5 15 9 10 1 -> 6 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 1 , 1 2 11 10 1 3 8 9 10 0 15 13 14 1 -> 1 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 1 , 6 7 14 15 12 2 11 12 11 12 11 13 14 1 -> 0 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 1 , 6 8 12 5 15 12 3 7 8 10 6 7 14 1 -> 0 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 1 , 1 3 7 14 1 5 1 11 12 2 3 7 14 1 -> 1 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 1 , 0 15 9 12 11 12 11 12 2 2 3 7 14 1 -> 0 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 1 , 15 13 8 12 11 12 5 15 13 8 9 10 0 1 -> 0 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 1 , 1 2 3 8 12 5 0 15 12 11 9 10 0 1 -> 0 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 1 , 0 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 15 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 6 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 0 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 6 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 15 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 15 10 6 14 0 6 14 6 14 15 10 1 3 4 ->= 0 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 2 , 0 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 0 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 1 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 1 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 0 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 15 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 15 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 6 7 4 5 15 12 2 11 13 4 2 5 15 13 -> 1 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 6 , 6 14 6 4 11 9 12 5 15 12 11 12 11 13 -> 15 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 3 , 1 3 4 11 10 0 6 8 13 4 11 12 11 13 -> 1 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 6 , 6 8 10 1 5 1 5 0 0 6 8 9 13 7 -> 1 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 7 , 1 5 1 5 0 1 5 1 11 12 5 15 13 7 -> 0 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 7 , 6 14 6 7 14 0 1 3 7 8 13 4 3 7 -> 0 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 7 , 6 14 6 8 12 3 4 11 12 3 8 9 10 6 -> 0 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 6 , 1 3 14 15 9 13 4 11 12 5 15 9 10 6 -> 6 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 6 , 1 2 11 10 1 3 8 9 10 0 15 13 14 6 -> 1 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 6 , 6 7 14 15 12 2 11 12 11 12 11 13 14 6 -> 0 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 6 , 6 8 12 5 15 12 3 7 8 10 6 7 14 6 -> 0 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 6 , 1 3 7 14 1 5 1 11 12 2 3 7 14 6 -> 1 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 6 , 0 15 9 12 11 12 11 12 2 2 3 7 14 6 -> 0 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 6 , 15 13 8 12 11 12 5 15 13 8 9 10 0 6 -> 0 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 6 , 1 2 3 8 12 5 0 15 12 11 9 10 0 6 -> 0 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 6 , 0 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 15 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 6 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 0 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 6 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 15 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 15 10 6 14 0 6 14 6 14 15 10 1 3 7 ->= 0 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 3 , 0 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 0 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 0 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 0 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 1 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 0 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 1 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 6 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 0 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 1 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 15 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 1 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 15 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 15 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 6 7 4 5 15 12 2 11 13 4 2 5 15 9 -> 1 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 15 , 6 14 6 4 11 9 12 5 15 12 11 12 11 9 -> 15 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 11 , 1 3 4 11 10 0 6 8 13 4 11 12 11 9 -> 1 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 15 , 6 8 10 1 5 1 5 0 0 6 8 9 13 8 -> 1 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 8 , 1 5 1 5 0 1 5 1 11 12 5 15 13 8 -> 0 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 8 , 6 14 6 7 14 0 1 3 7 8 13 4 3 8 -> 0 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 8 , 6 14 6 8 12 3 4 11 12 3 8 9 10 15 -> 0 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 15 , 1 3 14 15 9 13 4 11 12 5 15 9 10 15 -> 6 