YES After renaming modulo { 1->0, 5->1, 3->2, 0->3, 4->4, 2->5 }, it remains to prove termination of the 60-rule system { 0 1 0 -> 0 2 3 3 4 0 2 3 2 4 , 2 0 1 -> 2 0 0 2 3 1 5 3 1 5 , 1 1 0 -> 1 5 2 2 0 1 5 2 3 4 , 1 1 1 -> 1 5 0 2 0 0 0 2 5 5 , 0 3 2 4 -> 0 0 3 5 3 0 0 2 4 0 , 5 0 1 2 -> 5 0 2 0 4 2 5 2 3 3 , 2 3 1 1 -> 2 2 1 3 1 5 2 2 3 5 , 4 3 0 3 -> 3 5 2 4 0 5 2 5 2 2 , 4 3 1 1 -> 3 4 2 5 5 5 2 0 5 2 , 4 5 0 5 -> 5 3 5 3 5 0 3 5 2 2 , 4 1 1 4 -> 4 4 4 4 3 0 2 5 0 2 , 1 1 4 3 -> 1 5 4 2 5 2 1 5 4 3 , 3 2 1 1 4 -> 3 3 4 5 5 2 0 4 2 4 , 0 3 0 5 0 -> 0 0 1 4 5 1 5 5 2 3 , 0 3 1 1 1 -> 0 0 1 3 2 5 2 4 0 1 , 5 4 5 1 4 -> 5 3 4 5 1 5 5 2 2 0 , 2 1 0 3 1 -> 2 4 2 2 1 5 5 2 1 5 , 4 4 1 1 0 -> 3 5 5 2 2 4 4 2 1 0 , 4 1 1 0 5 -> 3 5 1 2 4 5 2 5 5 2 , 1 1 0 1 1 -> 1 3 2 0 0 3 3 4 2 5 , 1 1 2 5 0 -> 1 5 5 4 5 1 5 2 3 0 , 3 3 1 0 4 1 -> 3 2 4 2 4 3 3 2 3 5 , 3 4 3 1 0 5 -> 4 5 4 0 5 3 5 2 2 5 , 3 4 3 1 4 3 -> 4 2 1 3 4 2 4 4 0 2 , 3 4 4 3 0 1 -> 3 4 0 3 0 4 2 0 3 5 , 3 4 4 1 1 0 -> 5 2 1 3 5 4 4 4 0 4 , 5 1 0 1 5 0 -> 4 5 5 2 0 2 1 3 4 0 , 5 1 5 0 1 1 -> 5 2 2 5 1 0 2 2 2 2 , 5 1 1 2 0 1 -> 5 5 1 0 4 4 2 5 5 1 , 2 0 5 0 4 3 -> 2 2 1 0 0 5 3 5 2 3 , 2 1 0 3 4 3 -> 2 2 2 2 1 1 5 2 5 3 , 2 1 2 4 1 4 -> 2 1 2 3 0 3 0 4 2 4 , 1 4 4 5 1 0 -> 1 3 5 3 3 5 5 2 0 4 , 1 1 0 1 4 3 -> 1 1 3 5 4 1 2 3 5 3 , 1 1 1 1 1 4 -> 1 2 2 2 1 4 3 0 4 0 , 3 2 4 4 1 4 1 -> 3 4 2 4 2 5 2 4 0 3 , 3 4 3 1 4 1 4 -> 5 1 4 2 4 4 2 3 3 4 , 3 4 3 1 1 0 3 -> 1 4 5 2 3 4 2 1 3 3 , 3 4 0 3 1 5 1 -> 5 2 2 3 3 1 0 2 5 1 , 3 1 2 1 2 1 0 -> 3 0 4 0 2 0 5 1 0 0 , 3 1 1 0 3 2 0 -> 5 2 3 2 4 4 3 2 2 0 , 0 0 3 0 1 0 1 -> 0 0 0 0 4 1 3 5 0 1 , 0 5 0 1 2 4 1 -> 0 1 3 2 1 2 2 3 3 2 , 0 1 3 1 2 3 1 -> 0 4 2 0 4 0 2 1 2 1 , 5 2 1 1 1 5 1 -> 5 2 5 1 3 3 3 5 4 3 , 2 3 3 1 0 4 1 -> 2 3 3 2 3 2 0 3 4 1 , 2 3 1 4 4 5 0 -> 2 1 4 2 2 4 0 2 5 4 , 2 0 4 3 3 4 5 -> 2 2 3 5 0 4 1 2 5 5 , 2 0 1 1 0 3 4 -> 2 2 0 5 2 0 3 2 2 4 , 2 4 1 1 1 1 1 -> 2 0 0 1 5 5 4 1 2 1 , 2 1 4 1 5 1 2 -> 2 5 2 4 5 2 1 3 0 3 , 4 3 1 1 2 4 1 -> 4 3 5 2 4 0 3 3 1 1 , 4 1 4 3 0 3 1 -> 0 4 4 1 0 5 2 4 2 2 , 1 0 3 1 4 4 1 -> 1 4 2 1 1 2 2 0 4 2 , 3 0 ->= 5 2 5 4 2 5 3 5 3 4 , 5 0 1 ->= 5 3 2 5 2 4 2 2 1 2 , 3 3 1 0 ->= 3 4 0 2 2 4 0 3 5 0 , 3 4 4 3 1 0 ->= 4 3 5 2 5 3 1 1 5 0 , 3 2 5 0 1 4 1 ->= 4 4 0 5 4 2 3 1 5 1 , 3 1 0 5 0 1 1 ->= 5 3 1 1 0 3 1 2 2 5 } The system was reversed. After renaming modulo { 0->0, 1->1, 4->2, 2->3, 3->4, 5->5 }, it remains to prove termination of the 60-rule system { 0 1 0 -> 2 3 4 3 0 2 4 4 3 0 , 1 0 3 -> 5 1 4 5 1 4 3 0 0 3 , 0 1 1 -> 2 4 3 5 1 0 3 3 5 1 , 1 1 1 -> 5 5 3 0 0 0 3 0 5 1 , 2 3 4 0 -> 0 2 3 0 0 4 5 4 0 0 , 3 1 0 5 -> 4 4 3 5 3 2 0 3 0 5 , 1 1 4 3 -> 5 4 3 3 5 1 4 1 3 3 , 4 0 4 2 -> 3 3 5 3 5 0 2 3 5 4 , 1 1 4 2 -> 3 5 0 3 5 5 5 3 2 4 , 5 0 5 2 -> 3 3 5 4 0 5 4 5 4 5 , 2 1 1 2 -> 3 0 5 3 0 4 2 2 2 2 , 4 2 1 1 -> 4 2 5 1 3 5 3 2 5 1 , 2 1 1 3 4 -> 2 3 2 0 3 5 5 2 4 4 , 0 5 0 4 0 -> 4 3 5 5 1 5 2 1 0 0 , 1 1 1 4 0 -> 1 0 2 3 5 3 4 1 0 0 , 2 1 5 2 5 -> 0 3 3 5 5 1 5 2 4 5 , 1 4 0 1 3 -> 5 1 3 5 5 1 3 3 2 3 , 0 1 1 2 2 -> 0 1 3 2 2 3 3 5 5 4 , 5 0 1 1 2 -> 3 5 5 3 5 2 3 1 5 4 , 1 1 0 1 1 -> 5 3 2 4 4 0 0 3 4 1 , 0 5 3 1 1 -> 0 4 3 5 1 5 2 5 5 1 , 1 2 0 1 4 4 -> 5 4 3 4 4 2 3 2 3 4 , 5 0 1 4 2 4 -> 5 3 3 5 4 5 0 2 5 2 , 4 2 1 4 2 4 -> 3 0 2 2 3 2 4 1 3 2 , 1 0 4 2 2 4 -> 5 4 0 3 2 0 4 0 2 4 , 0 1 1 2 2 4 -> 2 0 2 2 2 5 4 1 3 5 , 0 5 1 0 1 5 -> 0 2 4 1 3 0 3 5 5 2 , 1 1 0 5 1 5 -> 3 3 3 3 0 1 5 3 3 5 , 1 0 3 1 1 5 -> 1 5 5 3 2 2 0 1 5 5 , 4 2 0 5 0 3 -> 4 3 5 4 5 0 0 1 3 3 , 4 2 4 0 1 3 -> 4 5 3 5 1 1 3 3 3 3 , 2 1 2 3 1 3 -> 2 3 2 0 4 0 4 3 1 3 , 0 1 5 2 2 1 -> 2 0 3 5 5 4 4 5 4 1 , 4 2 1 0 1 1 -> 4 5 4 3 1 2 5 4 1 1 , 2 1 1 1 1 1 -> 0 2 0 4 2 1 3 3 3 1 , 1 2 1 2 2 3 4 -> 4 0 2 3 5 3 2 3 2 4 , 2 1 2 1 4 2 4 -> 2 4 4 3 2 2 3 2 1 5 , 4 0 1 1 4 2 4 -> 4 4 1 3 2 4 3 5 2 1 , 1 5 1 4 0 2 4 -> 1 5 3 0 1 4 4 3 3 5 , 0 1 3 1 3 1 4 -> 0 0 1 5 0 3 0 2 0 4 , 0 3 4 0 1 1 4 -> 0 3 3 4 2 2 3 4 3 5 , 1 0 1 0 4 0 0 -> 1 0 5 4 1 2 0 0 0 0 , 1 2 3 1 0 5 0 -> 3 4 4 3 3 1 3 4 1 0 , 1 4 3 1 4 1 0 -> 1 3 1 3 0 2 0 3 2 0 , 1 5 1 1 1 3 5 -> 4 2 5 4 4 4 1 5 3 5 , 1 2 0 1 4 4 3 -> 1 2 4 0 3 4 3 4 4 3 , 0 5 2 2 1 4 3 -> 2 5 3 0 2 3 3 2 1 3 , 5 2 4 4 2 0 3 -> 5 5 3 1 2 0 5 4 3 3 , 2 4 0 1 1 0 3 -> 2 3 3 4 0 3 5 0 3 3 , 1 1 1 1 1 2 3 -> 1 3 1 2 5 5 1 0 0 3 , 3 1 5 1 2 1 3 -> 4 0 4 1 3 5 2 3 5 3 , 1 2 3 1 1 4 2 -> 1 1 4 4 0 2 3 5 4 2 , 1 4 0 4 2 1 2 -> 3 3 2 3 5 0 1 2 2 0 , 1 2 2 1 4 0 1 -> 3 2 0 3 3 1 1 3 2 1 , 0 4 ->= 2 4 5 4 5 3 2 5 3 5 , 1 0 5 ->= 3 1 3 3 2 3 5 3 4 5 , 0 1 4 4 ->= 0 5 4 0 2 3 3 0 2 4 , 0 1 4 2 2 4 ->= 0 5 1 1 4 5 3 5 4 2 , 1 2 1 0 5 3 4 ->= 1 5 1 4 3 2 5 0 2 2 , 1 1 0 5 0 1 4 ->= 5 3 3 1 4 0 1 1 4 5 } 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, 3]->4, [3, 4]->5, [4, 3]->6, [3, 0]->7, [2, 4]->8, [4, 4]->9, [0, 3]->10, [0, 5]->11, [5, 1]->12, [1, 4]->13, [4, 5]->14, [1, 1]->15, [3, 5]->16, [3, 3]->17, [5, 5]->18, [5, 3]->19, [4, 0]->20, [0, 4]->21, [5, 4]->22, [3, 1]->23, [5, 0]->24, [3, 2]->25, [2, 0]->26, [4, 1]->27, [1, 3]->28, [4, 2]->29, [5, 2]->30, [2, 1]->31, [1, 2]->32, [2, 2]->33, [2, 5]->34, [1, 5]->35 }, it remains to prove termination of the 2160-rule system { 0 1 2 0 -> 3 4 5 6 7 3 8 9 6 7 0 , 1 2 10 7 -> 11 12 13 14 12 13 6 7 0 10 7 , 0 1 15 2 -> 3 8 6 16 12 2 10 17 16 12 2 , 1 15 15 2 -> 11 18 19 7 0 0 10 7 11 12 2 , 3 4 5 20 0 -> 0 3 4 7 0 21 14 22 20 0 0 , 10 23 2 11 24 -> 21 9 6 16 19 25 26 10 7 11 24 , 1 15 13 6 7 -> 11 22 6 17 16 12 13 27 28 17 7 , 21 20 21 29 26 -> 10 17 16 19 16 24 3 4 16 22 20 , 1 15 13 29 