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 15 , 1 2 11 10 1 3 8 9 10 0 15 13 14 15 -> 1 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 15 , 6 7 14 15 12 2 11 12 11 12 11 13 14 15 -> 0 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 15 , 6 8 12 5 15 12 3 7 8 10 6 7 14 15 -> 0 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 15 , 1 3 7 14 1 5 1 11 12 2 3 7 14 15 -> 1 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 15 , 0 15 9 12 11 12 11 12 2 2 3 7 14 15 -> 0 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 15 , 15 13 8 12 11 12 5 15 13 8 9 10 0 15 -> 0 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 15 , 1 2 3 8 12 5 0 15 12 11 9 10 0 15 -> 0 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 15 , 0 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 0 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 15 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 0 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 6 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 1 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 0 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 0 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 6 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 0 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 15 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 0 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 15 10 6 14 0 6 14 6 14 15 10 1 3 8 ->= 0 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 11 , 5 1 2 3 4 2 5 6 7 7 8 9 9 10 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 10 , 5 1 3 4 2 3 7 7 4 2 11 9 9 10 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 5 , 2 5 15 9 13 14 1 3 4 11 10 15 9 10 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 10 , 2 5 6 8 10 6 14 1 2 11 9 13 8 10 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 5 , 5 15 10 6 14 0 15 13 7 8 10 6 8 10 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 0 , 11 10 1 3 8 10 0 6 7 7 14 6 8 10 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 0 , 11 12 3 14 1 11 13 4 11 9 10 0 15 10 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 5 , 3 7 4 5 15 12 2 11 13 4 2 5 15 10 -> 2 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 0 , 3 14 6 4 11 9 12 5 15 12 11 12 11 10 -> 11 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 5 , 2 3 4 11 10 0 6 8 13 4 11 12 11 10 -> 2 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 0 , 3 8 10 1 5 1 5 0 0 6 8 9 13 14 -> 2 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 14 , 2 5 1 5 0 1 5 1 11 12 5 15 13 14 -> 5 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 14 , 3 14 6 7 14 0 1 3 7 8 13 4 3 14 -> 5 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 14 , 3 14 6 8 12 3 4 11 12 3 8 9 10 0 -> 5 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 0 , 2 3 14 15 9 13 4 11 12 5 15 9 10 0 -> 3 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 0 , 2 2 11 10 1 3 8 9 10 0 15 13 14 0 -> 2 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 0 , 3 7 14 15 12 2 11 12 11 12 11 13 14 0 -> 5 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 0 , 3 8 12 5 15 12 3 7 8 10 6 7 14 0 -> 5 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 0 , 2 3 7 14 1 5 1 11 12 2 3 7 14 0 -> 2 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 0 , 5 15 9 12 11 12 11 12 2 2 3 7 14 0 -> 5 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 0 , 11 13 8 12 11 12 5 15 13 8 9 10 0 0 -> 5 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 0 , 2 2 3 8 12 5 0 15 12 11 9 10 0 0 -> 5 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 0 , 5 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 11 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 3 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 5 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 3 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 11 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 11 10 6 14 0 6 14 6 14 15 10 1 3 14 ->= 5 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 5 , 5 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 5 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 2 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 2 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 5 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 11 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 11 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 3 7 4 5 15 12 2 11 13 4 2 5 15 12 -> 2 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 1 , 3 14 6 4 11 9 12 5 15 12 11 12 11 12 -> 11 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 2 , 2 3 4 11 10 0 6 8 13 4 11 12 11 12 -> 2 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 1 , 3 8 10 1 5 1 5 0 0 6 8 9 13 4 -> 2 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 4 , 2 5 1 5 0 1 5 1 11 12 5 15 13 4 -> 5 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 4 , 3 14 6 7 14 0 1 3 7 8 13 4 3 4 -> 5 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 