26 -> 10 16 24 10 16 18 18 19 25 8 20 , 11 24 11 30 26 -> 10 17 16 22 20 11 22 14 22 14 24 , 3 31 15 32 26 -> 10 7 11 19 7 21 29 33 33 33 26 , 21 29 31 15 2 -> 21 29 34 12 28 16 19 25 34 12 2 , 3 31 15 28 5 20 -> 3 4 25 26 10 16 18 30 8 9 20 , 0 11 24 21 20 0 -> 21 6 16 18 12 35 30 31 2 0 0 , 1 15 15 13 20 0 -> 1 2 3 4 16 19 5 27 2 0 0 , 3 31 35 30 34 24 -> 0 10 17 16 18 12 35 30 8 14 24 , 1 13 20 1 28 7 -> 11 12 28 16 18 12 28 17 25 4 7 , 0 1 15 32 33 26 -> 0 1 28 25 33 4 17 16 18 22 20 , 11 24 1 15 32 26 -> 10 16 18 19 16 30 4 23 35 22 20 , 1 15 2 1 15 2 -> 11 19 25 8 9 20 0 10 5 27 2 , 0 11 19 23 15 2 -> 0 21 6 16 12 35 30 34 18 12 2 , 1 32 26 1 13 9 20 -> 11 22 6 5 9 29 4 25 4 5 20 , 11 24 1 13 29 8 20 -> 11 19 17 16 22 14 24 3 34 30 26 , 21 29 31 13 29 8 20 -> 10 7 3 33 4 25 8 27 28 25 26 , 1 2 21 29 33 8 20 -> 11 22 20 10 25 26 21 20 3 8 20 , 0 1 15 32 33 8 20 -> 3 26 3 33 33 34 22 27 28 16 24 , 0 11 12 2 1 35 24 -> 0 3 8 27 28 7 10 16 18 30 26 , 1 15 2 11 12 35 24 -> 10 17 17 17 7 1 35 19 17 16 24 , 1 2 10 23 15 35 24 -> 1 35 18 19 25 33 26 1 35 18 24 , 21 29 26 11 24 10 7 -> 21 6 16 22 14 24 0 1 28 17 7 , 21 29 8 20 1 28 7 -> 21 14 19 16 12 15 28 17 17 17 7 , 3 31 32 4 23 28 7 -> 3 4 25 26 21 20 21 6 23 28 7 , 0 1 35 30 33 31 2 -> 3 26 10 16 18 22 9 14 22 27 2 , 21 29 31 2 1 15 2 -> 21 14 22 6 23 32 34 22 27 15 2 , 3 31 15 15 15 15 2 -> 0 3 26 21 29 31 28 17 17 23 2 , 1 32 31 32 33 4 5 20 -> 21 20 3 4 16 19 25 4 25 8 20 , 3 31 32 31 13 29 8 20 -> 3 8 9 6 25 33 4 25 31 35 24 , 21 20 1 15 13 29 8 20 -> 21 9 27 28 25 8 6 16 30 31 2 , 1 35 12 13 20 3 8 20 -> 1 35 19 7 1 13 9 6 17 16 24 , 0 1 28 23 28 23 13 20 -> 0 0 1 35 24 10 7 3 26 21 20 , 0 10 5 20 1 15 13 20 -> 0 10 17 5 29 33 4 5 6 16 24 , 1 2 1 2 21 20 0 0 -> 1 2 11 22 27 32 26 0 0 0 0 , 1 32 4 23 2 11 24 0 -> 10 5 9 6 17 23 28 5 27 2 0 , 1 13 6 23 13 27 2 0 -> 1 28 23 28 7 3 26 10 25 26 0 , 1 35 12 15 15 28 16 24 -> 21 29 34 22 9 9 27 35 19 16 24 , 1 32 26 1 13 9 6 7 -> 1 32 8 20 10 5 6 5 9 6 7 , 0 11 30 33 31 13 6 7 -> 3 34 19 7 3 4 17 25 31 28 7 , 11 30 8 9 29 26 10 7 -> 11 18 19 23 32 26 11 22 6 17 7 , 3 8 20 1 15 2 10 7 -> 3 4 17 5 20 10 16 24 10 17 7 , 1 15 15 15 15 32 4 7 -> 1 28 23 32 34 18 12 2 0 10 7 , 10 23 35 12 32 31 28 7 -> 21 20 21 27 28 16 30 4 16 19 7 , 1 32 4 23 15 13 29 26 -> 1 15 13 9 20 3 4 16 22 29 26 , 1 13 20 21 29 31 32 26 -> 10 17 25 4 16 24 1 32 33 26 0 , 1 32 33 31 13 20 1 2 -> 10 25 26 10 17 23 15 28 25 31 2 , 0 21 20 ->= 3 8 14 22 14 19 25 34 19 16 24 , 1 2 11 24 ->= 10 23 28 17 25 4 16 19 5 14 24 , 0 1 13 9 20 ->= 0 11 22 20 3 4 17 7 3 8 20 , 0 1 13 29 33 8 20 ->= 0 11 12 15 13 14 19 16 22 29 26 , 1 32 31 2 11 19 5 20 ->= 1 35 12 13 6 25 34 24 3 33 26 , 1 15 2 11 24 1 13 20 ->= 11 19 17 23 13 20 1 15 13 14 24 , 0 1 2 1 -> 3 4 5 6 7 3 8 9 6 7 1 , 1 2 10 23 -> 11 12 13 14 12 13 6 7 0 10 23 , 0 1 15 15 -> 3 8 6 16 12 2 10 17 16 12 15 , 1 15 15 15 -> 11 18 19 7 0 0 10 7 11 12 15 , 3 4 5 20 1 -> 0 3 4 7 0 21 14 22 20 0 1 , 10 23 2 11 12 -> 21 9 6 16 19 25 26 10 7 11 12 , 1 15 13 6 23 -> 11 22 6 17 16 12 13 27 28 17 23 , 21 20 21 29 31 -> 10 17 16 19 16 24 3 4 16 22 27 , 1 15 13 29 31 -> 10 16 24 10 16 18 18 19 25 8 27 , 11 24 11 30 31 -> 10 17 16 22 20 11 22 14 22 14 12 , 3 31 15 32 31 -> 10 7 11 19 7 21 29 33 33 33 31 , 21 29 31 15 15 -> 21 29 34 12 28 16 19 25 34 12 15 , 3 31 15 28 5 27 -> 3 4 25 26 10 16 18 30 8 9 27 , 0 11 24 21 20 1 -> 21 6 16 18 12 35 30 31 2 0 1 , 1 15 15 13 20 1 -> 1 2 3 4 16 19 5 27 2 0 1 , 3 31 35 30 34 12 -> 0 10 17 16 18 12 35 30 8 14 12 , 1 13 20 1 28 23 -> 11 12 28 16 18 12 28 17 25 4 23 , 0 1 15 32 33 31 -> 0 1 28 25 33 4 17 16 18 22 27 , 11 24 1 15 32 31 -> 10 16 18 19 16 30 4 23 35 22 27 , 1 15 2 1 15 15 -> 11 19 25 8 9 20 0 10 5 27 15 , 0 11 19 23 15 15 -> 0 21 6 16 12 35 30 34 18 12 15 , 1 32 26 1 13 9 27 -> 11 22 6 5 9 29 4 25 4 5 27 , 11 24 1 13 29 8 27 -> 11 19 17 16 22 14 24 3 34 30 31 , 21 29 31 13 29 8 27 -> 10 7 3 33 4 25 8 27 28 25 31 , 1 2 21 29 33 8 27 -> 11 22 20 10 25 26 21 20 3 8 27 , 0 1 15 32 33 8 27 -> 3 26 3 33 33 34 22 27 28 16 12 , 0 11 12 2 1 35 12 -> 0 3 8 27 28 7 10 16 18 30 31 , 1 15 2 11 12 35 12 -> 10 17 17 17 7 1 35 19 17 16 12 , 1 2 10 23 15 35 12 -> 1 35 18 19 25 33 26 1 35 18 12 , 21 29 26 11 24 10 23 -> 21 6 16 22 14 24 0 1 28 17 23 , 21 29 8 20 1 28 23 -> 21 14 19 16 12 15 28 17 17 17 23 , 3 31 32 4 23 28 23 -> 3 4 25 26 21 20 21 6 23 28 23 , 0 1 35 30 33 31 15 -> 3 26 10 16 18 22 9 14 22 27 15 , 21 29 31 2 1 15 15 -> 21 14 22 6 23 32 34 22 27 15 15 , 3 31 15 15 15 15 15 -> 0 3 26 21 29 31 28 17 17 23 15 , 1 32 31 32 33 4 5 27 -> 21 20 3 4 16 19 25 4 25 8 27 , 3 31 32 31 13 29 8 27 -> 3 8 9 6 25 33 4 25 31 35 12 , 21 20 1 15 13 29 8 27 -> 21 9 27 28 25 8 6 16 30 31 15 , 1 35 12 13 20 3 8 27 -> 1 35 19 7 1 13 9 6 17 16 12 , 0 1 28 23 28 23 13 27 -> 0 0 1 35 24 10 7 3 26 21 27 , 0 10 5 20 1 15 13 27 -> 0 10 17 5 29 33 4 5 6 16 12 , 1 2 1 2 21 20 0 1 -> 1 2 11 22 27 32 26 0 0 0 1 , 1 32 4 23 2 11 24 1 -> 10 5 9 6 17 23 28 5 27 2 1 , 1 13 6 23 13 27 2 1 -> 1 28 23 28 7 3 26 10 25 26 1 , 1 35 12 15 15 28 16 12 -> 21 29 34 22 9 9 27 35 19 16 12 , 1 32 26 1 13 9 6 23 -> 1 32 8 20 10 5 6 5 9 6 23 , 0 11 30 33 31 13 6 23 -> 3 34 19 7 3 4 17 25 31 28 23 , 11 30 8 9 29 26 10 23 -> 11 18 19 23 32 26 11 22 6 17 23 , 3 8 20 1 15 2 10 23 -> 3 4 17 5 20 10 16 24 10 17 23 , 1 15 15 15 15 32 4 23 -> 1 28 23 32 34 18 12 2 0 10 23 , 10 23 35 12 32 31 28 23 -> 21 20 21 27 28 16 30 4 16 19 23 , 1 32 4 23 15 13 29 31 -> 1 15 13 9 20 3 4 16 22 29 31 , 1 13 20 21 29 31 32 31 -> 10 17 25 4 16 24 1 32 33 26 1 , 1 32 33 31 13 20 1 15 -> 10 25 26 10 17 23 15 28 25 31 15 , 0 21 27 ->= 3 8 14 22 14 19 25 34 19 16 12 , 1 2 11 12 ->= 10 23 28 17 25 4 16 19 5 14 12 , 0 1 13 9 27 ->= 0 11 22 20 3 4 17 7 3 8 27 , 0 1 13 29 33 8 27 ->= 0 11 12 15 13 14 19 16 22 29 31 , 1 32 31 2 11 19 5 27 ->= 1 35 12 13 6 25 34 24 3 33 31 , 1 15 2 11 24 1 13 27 ->= 11 19 17 23 13 20 1 15 13 14 12 , 0 1 2 3 -> 3 4 5 6 7 3 8 9 6 7 3 , 1 2 10 25 -> 11 12 13 14 12 13 6 7 0 10 25 , 0 1 15 32 -> 3 8 6 16 12 2 10 17 16 12 32 , 1 15 15 32 -> 11 18 19 7 0 0 10 7 11 12 32 , 3 4 5 20 3 -> 0 3 4 7 0 21 14 22 20 0 3 , 10 23 2 11 30 -> 21 9 6 16 19 25 26 10 7 11 30 , 1 15 13 6 25 -> 11 22 6 17 16 12 13 27 28 17 25 , 21 20 21 29 33 -> 10 17 16 19 16 24 3 4 16 22 29 , 1 15 13 29 33 -> 10 16 24 10 16 18 18 19 25 8 29 , 11 24 11 30 33 -> 10 17 16 22 20 11 22 14 22 14 30 , 3 31 15 32 33 -> 10 7 11 19 7 21 29 33 33 33 33 , 21 29 31 15 32 -> 21 29 34 12 28 16 19 25 34 12 32 , 3 31 15 28 5 29 -> 3 4 25 26 10 16 18 30 8 9 29 , 0 11 24 21 20 3 -> 21 6 16 18 12 35 30 31 2 0 3 , 1 15 15 13 20 3 -> 1 2 3 4 16 19 5 27 2 0 3 , 3 31 35 30 34 30 -> 0 10 17 16 18 12 35 30 8 14 30 , 1 13 20 1 28 25 -> 11 12 28 16 18 12 28 17 25 4 25 , 0 1 15 32 33 33 -> 0 1 28 25 33 4 17 16 18 22 29 , 11 24 1 15 32 33 -> 10 16 18 19 16 30 4 23 35 22 29 , 1 15 2 1 15 32 -> 11 19 25 8 9 20 0 10 5 27 32 , 0 11 19 23 15 32 -> 0 21 6 16 12 35 30 34 18 12 32 , 1 32 26 1 13 9 29 -> 11 22 6 5 9 29 4 25 4 5 29 , 11 24 1 13 29 8 29 -> 11 19 17 16 22 14 24 3 34 30 33 , 21 29 31 13 29 8 29 -> 10 7 3 33 4 25 8 27 28 25 33 , 1 2 21 29 33 8 29 -> 11 22 20 10 25 26 21 20 3 8 29 , 0 1 15 32 33 8 29 -> 3 26 3 33 33 34 22 27 28 16 30 , 0 11 12 2 1 35 30 -> 0 3 8 27 28 7 10 16 18 30 33 , 1 15 2 11 12 35 30 -> 10 17 17 17 7 1 35 19 17 16 30 , 1 2 10 23 15 35 30 -> 1 35 18 19 25 33 26 1 35 18 30 , 21 29 26 11 24 10 25 -> 21 6 16 22 14 24 0 1 28 17 25 , 21 29 8 20 1 28 25 -> 21 14 19 16 12 15 28 17 17 17 25 , 3 31 32 4 23 28 25 -> 3 4 25 26 21 20 21 6 23 28 25 , 0 1 35 30 33 31 32 -> 3 26 10 16 18 22 9 14 22 27 32 , 21 29 31 2 1 15 32 -> 21 14 22 6 23 32 34 22 27 15 32 , 3 31 15 15 15 15 32 -> 0 3 26 21 29 31 28 17 17 23 32 , 1 32 31 32 33 4 5 29 -> 21 20 3 4 16 19 25 4 25 8 29 , 3 31 32 31 13 29 8 29 -> 3 8 9 6 25 33 4 25 31 35 30 , 21 20 1 15 13 29 8 29 -> 21 9 27 28 25 8 6 16 30 31 32 , 1 35 12 13 20 3 8 29 -> 1 35 19 7 1 13 9 6 17 16 30 , 0 1 28 23 28 23 13 29 -> 0 0 1 35 24 10 7 3 26 21 29 , 0 10 5 20 1 15 13 29 -> 0 10 17 5 29 33 4 5 6 16 30 , 1 2 1 2 21 20 0 3 -> 1 2 11 22 27 32 26 0 0 0 3 , 1 32 4 23 2 11 24 3 -> 10 5 9 6 17 23 28 5 27 2 3 , 1 13 6 23 13 27 2 3 -> 1 28 23 28 7 3 26 10 25 26 3 , 1 35 12 15 15 28 16 30 -> 21 29 34 22 9 9 27 35 19 16 30 , 1 32 26 1 13 9 6 25 -> 1 32 8 20 10 5 6 5 9 6 25 , 0 11 30 33 31 13 6 25 -> 3 34 19 7 3 4 17 25 31 28 25 , 11 30 8 9 29 26 10 25 -> 11 18 19 23 32 26 11 22 6 17 25 , 3 8 20 1 15 2 10 25 -> 3 4 17 5 20 10 16 24 10 17 25 , 1 15 15 15 15 32 4 25 -> 1 28 23 32 34 18 12 2 0 10 25 , 10 23 35 12 32 31 28 25 -> 21 20 21 27 28 16 30 4 16 19 25 , 1 32 4 23 15 13 29 33 -> 1 15 13 9 20 3 4 16 22 29 33 , 1 13 20 21 29 31 32 33 -> 10 17 25 4 16 24 1 32 33 26 3 , 1 32 33 31 13 20 1 32 -> 10 25 26 10 17 23 15 28 25 31 32 , 0 21 29 ->= 3 8 14 22 14 19 25 34 19 16 30 , 1 2 11 30 ->= 10 23 28 17 25 4 16 19 5 14 30 , 0 1 13 9 29 ->= 0 11 22 20 3 4 17 7 3 8 29 , 0 1 13 29 33 8 29 ->= 0 11 12 15 13 14 19 16 22 29 33 , 1 32 31 2 11 19 5 29 ->= 1 35 12 13 6 25 34 24 3 33 33 , 1 15 2 11 24 1 13 29 ->= 11 19 17 23 13 20 1 15 13 14 30 , 0 1 2 10 -> 3 4 5 6 7 3 8 9 6 7 10 , 1 2 10 17 -> 11 12 13 14 12 13 6 7 0 10 17 , 0 1 15 28 -> 3 8 6 16 12 2 10 17 16 12 28 , 1 15 15 28 -> 11 18 19 7 0 0 10 7 11 12 28 , 3 4 5 20 10 -> 0 3 4 7 0 21 14 22 20 0 10 , 10 23 2 11 19 -> 21 9 6 16 19 25 26 10 7 11 19 , 1 15 13 6 17 -> 11 22 6 17 16 12 13 27 28 17 17 , 21 20 21 29 4 -> 10 17 16 19 16 24 3 4 16 22 6 , 1 15 13 29 4 -> 10 16 24 10 16 18 18 19 25 8 6 , 11 24 11 30 4 -> 10 17 16 22 20 11 22 14 22 14 19 , 3 31 15 32 4 -> 10 7 11 19 7 21 29 33 33 33 4 , 21 29 31 15 28 -> 21 29 34 12 28 16 19 25 34 12 28 , 3 31 15 28 5 6 -> 3 4 25 26 10 16 18 30 8 9 6 , 0 11 24 21 20 10 -> 21 6 16 18 12 35 30 31 2 0 10 , 1 15 15 13 20 10 -> 1 2 3 4 16 19 5 27 2 0 10 , 3 31 35 30 34 19 -> 0 10 17 16 18 12 35 30 8 14 19 , 1 13 20 1 28 17 -> 11 12 28 16 18 12 28 17 25 4 17 , 0 1 15 32 33 4 -> 0 1 28 25 33 4 17 16 18 22 6 , 11 24 1 15 32 4 -> 10 16 18 19 16 30 4 23 35 22 6 , 1 15 2 1 15 28 -> 11 19 25 8 9 20 0 10 5 27 28 , 0 11 19 23 15 28 -> 0 21 6 16 12 35 30 34 18 12 28 , 1 32 26 1 13 9 6 -> 11 22 6 5 9 29 4 25 4 5 6 , 11 24 1 13 29 8 6 -> 11 19 17 16 22 14 24 3 34 30 4 , 21 29 31 13 29 8 6 -> 10 7 3 33 4 25 8 27 28 25 4 , 1 2 21 29 33 8 6 -> 11 22 20 10 25 26 21 20 3 8 6 , 0 1 15 32 33 8 6 -> 3 26 3 33 33 34 22 27 28 16 19 , 0 11 12 2 1 35 19 -> 0 3 8 27 28 7 10 16 18 30 4 , 1 15 2 11 12 35 19 -> 10 17 17 17 7 1 35 19 17 16 19 , 1 2 10 23 15 35 19 -> 1 35 18 19 25 33 26 1 35 18 19 , 21 29 26 11 24 10 17 -> 21 6 16 22 14 24 0 1 28 17 17 , 21 29 8 20 1 28 17 -> 21 14 19 16 12 15 28 17 17 17 17 , 3 31 32 4 23 28 17 -> 3 4 25 26 21 20 21 6 23 28 17 , 0 1 35 30 33 31 28 -> 3 26 10 16 18 22 9 14 22 27 28 , 21 29 31 2 1 15 28 -> 21 14 22 6 23 32 34 22 27 15 28 , 3 31 15 15 15 15 28 -> 0 3 26 21 29 31 28 17 17 23 28 , 1 32 31 32 33 4 5 6 -> 21 20 3 4 16 19 25 4 25 8 6 , 3 31 32 31 13 29 8 6 -> 3 8 9 6 25 33 4 25 