4 , 3 14 6 8 12 3 4 11 12 3 8 9 10 1 -> 5 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 1 , 2 3 14 15 9 13 4 11 12 5 15 9 10 1 -> 3 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 1 , 2 2 11 10 1 3 8 9 10 0 15 13 14 1 -> 2 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 1 , 3 7 14 15 12 2 11 12 11 12 11 13 14 1 -> 5 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 1 , 3 8 12 5 15 12 3 7 8 10 6 7 14 1 -> 5 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 1 , 2 3 7 14 1 5 1 11 12 2 3 7 14 1 -> 2 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 1 , 5 15 9 12 11 12 11 12 2 2 3 7 14 1 -> 5 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 1 , 11 13 8 12 11 12 5 15 13 8 9 10 0 1 -> 5 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 1 , 2 2 3 8 12 5 0 15 12 11 9 10 0 1 -> 5 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 1 , 5 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 5 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 11 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 5 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 3 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 2 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 5 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 5 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 3 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 5 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 11 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 5 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 11 10 6 14 0 6 14 6 14 15 10 1 3 4 ->= 5 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 2 , 5 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 5 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 5 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 5 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 2 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 5 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 2 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 3 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 5 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 2 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 11 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 2 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 11 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 11 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 3 7 4 5 15 12 2 11 13 4 2 5 15 13 -> 2 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 6 , 3 14 6 4 11 9 12 5 15 12 11 12 11 13 -> 11 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 3 , 2 3 4 11 10 0 6 8 13 4 11 12 11 13 -> 2 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 6 , 3 8 10 1 5 1 5 0 0 6 8 9 13 7 -> 2 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 7 , 2 5 1 5 0 1 5 1 11 12 5 15 13 7 -> 5 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 7 , 3 14 6 7 14 0 1 3 7 8 13 4 3 7 -> 5 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 7 , 3 14 6 8 12 3 4 11 12 3 8 9 10 6 -> 5 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 6 , 2 3 14 15 9 13 4 11 12 5 15 9 10 6 -> 3 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 6 , 2 2 11 10 1 3 8 9 10 0 15 13 14 6 -> 2 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 6 , 3 7 14 15 12 2 11 12 11 12 11 13 14 6 -> 5 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 6 , 3 8 12 5 15 12 3 7 8 10 6 7 14 6 -> 5 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 6 , 2 3 7 14 1 5 1 11 12 2 3 7 14 6 -> 2 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 6 , 5 15 9 12 11 12 11 12 2 2 3 7 14 6 -> 5 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 6 , 11 13 8 12 11 12 5 15 13 8 9 10 0 6 -> 5 1 2 2 2 11 12 3 4 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12 11 12 -> 8 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 2 , 4 3 4 11 10 0 6 8 13 4 11 12 11 12 -> 4 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 1 , 7 8 10 1 5 1 5 0 0 6 8 9 13 4 -> 4 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 4 , 4 5 1 5 0 1 5 1 11 12 5 15 13 4 -> 14 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 4 , 7 14 6 7 14 0 1 3 7 8 13 4 3 4 -> 14 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 4 , 7 14 6 8 12 3 4 11 12 3 8 9 10 1 -> 14 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 1 , 4 3 14 15 9 13 4 11 12 5 15 9 10 1 -> 7 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 1 , 4 2 11 10 1 3 8 9 10 0 15 13 14 1 -> 4 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 1 , 7 7 14 15 12 2 11 12 11 12 11 13 14 1 -> 14 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 1 , 7 8 12 5 15 12 3 7 8 10 6 7 14 1 -> 14 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 1 , 4 3 7 14 1 5 1 11 12 2 3 7 14 1 -> 4 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 1 , 14 15 9 12 11 12 11 12 2 2 3 7 14 1 -> 14 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 1 , 8 13 8 12 11 12 5 15 13 8 9 10 0 1 -> 14 