31 35 19 , 21 20 1 15 13 29 8 6 -> 21 9 27 28 25 8 6 16 30 31 28 , 1 35 12 13 20 3 8 6 -> 1 35 19 7 1 13 9 6 17 16 19 , 0 1 28 23 28 23 13 6 -> 0 0 1 35 24 10 7 3 26 21 6 , 0 10 5 20 1 15 13 6 -> 0 10 17 5 29 33 4 5 6 16 19 , 1 2 1 2 21 20 0 10 -> 1 2 11 22 27 32 26 0 0 0 10 , 1 32 4 23 2 11 24 10 -> 10 5 9 6 17 23 28 5 27 2 10 , 1 13 6 23 13 27 2 10 -> 1 28 23 28 7 3 26 10 25 26 10 , 1 35 12 15 15 28 16 19 -> 21 29 34 22 9 9 27 35 19 16 19 , 1 32 26 1 13 9 6 17 -> 1 32 8 20 10 5 6 5 9 6 17 , 0 11 30 33 31 13 6 17 -> 3 34 19 7 3 4 17 25 31 28 17 , 11 30 8 9 29 26 10 17 -> 11 18 19 23 32 26 11 22 6 17 17 , 3 8 20 1 15 2 10 17 -> 3 4 17 5 20 10 16 24 10 17 17 , 1 15 15 15 15 32 4 17 -> 1 28 23 32 34 18 12 2 0 10 17 , 10 23 35 12 32 31 28 17 -> 21 20 21 27 28 16 30 4 16 19 17 , 1 32 4 23 15 13 29 4 -> 1 15 13 9 20 3 4 16 22 29 4 , 1 13 20 21 29 31 32 4 -> 10 17 25 4 16 24 1 32 33 26 10 , 1 32 33 31 13 20 1 28 -> 10 25 26 10 17 23 15 28 25 31 28 , 0 21 6 ->= 3 8 14 22 14 19 25 34 19 16 19 , 1 2 11 19 ->= 10 23 28 17 25 4 16 19 5 14 19 , 0 1 13 9 6 ->= 0 11 22 20 3 4 17 7 3 8 6 , 0 1 13 29 33 8 6 ->= 0 11 12 15 13 14 19 16 22 29 4 , 1 32 31 2 11 19 5 6 ->= 1 35 12 13 6 25 34 24 3 33 4 , 1 15 2 11 24 1 13 6 ->= 11 19 17 23 13 20 1 15 13 14 19 , 0 1 2 21 -> 3 4 5 6 7 3 8 9 6 7 21 , 1 2 10 5 -> 11 12 13 14 12 13 6 7 0 10 5 , 0 1 15 13 -> 3 8 6 16 12 2 10 17 16 12 13 , 1 15 15 13 -> 11 18 19 7 0 0 10 7 11 12 13 , 3 4 5 20 21 -> 0 3 4 7 0 21 14 22 20 0 21 , 10 23 2 11 22 -> 21 9 6 16 19 25 26 10 7 11 22 , 1 15 13 6 5 -> 11 22 6 17 16 12 13 27 28 17 5 , 21 20 21 29 8 -> 10 17 16 19 16 24 3 4 16 22 9 , 1 15 13 29 8 -> 10 16 24 10 16 18 18 19 25 8 9 , 11 24 11 30 8 -> 10 17 16 22 20 11 22 14 22 14 22 , 3 31 15 32 8 -> 10 7 11 19 7 21 29 33 33 33 8 , 21 29 31 15 13 -> 21 29 34 12 28 16 19 25 34 12 13 , 3 31 15 28 5 9 -> 3 4 25 26 10 16 18 30 8 9 9 , 0 11 24 21 20 21 -> 21 6 16 18 12 35 30 31 2 0 21 , 1 15 15 13 20 21 -> 1 2 3 4 16 19 5 27 2 0 21 , 3 31 35 30 34 22 -> 0 10 17 16 18 12 35 30 8 14 22 , 1 13 20 1 28 5 -> 11 12 28 16 18 12 28 17 25 4 5 , 0 1 15 32 33 8 -> 0 1 28 25 33 4 17 16 18 22 9 , 11 24 1 15 32 8 -> 10 16 18 19 16 30 4 23 35 22 9 , 1 15 2 1 15 13 -> 11 19 25 8 9 20 0 10 5 27 13 , 0 11 19 23 15 13 -> 0 21 6 16 12 35 30 34 18 12 13 , 1 32 26 1 13 9 9 -> 11 22 6 5 9 29 4 25 4 5 9 , 11 24 1 13 29 8 9 -> 11 19 17 16 22 14 24 3 34 30 8 , 21 29 31 13 29 8 9 -> 10 7 3 33 4 25 8 27 28 25 8 , 1 2 21 29 33 8 9 -> 11 22 20 10 25 26 21 20 3 8 9 , 0 1 15 32 33 8 9 -> 3 26 3 33 33 34 22 27 28 16 22 , 0 11 12 2 1 35 22 -> 0 3 8 27 28 7 10 16 18 30 8 , 1 15 2 11 12 35 22 -> 10 17 17 17 7 1 35 19 17 16 22 , 1 2 10 23 15 35 22 -> 1 35 18 19 25 33 26 1 35 18 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34 22 9 9 27 35 19 16 18 , 1 32 26 1 13 9 6 16 -> 1 32 8 20 10 5 6 5 9 6 16 , 0 11 30 33 31 13 6 16 -> 3 34 19 7 3 4 17 25 31 28 16 , 11 30 8 9 29 26 10 16 -> 11 18 19 23 32 26 11 22 6 17 16 , 3 8 20 1 15 2 10 16 -> 3 4 17 5 20 10 16 24 10 17 16 , 1 15 15 15 15 32 4 16 -> 1 28 23 32 34 18 12 2 0 10 16 , 10 23 35 12 32 31 28 16 -> 21 20 21 27 28 16 30 4 16 19 16 , 1 32 4 23 15 13 29 34 -> 1 15 13 9 20 3 4 16 22 29 34 , 1 13 20 21 29 31 32 34 -> 10 17 25 4 16 24 1 32 33 26 11 , 1 32 33 31 13 20 1 35 -> 10 25 26 10 17 23 15 28 25 31 35 , 0 21 14 ->= 3 8 14 22 14 19 25 34 19 16 18 , 1 2 11 18 ->= 10 23 28 17 25 4 16 19 5 14 18 , 0 1 13 9 14 ->= 0 11 22 20 3 4 17 7 3 8 14 , 0 1 13 29 33 8 14 ->= 0 11 12 15 13 14 19 16 22 29 34 , 1 32 31 2 11 19 5 14 ->= 1 35 12 13 6 25 34 24 3 33 34 , 1 15 2 11 24 1 13 14 ->= 11 19 17 23 13 20 1 15 13 14 18 , 2 1 2 0 -> 32 4 5 6 7 3 8 9 6 7 0 , 15 2 10 7 -> 35 12 13 14 12 13 6 7 0 10 7 , 2 1 15 2 -> 32 8 6 16 12 2 10 17 16 12 2 , 15 15 15 2 -> 35 18 19 7 0 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11 22 27 32 26 0 0 0 0 , 15 32 4 23 2 11 24 0 -> 28 5 9 6 17 23 28 5 27 2 0 , 15 13 6 23 13 27 2 0 -> 15 28 23 28 7 3 26 10 25 26 0 , 15 35 12 15 15 28 16 24 -> 13 29 34 22 9 9 27 35 19 16 24 , 15 32 26 1 13 9 6 7 -> 15 32 8 20 10 5 6 5 9 6 7 , 2 11 30 33 31 13 6 7 -> 32 34 19 7 3 4 17 25 31 28 7 , 35 30 8 9 29 26 10 7 -> 35 18 19 23 32 26 11 22 6 17 7 , 32 8 20 1 15 2 10 7 -> 32 4 17 5 20 10 16 24 10 17 7 , 15 15 15 15 15 32 4 7 -> 15 28 23 32 34 18 12 2 0 10 7 , 28 23 35 12 32 31 28 7 -> 13 20 21 27 28 16 30 4 16 19 7 , 15 32 4 23 15 13 29 26 -> 15 15 13 9 20 3 4 16 22 29 26 , 15 13 20 21 29 31 32 26 -> 28 17 25 4 16 24 1 32 33 26 0 , 15 32 33 31 13 20 1 2 -> 28 25 26 10 17 23 15 28 25 31 2 , 2 21 20 ->= 32 8 14 22 14 19 25 34 19 16 24 , 15 2 11 24 ->= 28 23 28 17 25 4 16 19 5 14 24 , 2 1 13 9 20 ->= 2 11 22 20 3 4 17 7 3 8 20 , 2 1 13 29 33 8 20 ->= 2 11 12 15 13 14 19 16 22 29 26 , 15 32 31 2 11 19 5 20 ->= 15 35 12 13 6 25 34 24 3 33 26 , 15 15 2 11 24 1 13 20 ->= 35 19 17 23 13 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27 15 , 2 11 19 23 15 15 -> 2 21 6 16 12 35 30 34 18 12 15 , 15 32 26 1 13 9 27 -> 35 22 6 5 9 29 4 25 4 5 27 , 35 24 1 13 29 8 27 -> 35 19 17 16 22 14 24 3 34 30 31 , 13 29 31 13 29 8 27 -> 28 7 3 33 4 25 8 27 28 25 31 , 15 2 21 29 33 8 27 -> 35 22 20 10 25 26 21 20 3 8 27 , 2 1 15 32 33 8 27 -> 32 26 3 33 33 34 22 27 28 16 12 , 2 11 12 2 1 35 12 -> 2 3 8 27 28 7 10 16 18 30 31 , 15 15 2 11 12 35 12 -> 28 17 17 17 7 1 35 19 17 16 12 , 15 2 10 23 15 35 12 -> 15 35 18 19 25 33 26 1 35 18 12 , 13 29 26 11 24 10 23 -> 13 6 16 22 14 24 0 1 28 17 23 , 13 29 8 20 1 28 23 -> 13 14 19 16 12 15 28 17 17 17 23 , 32 31 32 4 23 28 23 -> 32 4 25 26 21 20 21 6 23 28 23 , 2 1 35 30 33 31 15 -> 32 26 10 16 18 22 9 14 22 27 15 , 13 29 31 2 1 15 15 -> 13 14 22 6 23 32 34 22 27 15 15 , 32 31 15 15 15 15 15 -> 2 3 26 21 29 31 28 17 17 23 15 , 15 32 31 32 33 4 5 27 -> 13 20 3 4 16 19 25 4 25 8 27 , 32 31 32 31 13 29 8 27 -> 32 8 9 6 25 33 4 25 31 35 12 , 13 20 1 15 13 29 8 27 -> 13 9 27 28 25 8 6 16 30 31 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28 23 2 11 18 -> 13 9 6 16 19 25 26 10 7 11 18 , 15 15 13 6 16 -> 35 22 6 17 16 12 13 27 28 17 16 , 13 20 21 29 34 -> 28 17 16 19 16 24 3 4 16 22 14 , 15 15 13 29 34 -> 28 16 24 10 16 18 18 19 25 8 14 , 35 24 11 30 34 -> 28 17 16 22 20 11 22 14 22 14 18 , 32 31 15 32 34 -> 28 7 11 19 7 21 29 33 33 33 34 , 13 29 31 15 35 -> 13 29 34 12 28 16 19 25 34 12 35 , 32 31 15 28 5 14 -> 32 4 25 26 10 16 18 30 8 9 14 , 2 11 24 21 20 11 -> 13 6 16 18 12 35 30 31 2 0 11 , 15 15 15 13 20 11 -> 15 2 3 4 16 19 5 27 2 0 11 , 32 31 35 30 34 18 -> 2 10 17 16 18 12 35 30 8 14 18 , 15 13 20 1 28 16 -> 35 12 28 16 18 12 28 17 25 4 16 , 2 1 15 32 33 34 -> 2 1 28 25 33 4 17 16 18 22 14 , 35 24 1 15 32 34 -> 28 16 18 19 16 30 4 23 35 22 14 , 15 15 2 1 15 35 -> 35 19 25 8 9 20 0 10 5 27 35 , 2 11 19 23 15 35 -> 2 21 6 16 12 35 30 34 18 12 35 , 15 32 26 1 13 9 14 -> 35 22 6 5 9 29 4 25 4 5 14 , 35 24 1 13 29 8 14 -> 35 19 17 16 22 14 24 3 34 30 34 , 13 29 31 13 29 8 14 -> 28 7 3 33 4 25 8 27 28 25 34 , 15 2 21 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22 29 31 15 15 -> 22 29 34 12 28 16 19 25 34 12 15 , 30 31 15 28 5 27 -> 30 4 25 26 10 16 18 30 8 9 27 , 24 11 24 21 20 1 -> 22 6 16 18 12 35 30 31 2 0 1 , 12 15 15 13 20 1 -> 12 2 3 4 16 19 5 27 2 0 1 , 30 31 35 30 34 12 -> 24 10 17 16 18 12 35 30 8 14 12 , 12 13 20 1 28 23 -> 18 12 28 16 18 12 28 17 25 4 23 , 24 1 15 32 33 31 -> 24 1 28 25 33 4 17 16 18 22 27 , 18 24 1 15 32 31 -> 19 16 18 19 16 30 4 23 35 22 27 , 12 15 2 1 15 15 -> 18 19 25 8 9 20 0 10 5 27 15 , 24 11 19 23 15 15 -> 24 21 6 16 12 35 30 34 18 12 15 , 12 32 26 1 13 9 27 -> 18 22 6 5 9 29 4 25 4 5 27 , 18 24 1 13 29 8 27 -> 18 19 17 16 22 14 24 3 34 30 31 , 22 29 31 13 29 8 27 -> 19 7 3 33 4 25 8 27 28 25 31 , 12 2 21 29 33 8 27 -> 18 22 20 10 25 26 21 20 3 8 27 , 24 1 15 32 33 8 27 -> 30 26 3 33 33 34 22 27 28 16 12 , 24 11 12 2 1 35 12 -> 24 3 8 27 28 7 10 16 18 30 31 , 12 15 2 11 12 35 12 -> 19 17 17 17 7 1 35 19 17 16 12 , 12 2 10 23 15 35 12 -> 12 35 18 19 25 33 26 1 35 18 12 , 22 29 26 11 24 10 23 -> 22 6 16 22 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18 18 19 23 32 26 11 22 6 17 23 , 30 8 20 1 15 2 10 23 -> 30 4 17 5 20 10 16 24 10 17 23 , 12 15 15 15 15 32 4 23 -> 12 28 23 32 34 18 12 2 0 10 23 , 19 23 35 12 32 31 28 23 -> 22 20 21 27 28 16 30 4 16 19 23 , 12 32 4 23 15 13 29 31 -> 12 15 13 9 20 3 4 16 22 29 31 , 12 13 20 21 29 31 32 31 -> 19 17 25 4 16 24 1 32 33 26 1 , 12 32 33 31 13 20 1 15 -> 19 25 26 10 17 23 15 28 25 31 15 , 24 21 27 ->= 30 8 14 22 14 19 25 34 19 16 12 , 12 2 11 12 ->= 19 23 28 17 25 4 16 19 5 14 12 , 24 1 13 9 27 ->= 24 11 22 20 3 4 17 7 3 8 27 , 24 1 13 29 33 8 27 ->= 24 11 12 15 13 14 19 16 22 29 31 , 12 32 31 2 11 19 5 27 ->= 12 35 12 13 6 25 34 24 3 33 31 , 12 15 2 11 24 1 13 27 ->= 18 19 17 23 13 20 1 15 13 14 12 , 24 1 2 3 -> 30 4 5 6 7 3 8 9 6 7 3 , 12 2 10 25 -> 18 12 13 14 12 13 6 7 0 10 25 , 24 1 15 32 -> 30 8 6 16 12 2 10 17 16 12 32 , 12 15 15 32 -> 18 18 19 7 0 0 10 7 11 12 32 , 30 4 5 20 3 -> 24 3 4 7 0 21 14 22 20 0 3 , 19 23 2 11 30 -> 22 9 6 16 19 25 26 10 7 11 30 , 12 15 13 6 25 -> 18 22 6 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24 0 1 35 24 10 7 3 26 21 6 , 24 10 5 20 1 15 13 6 -> 24 10 17 5 29 33 4 5 6 16 19 , 12 2 1 2 21 20 0 10 -> 12 2 11 22 27 32 26 0 0 0 10 , 12 32 4 23 2 11 24 10 -> 19 5 9 6 17 23 28 5 27 2 10 , 12 13 6 23 13 27 2 10 -> 12 28 23 28 7 3 26 10 25 26 10 , 12 35 12 15 15 28 16 19 -> 22 29 34 22 9 9 27 35 19 16 19 , 12 32 26 1 13 9 6 17 -> 12 32 8 20 10 5 6 5 9 6 17 , 24 11 30 33 31 13 6 17 -> 30 34 19 7 3 4 17 25 31 28 17 , 18 30 8 9 29 26 10 17 -> 18 18 19 23 32 26 11 22 6 17 17 , 30 8 20 1 15 2 10 17 -> 30 4 17 5 20 10 16 24 10 17 17 , 12 15 15 15 15 32 4 17 -> 12 28 23 32 34 18 12 2 0 10 17 , 19 23 35 12 32 31 28 17 -> 22 20 21 27 28 16 30 4 16 19 17 , 12 32 4 23 15 13 29 4 -> 12 15 13 9 20 3 4 16 22 29 4 , 12 13 20 21 29 31 32 4 -> 19 17 25 4 16 24 1 32 33 26 10 , 12 32 33 31 13 20 1 28 -> 19 25 26 10 17 23 15 28 25 31 28 , 24 21 6 ->= 30 8 14 22 14 19 25 34 19 16 19 , 12 2 11 19 ->= 19 23 28 17 25 4 16 19 5 14 19 , 24 1 13 9 6 ->= 24 11 22 20 3 4 17 7 3 8 6 , 24 1 13 29 33 8 6 ->= 24 11 12 15 13 14 19 16 22 29 4 , 12 32 31 2 11 19 5 6 ->= 12 35 12 13 6 25 34 24 3 33 4 , 12 15 2 11 24 1 13 6 ->= 18 19 17 23 13 20 1 15 13 14 19 , 24 1 2 21 -> 30 4 5 6 7 3 8 9 6 7 21 , 12 2 10 5 -> 18 12 13 14 12 13 6 7 0 10 5 , 24 1 15 13 -> 30 8 6 16 12 2 10 17 16 12 13 , 12 15 15 13 -> 18 18 19 7 0 0 10 7 11 12 13 , 30 4 5 20 21 -> 24 3 4 7 0 21 14 22 20 0 21 , 19 23 2 11 22 -> 22 9 6 16 19 25 26 10 7 11 22 , 12 15 13 6 5 -> 18 22 6 17 16 12 13 27 28 17 5 , 22 20 21 29 8 -> 19 17 16 19 16 24 3 4 16 22 9 , 12 15 13 29 8 -> 19 16 24 10 16 18 18 19 25 8 9 , 18 24 11 30 8 -> 19 17 16 22 20 11 22 14 22 14 22 , 30 31 15 32 8 -> 19 7 11 19 7 21 29 33 33 33 8 , 22 29 31 15 13 -> 22 29 34 12 28 16 19 25 34 12 13 , 30 31 15 28 5 9 -> 30 4 25 26 10 16 18 30 8 9 9 , 24 11 24 21 20 21 -> 22 6 16 18 12 35 30 31 2 0 21 , 12 15 15 13 20 21 -> 12 2 3 4 16 19 5 27 2 0 21 , 30 31 35 30 