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 1 , 4 2 3 8 12 5 0 15 12 11 9 10 0 1 -> 14 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 1 , 14 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 8 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 7 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 14 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 7 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 8 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 8 10 6 14 0 6 14 6 14 15 10 1 3 4 ->= 14 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 2 , 14 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 14 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 4 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 4 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 14 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 8 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 8 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 7 7 4 5 15 12 2 11 13 4 2 5 15 13 -> 4 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 6 , 7 14 6 4 11 9 12 5 15 12 11 12 11 13 -> 8 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 3 , 4 3 4 11 10 0 6 8 13 4 11 12 11 13 -> 4 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 6 , 7 8 10 1 5 1 5 0 0 6 8 9 13 7 -> 4 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 7 , 4 5 1 5 0 1 5 1 11 12 5 15 13 7 -> 14 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 7 , 7 14 6 7 14 0 1 3 7 8 13 4 3 7 -> 14 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 7 , 7 14 6 8 12 3 4 11 12 3 8 9 10 6 -> 14 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 6 , 4 3 14 15 9 13 4 11 12 5 15 9 10 6 -> 7 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 6 , 4 2 11 10 1 3 8 9 10 0 15 13 14 6 -> 4 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 6 , 7 7 14 15 12 2 11 12 11 12 11 13 14 6 -> 14 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 6 , 7 8 12 5 15 12 3 7 8 10 6 7 14 6 -> 14 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 6 , 4 3 7 14 1 5 1 11 12 2 3 7 14 6 -> 4 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 6 , 14 15 9 12 11 12 11 12 2 2 3 7 14 6 -> 14 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 6 , 8 13 8 12 11 12 5 15 13 8 9 10 0 6 -> 14 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 6 , 4 2 3 8 12 5 0 15 12 11 9 10 0 6 -> 14 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 6 , 14 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 14 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 8 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 14 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 7 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 4 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 14 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 14 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 7 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 14 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 8 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 14 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 8 10 6 14 0 6 14 6 14 15 10 1 3 7 ->= 14 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 3 , 14 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 14 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 14 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 14 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 4 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 14 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 4 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 7 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 14 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 4 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 8 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 4 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 8 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 8 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 7 7 4 5 15 12 2 11 13 4 2 5 15 9 -> 4 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 15 , 7 14 6 4 11 9 12 5 15 12 11 12 11 9 -> 8 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 11 , 4 3 4 11 10 0 6 8 13 4 11 12 11 9 -> 4 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 15 , 7 8 10 1 5 1 5 0 0 6 8 9 13 8 -> 4 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 8 , 4 5 1 5 0 1 5 1 11 12 5 15 13 8 -> 14 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 8 , 7 14 6 7 14 0 1 3 7 8 13 4 3 8 -> 14 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 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12 11 12 11 10 -> 9 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 5 , 12 3 4 11 10 0 6 8 13 4 11 12 11 10 -> 12 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 0 , 13 8 10 1 5 1 5 0 0 6 8 9 13 14 -> 12 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 14 , 12 5 1 5 0 1 5 1 11 12 5 15 13 14 -> 10 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 14 , 13 14 6 7 14 0 1 3 7 8 13 4 3 14 -> 10 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 14 , 13 14 6 8 12 3 4 11 12 3 8 9 10 0 -> 10 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 0 , 12 3 14 15 9 13 4 11 12 5 15 9 10 0 -> 13 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 0 , 12 2 11 10 1 3 8 9 10 0 15 13 14 0 -> 12 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 0 , 13 7 14 15 12 2 11 12 11 12 11 13 14 0 -> 10 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 0 , 13 8 12 5 15 12 3 7 8 10 6 7 14 0 -> 10 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 0 , 12 3 7 14 1 5 1 11 12 2 3 7 14 0 -> 12 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 0 , 10 15 9 12 11 12 11 12 2 2 3 7 14 0 -> 10 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 0 , 9 13 8 12 11 12 5 15 13 8 9 10 0 0 -> 10 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 0 , 12 2 3 8 12 5 0 15 12 11 9 10 0 0 -> 10 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 0 , 10 6 4 5 1 5 15 13 8 12 11 10 0 0 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 0 , 9 10 6 8 13 7 14 6 14 15 13 14 0 0 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 0 , 13 7 4 2 5 6 4 5 15 13 7 4 5 0 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 0 , 10 15 10 0 0 1 3 8 12 11 10 1 5 0 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 0 , 13 14 1 5 1 5 1 3 7 7 14 1 5 0 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 0 , 9 13 8 9 12 2 11 13 8 12 5 15 12 5 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 5 , 9 10 6 14 0 6 14 6 14 15 10 1 3 14 ->= 10 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 5 , 10 1 2 3 4 2 5 6 7 7 8 9 9 12 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 12 , 10 1 3 4 2 3 7 7 4 2 11 9 9 12 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 2 , 12 5 15 9 13 14 1 3 4 11 10 15 9 12 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 12 , 12 5 6 8 10 6 14 1 2 11 9 13 8 12 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 2 , 10 15 10 6 14 0 15 13 7 8 10 6 8 12 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 1 , 9 10 1 3 8 10 0 6 7 7 14 6 8 12 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 1 , 9 12 3 14 1 11 13 4 11 9 10 0 15 12 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 2 , 13 7 4 5 15 12 2 11 13 4 2 5 15 12 -> 12 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 1 , 13 14 6 4 11 9 12 5 15 12 11 12 11 12 -> 9 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 2 , 12 3 4 11 10 0 6 8 13 4 11 12 11 12 -> 12 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 1 , 13 8 10 1 5 1 5 0 0 6 8 9 13 4 -> 12 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 4 , 12 5 1 5 0 1 5 1 11 12 5 15 13 4 -> 10 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 4 , 13 14 6 7 14 0 1 3 7 8 13 4 3 4 -> 10 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 4 , 13 14 6 8 12 3 4 11 12 3 8 9 10 1 -> 10 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 1 , 12 3 14 15 9 13 4 11 12 5 15 9 10 1 -> 13 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 1 , 12 2 11 10 1 3 8 9 10 0 15 13 14 1 -> 12 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 1 , 13 7 14 15 12 2 11 12 11 12 11 13 14 1 -> 10 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 1 , 13 8 12 5 15 12 3 7 8 10 6 7 14 1 -> 10 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 1 , 12 3 7 14 1 5 1 11 12 2 3 7 14 1 -> 12 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 1 , 10 15 9 12 11 12 11 12 2 2 3 7 14 1 -> 10 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 1 , 9 13 8 12 11 12 5 15 13 8 9 10 0 1 -> 10 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 1 , 12 2 3 8 12 5 0 15 12 11 9 10 0 1 -> 10 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 1 , 10 6 4 5 1 5 15 13 8 12 11 10 0 1 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 1 , 9 10 6 8 13 7 14 6 14 15 13 14 0 1 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 1 , 13 7 4 2 5 6 4 5 15 13 7 4 5 1 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 1 , 10 15 10 0 0 1 3 8 12 11 10 1 5 1 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 1 , 13 14 1 5 1 5 1 3 7 7 14 1 5 1 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 1 , 9 13 8 9 12 2 11 13 8 12 5 15 12 2 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 2 , 9 10 6 14 0 6 14 6 14 15 10 1 3 4 ->= 10 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 2 , 10 1 2 3 4 2 5 6 7 7 8 9 9 13 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 13 , 10 1 3 4 2 3 7 7 4 2 11 9 9 13 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 3 , 12 5 15 9 13 14 1 3 4 11 10 15 9 13 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 13 , 12 5 6 8 10 6 14 1 2 11 9 13 8 13 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 3 , 10 15 10 6 14 0 15 13 7 8 10 6 8 13 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 6 , 9 10 1 3 8 10 0 6 7 7 14 6 8 13 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 6 , 9 12 3 14 1 11 13 4 11 9 10 0 15 13 