34 22 -> 24 10 17 16 18 12 35 30 8 14 22 , 12 13 20 1 28 5 -> 18 12 28 16 18 12 28 17 25 4 5 , 24 1 15 32 33 8 -> 24 1 28 25 33 4 17 16 18 22 9 , 18 24 1 15 32 8 -> 19 16 18 19 16 30 4 23 35 22 9 , 12 15 2 1 15 13 -> 18 19 25 8 9 20 0 10 5 27 13 , 24 11 19 23 15 13 -> 24 21 6 16 12 35 30 34 18 12 13 , 12 32 26 1 13 9 9 -> 18 22 6 5 9 29 4 25 4 5 9 , 18 24 1 13 29 8 9 -> 18 19 17 16 22 14 24 3 34 30 8 , 22 29 31 13 29 8 9 -> 19 7 3 33 4 25 8 27 28 25 8 , 12 2 21 29 33 8 9 -> 18 22 20 10 25 26 21 20 3 8 9 , 24 1 15 32 33 8 9 -> 30 26 3 33 33 34 22 27 28 16 22 , 24 11 12 2 1 35 22 -> 24 3 8 27 28 7 10 16 18 30 8 , 12 15 2 11 12 35 22 -> 19 17 17 17 7 1 35 19 17 16 22 , 12 2 10 23 15 35 22 -> 12 35 18 19 25 33 26 1 35 18 22 , 22 29 26 11 24 10 5 -> 22 6 16 22 14 24 0 1 28 17 5 , 22 29 8 20 1 28 5 -> 22 14 19 16 12 15 28 17 17 17 5 , 30 31 32 4 23 28 5 -> 30 4 25 26 21 20 21 6 23 28 5 , 24 1 35 30 33 31 13 -> 30 26 10 16 18 22 9 14 22 27 13 , 22 29 31 2 1 15 13 -> 22 14 22 6 23 32 34 22 27 15 13 , 30 31 15 15 15 15 13 -> 24 3 26 21 29 31 28 17 17 23 13 , 12 32 31 32 33 4 5 9 -> 22 20 3 4 16 19 25 4 25 8 9 , 30 31 32 31 13 29 8 9 -> 30 8 9 6 25 33 4 25 31 35 22 , 22 20 1 15 13 29 8 9 -> 22 9 27 28 25 8 6 16 30 31 13 , 12 35 12 13 20 3 8 9 -> 12 35 19 7 1 13 9 6 17 16 22 , 24 1 28 23 28 23 13 9 -> 24 0 1 35 24 10 7 3 26 21 9 , 24 10 5 20 1 15 13 9 -> 24 10 17 5 29 33 4 5 6 16 22 , 12 2 1 2 21 20 0 21 -> 12 2 11 22 27 32 26 0 0 0 21 , 12 32 4 23 2 11 24 21 -> 19 5 9 6 17 23 28 5 27 2 21 , 12 13 6 23 13 27 2 21 -> 12 28 23 28 7 3 26 10 25 26 21 , 12 35 12 15 15 28 16 22 -> 22 29 34 22 9 9 27 35 19 16 22 , 12 32 26 1 13 9 6 5 -> 12 32 8 20 10 5 6 5 9 6 5 , 24 11 30 33 31 13 6 5 -> 30 34 19 7 3 4 17 25 31 28 5 , 18 30 8 9 29 26 10 5 -> 18 18 19 23 32 26 11 22 6 17 5 , 30 8 20 1 15 2 10 5 -> 30 4 17 5 20 10 16 24 10 17 5 , 12 15 15 15 15 32 4 5 -> 12 28 23 32 34 18 12 2 0 10 5 , 19 23 35 12 32 31 28 5 -> 22 20 21 27 28 16 30 4 16 19 5 , 12 32 4 23 15 13 29 8 -> 12 15 13 9 20 3 4 16 22 29 8 , 12 13 20 21 29 31 32 8 -> 19 17 25 4 16 24 1 32 33 26 21 , 12 32 33 31 13 20 1 13 -> 19 25 26 10 17 23 15 28 25 31 13 , 24 21 9 ->= 30 8 14 22 14 19 25 34 19 16 22 , 12 2 11 22 ->= 19 23 28 17 25 4 16 19 5 14 22 , 24 1 13 9 9 ->= 24 11 22 20 3 4 17 7 3 8 9 , 24 1 13 29 33 8 9 ->= 24 11 12 15 13 14 19 16 22 29 8 , 12 32 31 2 11 19 5 9 ->= 12 35 12 13 6 25 34 24 3 33 8 , 12 15 2 11 24 1 13 9 ->= 18 19 17 23 13 20 1 15 13 14 22 , 24 1 2 11 -> 30 4 5 6 7 3 8 9 6 7 11 , 12 2 10 16 -> 18 12 13 14 12 13 6 7 0 10 16 , 24 1 15 35 -> 30 8 6 16 12 2 10 17 16 12 35 , 12 15 15 35 -> 18 18 19 7 0 0 10 7 11 12 35 , 30 4 5 20 11 -> 24 3 4 7 0 21 14 22 20 0 11 , 19 23 2 11 18 -> 22 9 6 16 19 25 26 10 7 11 18 , 12 15 13 6 16 -> 18 22 6 17 16 12 13 27 28 17 16 , 22 20 21 29 34 -> 19 17 16 19 16 24 3 4 16 22 14 , 12 15 13 29 34 -> 19 16 24 10 16 18 18 19 25 8 14 , 18 24 11 30 34 -> 19 17 16 22 20 11 22 14 22 14 18 , 30 31 15 32 34 -> 19 7 11 19 7 21 29 33 33 33 34 , 22 29 31 15 35 -> 22 29 34 12 28 16 19 25 34 12 35 , 30 31 15 28 5 14 -> 30 4 25 26 10 16 18 30 8 9 14 , 24 11 24 21 20 11 -> 22 6 16 18 12 35 30 31 2 0 11 , 12 15 15 13 20 11 -> 12 2 3 4 16 19 5 27 2 0 11 , 30 31 35 30 34 18 -> 24 10 17 16 18 12 35 30 8 14 18 , 12 13 20 1 28 16 -> 18 12 28 16 18 12 28 17 25 4 16 , 24 1 15 32 33 34 -> 24 1 28 25 33 4 17 16 18 22 14 , 18 24 1 15 32 34 -> 19 16 18 19 16 30 4 23 35 22 14 , 12 15 2 1 15 35 -> 18 19 25 8 9 20 0 10 5 27 35 , 24 11 19 23 15 35 -> 24 21 6 16 12 35 30 34 18 12 35 , 12 32 26 1 13 9 14 -> 18 22 6 5 9 29 4 25 4 5 14 , 18 24 1 13 29 8 14 -> 18 19 17 16 22 14 24 3 34 30 34 , 22 29 31 13 29 8 14 -> 19 7 3 33 4 25 8 27 28 25 34 , 12 2 21 29 33 8 14 -> 18 22 20 10 25 26 21 20 3 8 14 , 24 1 15 32 33 8 14 -> 30 26 3 33 33 34 22 27 28 16 18 , 24 11 12 2 1 35 18 -> 24 3 8 27 28 7 10 16 18 30 34 , 12 15 2 11 12 35 18 -> 19 17 17 17 7 1 35 19 17 16 18 , 12 2 10 23 15 35 18 -> 12 35 18 19 25 33 26 1 35 18 18 , 22 29 26 11 24 10 16 -> 22 6 16 22 14 24 0 1 28 17 16 , 22 29 8 20 1 28 16 -> 22 14 19 16 12 15 28 17 17 17 16 , 30 31 32 4 23 28 16 -> 30 4 25 26 21 20 21 6 23 28 16 , 24 1 35 30 33 31 35 -> 30 26 10 16 18 22 9 14 22 27 35 , 22 29 31 2 1 15 35 -> 22 14 22 6 23 32 34 22 27 15 35 , 30 31 15 15 15 15 35 -> 24 3 26 21 29 31 28 17 17 23 35 , 12 32 31 32 33 4 5 14 -> 22 20 3 4 16 19 25 4 25 8 14 , 30 31 32 31 13 29 8 14 -> 30 8 9 6 25 33 4 25 31 35 18 , 22 20 1 15 13 29 8 14 -> 22 9 27 28 25 8 6 16 30 31 35 , 12 35 12 13 20 3 8 14 -> 12 35 19 7 1 13 9 6 17 16 18 , 24 1 28 23 28 23 13 14 -> 24 0 1 35 24 10 7 3 26 21 14 , 24 10 5 20 1 15 13 14 -> 24 10 17 5 29 33 4 5 6 16 18 , 12 2 1 2 21 20 0 11 -> 12 2 11 22 27 32 26 0 0 0 11 , 12 32 4 23 2 11 24 11 -> 19 5 9 6 17 23 28 5 27 2 11 , 12 13 6 23 13 27 2 11 -> 12 28 23 28 7 3 26 10 25 26 11 , 12 35 12 15 15 28 16 18 -> 22 29 34 22 9 9 27 35 19 16 18 , 12 32 26 1 13 9 6 16 -> 12 32 8 20 10 5 6 5 9 6 16 , 24 11 30 33 31 13 6 16 -> 30 34 19 7 3 4 17 25 31 28 16 , 18 30 8 9 29 26 10 16 -> 18 18 19 23 32 26 11 22 6 17 16 , 30 8 20 1 15 2 10 16 -> 30 4 17 5 20 10 16 24 10 17 16 , 12 15 15 15 15 32 4 16 -> 12 28 23 32 34 18 12 2 0 10 16 , 19 23 35 12 32 31 28 16 -> 22 20 21 27 28 16 30 4 16 19 16 , 12 32 4 23 15 13 29 34 -> 12 15 13 9 20 3 4 16 22 29 34 , 12 13 20 21 29 31 32 34 -> 19 17 25 4 16 24 1 32 33 26 11 , 12 32 33 31 13 20 1 35 -> 19 25 26 10 17 23 15 28 25 31 35 , 24 21 14 ->= 30 8 14 22 14 19 25 34 19 16 18 , 12 2 11 18 ->= 19 23 28 17 25 4 16 19 5 14 18 , 24 1 13 9 14 ->= 24 11 22 20 3 4 17 7 3 8 14 , 24 1 13 29 33 8 14 ->= 24 11 12 15 13 14 19 16 22 29 34 , 12 32 31 2 11 19 5 14 ->= 12 35 12 13 6 25 34 24 3 33 34 , 12 15 2 11 24 1 13 14 ->= 18 19 17 23 13 20 1 15 13 14 18 } 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 / \ | 1 844 | | 0 1 | \ / 2 is interpreted by / \ | 1 815 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 69 | | 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 | \ / 9 is interpreted by / \ | 1 84 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 308 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 309 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 527 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 928 | | 0 1 | \ / 21 is interpreted by / \ | 1 68 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 802 | | 0 1 | \ / 24 is interpreted by / \ | 1 915 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 15 | | 0 1 | \ / 27 is interpreted by / \ | 1 111 | | 0 1 | \ / 28 is interpreted by / \ | 1 224 | | 0 1 | \ / 29 is interpreted by / \ | 1 996 | | 0 1 | \ / 30 is interpreted by / \ | 1 914 | | 0 1 | \ / 31 is interpreted by / \ | 1 197 | | 0 1 | \ / 32 is interpreted by / \ | 1 883 | | 0 1 | \ / 33 is interpreted by / \ | 1 78 | | 0 1 | \ / 34 is interpreted by / \ | 1 0 | | 0 1 | \ / 35 is interpreted by / \ | 1 223 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 13->2, 29->3, 33->4, 8->5, 27->6, 11->7, 12->8, 15->9, 14->10, 19->11, 16->12, 22->13, 31->14, 35->15, 24->16, 30->17, 26->18, 28->19, 17->20, 20->21, 23->22, 32->23, 7->24, 21->25, 4->26, 2->27, 25->28, 6->29, 34->30, 5->31, 18->32, 3->33, 10->34 }, it remains to prove termination of the 33-rule system { 0 1 2 3 4 5 6 ->= 0 7 8 9 2 10 11 12 13 3 14 , 15 16 7 17 18 -> 19 20 12 13 21 7 13 10 13 10 16 , 19 22 15 8 23 14 19 24 -> 2 21 25 6 19 12 17 26 12 11 24 , 19 22 15 8 23 14 19 22 -> 2 21 25 6 19 12 17 26 12 11 22 , 27 1 2 3 4 5 6 ->= 27 7 8 9 2 10 11 12 13 3 14 , 19 22 15 8 23 14 19 28 -> 2 21 25 6 19 12 17 26 12 11 28 , 19 22 15 8 23 14 19 20 -> 2 21 25 6 19 12 17 26 12 11 20 , 27 25 29 ->= 23 5 10 13 10 11 28 30 11 12 11 , 19 22 15 8 23 14 19 31 -> 2 21 25 6 19 12 17 26 12 11 31 , 19 22 15 8 23 14 19 12 -> 2 21 25 6 19 12 17 26 12 11 12 , 27 25 10 ->= 23 5 10 13 10 11 28 30 11 12 32 , 18 1 2 3 4 5 6 ->= 18 7 8 9 2 10 11 12 13 3 14 , 24 7 16 25 21 0 -> 31 29 12 32 8 15 17 14 27 0 0 , 24 7 16 25 21 1 -> 31 29 12 32 8 15 17 14 27 0 1 , 24 1 2 3 4 5 6 ->= 24 7 8 9 2 10 11 12 13 3 14 , 24 7 16 25 21 33 -> 31 29 12 32 8 15 17 14 27 0 33 , 24 7 16 25 21 34 -> 31 29 12 32 8 15 17 14 27 0 34 , 24 7 16 25 21 25 -> 31 29 12 32 8 15 17 14 27 0 25 , 24 7 16 25 21 7 -> 31 29 12 32 8 15 17 14 27 0 7 , 21 1 2 3 4 5 6 ->= 21 7 8 9 2 10 11 12 13 3 14 , 21 25 29 ->= 3 5 10 13 10 11 28 30 11 12 11 , 21 25 10 ->= 3 5 10 13 10 11 28 30 11 12 32 , 17 26 31 21 0 -> 16 33 26 24 0 25 10 13 21 0 0 , 17 26 31 21 1 -> 16 33 26 24 0 25 10 13 21 0 1 , 8 2 21 25 3 14 23 14 -> 11 20 28 26 12 16 1 23 4 18 1 , 16 1 2 3 4 5 6 ->= 16 7 8 9 2 10 11 12 13 3 14 , 17 26 31 21 33 -> 16 33 26 24 0 25 10 13 21 0 33 , 8 9 2 3 4 -> 11 12 16 34 12 32 32 11 28 5 3 , 17 26 31 21 34 -> 16 33 26 24 0 25 10 13 21 0 34 , 8 9 27 7 16 1 2 29 ->= 32 11 20 22 2 21 1 9 2 10 11 , 17 26 31 21 25 -> 16 33 26 24 0 25 10 13 21 0 25 , 17 26 31 21 7 -> 16 33 26 24 0 25 10 13 21 0 7 , 8 9 27 7 16 1 2 10 ->= 32 11 20 22 2 21 1 9 2 10 32 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 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 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 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 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 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, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 19->15, 22->16, 15->17, 23->18, 24->19, 21->20, 25->21, 17->22, 26->23, 27->24, 28->25, 20->26, 29->27, 30->28, 31->29, 32->30, 18->31, 16->32, 33->33, 34->34 }, it remains to prove termination of the 32-rule system { 0 1 2 3 4 5 6 ->= 0 7 8 9 2 10 11 12 13 3 14 , 15 16 17 8 18 14 15 19 -> 2 20 21 6 15 12 22 23 12 11 19 , 15 16 17 8 18 14 15 16 -> 2 20 21 6 15 12 22 23 12 11 16 , 24 1 2 3 4 5 6 ->= 24 7 8 9 2 10 11 12 13 3 14 , 15 16 17 8 18 14 15 25 -> 2 20 21 6 15 12 22 23 12 11 25 , 15 16 17 8 18 14 15 26 -> 2 20 21 6 15 12 22 23 12 11 26 , 24 21 27 ->= 18 5 10 13 10 11 25 28 11 12 11 , 15 16 17 8 18 14 15 29 -> 2 20 21 6 15 12 22 23 12 11 29 , 15 16 17 8 18 14 15 12 -> 2 20 21 6 15 12 22 23 12 11 12 , 24 21 10 ->= 18 5 10 13 10 11 25 28 11 12 30 , 31 1 2 3 4 5 6 ->= 31 7 8 9 2 10 11 12 13 3 14 , 19 7 32 21 20 0 -> 29 27 12 30 8 17 22 14 24 0 0 , 19 7 32 21 20 1 -> 29 27 12 30 8 17 22 14 24 0 1 , 19 1 2 3 4 5 6 ->= 19 7 8 9 2 10 11 12 13 3 14 , 19 7 32 21 20 33 -> 29 27 12 30 8 17 22 14 24 0 33 , 19 7 32 21 20 34 -> 29 27 12 30 8 17 22 14 24 0 34 , 19 7 32 21 20 21 -> 29 27 12 30 8 17 22 14 24 0 21 , 19 7 32 21 20 7 -> 29 27 12 30 8 17 22 14 24 0 7 , 20 1 2 3 4 5 6 ->= 20 7 8 9 2 10 11 12 13 3 14 , 20 21 27 ->= 3 5 10 13 10 11 25 28 11 12 11 , 20 21 10 ->= 3 5 10 13 10 11 25 28 11 12 30 , 22 23 29 20 0 -> 32 33 23 19 0 21 10 13 20 0 0 , 22 23 29 20 1 -> 32 33 23 19 0 21 10 13 20 0 1 , 8 2 20 21 3 14 18 14 -> 11 26 25 23 12 32 1 18 4 31 1 , 32 1 2 3 4 5 6 ->= 32 7 8 9 2 10 11 12 13 3 14 , 22 23 29 20 33 -> 32 33 23 19 0 21 10 13 20 0 33 , 8 9 2 3 4 -> 11 12 32 34 12 30 30 11 25 5 3 , 22 23 29 20 34 -> 32 33 23 19 0 21 10 13 20 0 34 , 8 9 24 7 32 1 