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 3 , 13 7 4 5 15 12 2 11 13 4 2 5 15 13 -> 12 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 6 , 13 14 6 4 11 9 12 5 15 12 11 12 11 13 -> 9 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 3 , 12 3 4 11 10 0 6 8 13 4 11 12 11 13 -> 12 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 6 , 13 8 10 1 5 1 5 0 0 6 8 9 13 7 -> 12 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 7 , 12 5 1 5 0 1 5 1 11 12 5 15 13 7 -> 10 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 7 , 13 14 6 7 14 0 1 3 7 8 13 4 3 7 -> 10 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 7 , 13 14 6 8 12 3 4 11 12 3 8 9 10 6 -> 10 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 6 , 12 3 14 15 9 13 4 11 12 5 15 9 10 6 -> 13 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 6 , 12 2 11 10 1 3 8 9 10 0 15 13 14 6 -> 12 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 6 , 13 7 14 15 12 2 11 12 11 12 11 13 14 6 -> 10 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 6 , 13 8 12 5 15 12 3 7 8 10 6 7 14 6 -> 10 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 6 , 12 3 7 14 1 5 1 11 12 2 3 7 14 6 -> 12 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 6 , 10 15 9 12 11 12 11 12 2 2 3 7 14 6 -> 10 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 6 , 9 13 8 12 11 12 5 15 13 8 9 10 0 6 -> 10 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 6 , 12 2 3 8 12 5 0 15 12 11 9 10 0 6 -> 10 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 6 , 10 6 4 5 1 5 15 13 8 12 11 10 0 6 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 6 , 9 10 6 8 13 7 14 6 14 15 13 14 0 6 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 6 , 13 7 4 2 5 6 4 5 15 13 7 4 5 6 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 6 , 10 15 10 0 0 1 3 8 12 11 10 1 5 6 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 6 , 13 14 1 5 1 5 1 3 7 7 14 1 5 6 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 6 , 9 13 8 9 12 2 11 13 8 12 5 15 12 3 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 3 , 9 10 6 14 0 6 14 6 14 15 10 1 3 7 ->= 10 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 3 , 10 1 2 3 4 2 5 6 7 7 8 9 9 9 -> 10 0 6 4 5 0 1 11 9 12 5 6 8 13 14 0 15 9 , 10 1 3 4 2 3 7 7 4 2 11 9 9 9 -> 10 0 6 14 6 14 0 0 6 4 2 2 11 13 14 15 12 11 , 12 5 15 9 13 14 1 3 4 11 10 15 9 9 -> 10 6 14 1 3 4 11 10 0 1 2 2 3 14 0 0 15 9 , 12 5 6 8 10 6 14 1 2 11 9 13 8 9 -> 13 4 5 0 6 14 0 0 15 12 11 10 0 6 14 0 1 11 , 10 15 10 6 14 0 15 13 7 8 10 6 8 9 -> 12 2 5 0 0 1 2 2 2 11 13 14 0 1 2 11 10 15 , 9 10 1 3 8 10 0 6 7 7 14 6 8 9 -> 12 2 3 4 2 3 14 1 2 11 12 5 6 8 10 1 5 15 , 9 12 3 14 1 11 13 4 11 9 10 0 15 9 -> 9 13 7 7 14 0 15 12 5 0 1 2 3 14 0 6 4 11 , 13 7 4 5 15 12 2 11 13 4 2 5 15 9 -> 12 11 10 0 0 1 2 5 0 0 15 10 0 0 1 3 14 15 , 13 14 6 4 11 9 12 5 15 12 11 12 11 9 -> 9 10 0 0 1 5 0 0 0 6 8 12 5 0 6 7 4 11 , 12 3 4 11 10 0 6 8 13 4 11 12 11 9 -> 12 11 10 0 6 14 0 1 2 11 12 11 12 5 0 1 5 15 , 13 8 10 1 5 1 5 0 0 6 8 9 13 8 -> 12 2 5 0 0 1 2 11 13 14 6 14 0 15 13 14 6 8 , 12 5 1 5 0 1 5 1 11 12 5 15 13 8 -> 10 6 14 6 4 5 0 1 2 5 0 0 6 14 0 1 3 8 , 13 14 6 7 14 0 1 3 7 8 13 4 3 8 -> 10 0 6 8 10 0 0 0 0 0 6 14 1 5 1 5 6 8 , 13 14 6 8 12 3 4 11 12 3 8 9 10 15 -> 10 6 14 0 15 13 4 2 2 11 9 13 8 12 2 5 0 15 , 12 3 14 15 9 13 4 11 12 5 15 9 10 15 -> 13 4 3 4 2 3 4 5 1 5 0 0 0 6 14 15 10 15 , 12 2 11 10 1 3 8 9 10 0 15 13 14 15 -> 12 2 2 2 3 14 0 6 7 7 14 1 3 14 0 15 10 15 , 13 7 14 15 12 2 11 12 11 12 11 13 14 15 -> 10 0 15 12 5 1 5 0 0 15 13 7 14 6 8 10 0 15 , 13 8 12 5 15 12 3 7 8 10 6 7 14 15 -> 10 0 1 2 5 0 6 8 13 14 1 2 2 2 2 5 0 15 , 12 3 7 14 1 5 1 11 12 2 3 7 14 15 -> 12 3 8 12 2 5 0 6 14 1 2 5 0 1 5 1 5 15 , 10 15 9 12 11 12 11 12 2 2 3 7 14 15 -> 10 1 2 5 1 2 5 1 2 2 3 14 15 10 0 15 10 15 , 9 13 8 12 11 12 5 15 13 8 9 10 0 15 -> 10 1 2 2 2 11 12 3 4 3 8 10 15 13 14 0 0 15 , 12 2 3 8 12 5 0 15 12 11 9 10 0 15 -> 10 0 0 15 10 0 0 15 10 6 14 6 8 13 7 14 0 15 , 10 6 4 5 1 5 15 13 8 12 11 10 0 15 -> 10 0 1 2 3 4 3 4 11 9 13 14 0 0 15 10 0 15 , 9 10 6 8 13 7 14 6 14 15 13 14 0 15 -> 10 0 0 0 0 0 6 8 10 0 6 4 11 10 15 10 0 15 , 13 7 4 2 5 6 4 5 15 13 7 4 5 15 -> 12 2 3 8 12 11 9 10 15 10 6 7 14 6 14 0 0 15 , 10 15 10 0 0 1 3 8 12 11 10 1 5 15 -> 10 1 2 5 0 1 5 0 1 3 8 9 12 5 0 6 14 15 , 13 14 1 5 1 5 1 3 7 7 14 1 5 15 -> 10 15 10 0 15 12 5 1 5 15 10 0 1 11 10 0 0 15 , 9 13 8 9 12 2 11 13 8 12 5 15 12 11 -> 10 1 2 11 10 6 8 10 1 2 2 5 0 6 8 9 12 11 , 9 10 6 14 0 6 14 6 14 15 10 1 3 8 ->= 10 0 0 15 10 0 15 10 0 6 14 0 6 14 6 14 1 11 } 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 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 3 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 3 | | 0 1 | \ / 8 is interpreted by / \ | 1 6 | | 0 1 | \ / 9 is interpreted by / \ | 1 2 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 3 | | 0 1 | \ / 12 is interpreted by / \ | 1 2 | | 0 1 | \ / 13 is interpreted by / \ | 1 3 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.