2 27 ->= 30 11 26 16 2 20 1 9 2 10 11 , 22 23 29 20 21 -> 32 33 23 19 0 21 10 13 20 0 21 , 22 23 29 20 7 -> 32 33 23 19 0 21 10 13 20 0 7 , 8 9 24 7 32 1 2 10 ->= 30 11 26 16 2 20 1 9 2 10 30 } 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 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 1 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 0 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 0 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 is interpreted by / \ | 1 0 | | 0 1 | \ / 30 is interpreted by / \ | 1 0 | | 0 1 | \ / 31 is interpreted by / \ | 1 0 | | 0 1 | \ / 32 is interpreted by / \ | 1 0 | | 0 1 | \ / 33 is interpreted by / \ | 1 0 | | 0 1 | \ / 34 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 24->15, 21->16, 27->17, 18->18, 25->19, 28->20, 30->21, 31->22, 19->23, 32->24, 20->25, 29->26, 17->27, 22->28, 33->29, 34->30, 23->31, 26->32, 16->33 }, it remains to prove termination of the 26-rule system { 0 1 2 3 4 5 6 ->= 0 7 8 9 2 10 11 12 13 3 14 , 15 1 2 3 4 5 6 ->= 15 7 8 9 2 10 11 12 13 3 14 , 15 16 17 ->= 18 5 10 13 10 11 19 20 11 12 11 , 15 16 10 ->= 18 5 10 13 10 11 19 20 11 12 21 , 22 1 2 3 4 5 6 ->= 22 7 8 9 2 10 11 12 13 3 14 , 23 7 24 16 25 0 -> 26 17 12 21 8 27 28 14 15 0 0 , 23 7 24 16 25 1 -> 26 17 12 21 8 27 28 14 15 0 1 , 23 1 2 3 4 5 6 ->= 23 7 8 9 2 10 11 12 13 3 14 , 23 7 24 16 25 29 -> 26 17 12 21 8 27 28 14 15 0 29 , 23 7 24 16 25 30 -> 26 17 12 21 8 27 28 14 15 0 30 , 23 7 24 16 25 16 -> 26 17 12 21 8 27 28 14 15 0 16 , 23 7 24 16 25 7 -> 26 17 12 21 8 27 28 14 15 0 7 , 25 1 2 3 4 5 6 ->= 25 7 8 9 2 10 11 12 13 3 14 , 25 16 17 ->= 3 5 10 13 10 11 19 20 11 12 11 , 25 16 10 ->= 3 5 10 13 10 11 19 20 11 12 21 , 28 31 26 25 0 -> 24 29 31 23 0 16 10 13 25 0 0 , 28 31 26 25 1 -> 24 29 31 23 0 16 10 13 25 0 1 , 8 2 25 16 3 14 18 14 -> 11 32 19 31 12 24 1 18 4 22 1 , 24 1 2 3 4 5 6 ->= 24 7 8 9 2 10 11 12 13 3 14 , 28 31 26 25 29 -> 24 29 31 23 0 16 10 13 25 0 29 , 8 9 2 3 4 -> 11 12 24 30 12 21 21 11 19 5 3 , 28 31 26 25 30 -> 24 29 31 23 0 16 10 13 25 0 30 , 8 9 15 7 24 1 2 17 ->= 21 11 32 33 2 25 1 9 2 10 11 , 28 31 26 25 16 -> 24 29 31 23 0 16 10 13 25 0 16 , 28 31 26 25 7 -> 24 29 31 23 0 16 10 13 25 0 7 , 8 9 15 7 24 1 2 10 ->= 21 11 32 33 2 25 1 9 2 10 21 } 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 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 0 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 0 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 is interpreted by / \ | 1 0 | | 0 1 | \ / 30 is interpreted by / \ | 1 0 | | 0 1 | \ / 31 is interpreted by / \ | 1 0 | | 0 1 | \ / 32 is interpreted by / \ | 1 0 | | 0 1 | \ / 33 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 15->0, 16->1, 17->2, 18->3, 5->4, 10->5, 13->6, 11->7, 19->8, 20->9, 12->10, 21->11, 23->12, 7->13, 24->14, 25->15, 0->16, 26->17, 8->18, 27->19, 28->20, 14->21, 1->22, 29->23, 30->24, 3->25, 31->26, 2->27, 32->28, 4->29, 22->30, 9->31, 33->32 }, it remains to prove termination of the 20-rule system { 0 1 2 ->= 3 4 5 6 5 7 8 9 7 10 7 , 0 1 5 ->= 3 4 5 6 5 7 8 9 7 10 11 , 12 13 14 1 15 16 -> 17 2 10 11 18 19 20 21 0 16 16 , 12 13 14 1 15 22 -> 17 2 10 11 18 19 20 21 0 16 22 , 12 13 14 1 15 23 -> 17 2 10 11 18 19 20 21 0 16 23 , 12 13 14 1 15 24 -> 17 2 10 11 18 19 20 21 0 16 24 , 12 13 14 1 15 1 -> 17 2 10 11 18 19 20 21 0 16 1 , 12 13 14 1 15 13 -> 17 2 10 11 18 19 20 21 0 16 13 , 15 1 2 ->= 25 4 5 6 5 7 8 9 7 10 7 , 15 1 5 ->= 25 4 5 6 5 7 8 9 7 10 11 , 20 26 17 15 16 -> 14 23 26 12 16 1 5 6 15 16 16 , 20 26 17 15 22 -> 14 23 26 12 16 1 5 6 15 16 22 , 18 27 15 1 25 21 3 21 -> 7 28 8 26 10 14 22 3 29 30 22 , 20 26 17 15 23 -> 14 23 26 12 16 1 5 6 15 16 23 , 18 31 27 25 29 -> 7 10 14 24 10 11 11 7 8 4 25 , 20 26 17 15 24 -> 14 23 26 12 16 1 5 6 15 16 24 , 18 31 0 13 14 22 27 2 ->= 11 7 28 32 27 15 22 31 27 5 7 , 20 26 17 15 1 -> 14 23 26 12 16 1 5 6 15 16 1 , 20 26 17 15 13 -> 14 23 26 12 16 1 5 6 15 16 13 , 18 31 0 13 14 22 27 5 ->= 11 7 28 32 27 15 22 31 27 5 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 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 0 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 0 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 is interpreted by / \ | 1 0 | | 0 1 | \ / 30 is interpreted by / \ | 1 0 | | 0 1 | \ / 31 is interpreted by / \ | 1 1 | | 0 1 | \ / 32 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 15->12, 25->13, 20->14, 26->15, 17->16, 16->17, 14->18, 23->19, 12->20, 22->21, 18->22, 27->23, 21->24, 28->25, 29->26, 30->27, 24->28, 13->29 }, it remains to prove termination of the 11-rule system { 0 1 2 ->= 3 4 5 6 5 7 8 9 7 10 7 , 0 1 5 ->= 3 4 5 6 5 7 8 9 7 10 11 , 12 1 2 ->= 13 4 5 6 5 7 8 9 7 10 7 , 12 1 5 ->= 13 4 5 6 5 7 8 9 7 10 11 , 14 15 16 12 17 -> 18 19 15 20 17 1 5 6 12 17 17 , 14 15 16 12 21 -> 18 19 15 20 17 1 5 6 12 17 21 , 22 23 12 1 13 24 3 24 -> 7 25 8 15 10 18 21 3 26 27 21 , 14 15 16 12 19 -> 18 19 15 20 17 1 5 6 12 17 19 , 14 15 16 12 28 -> 18 19 15 20 17 1 5 6 12 17 28 , 14 15 16 12 1 -> 18 19 15 20 17 1 5 6 12 17 1 , 14 15 16 12 29 -> 18 19 15 20 17 1 5 6 12 17 29 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 1 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 1 | | 0 1 | \ / 23 is interpreted by / \ | 1 1 | | 0 1 | \ / 24 is interpreted by / \ | 1 1 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 0 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 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.