YES After renaming modulo { 3->0, 5->1, 1->2, 0->3, 4->4, 2->5 }, it remains to prove termination of the 60-rule system { 0 1 0 -> 2 3 0 4 4 0 2 4 1 4 , 1 3 3 -> 1 3 0 5 2 5 0 4 3 3 , 3 2 3 4 -> 4 5 2 5 0 4 4 0 3 4 , 4 1 3 4 -> 4 3 4 3 4 3 0 4 4 4 , 1 1 1 1 -> 1 5 3 3 0 5 2 4 4 0 , 1 1 1 1 -> 1 4 3 3 2 2 2 4 0 1 , 2 1 0 2 0 -> 2 0 4 4 5 3 5 0 2 5 , 5 0 1 1 3 -> 4 3 2 4 5 2 5 3 2 3 , 5 1 1 1 1 -> 5 3 1 2 5 3 0 5 2 1 , 4 2 3 3 3 -> 4 2 4 2 3 1 2 5 4 5 , 4 2 1 1 0 -> 5 2 5 0 3 0 5 1 2 5 , 4 0 2 1 1 -> 4 3 0 2 5 0 5 2 2 1 , 1 3 5 4 5 -> 1 5 2 5 0 3 3 0 4 5 , 1 0 2 1 2 -> 0 5 2 2 3 0 3 2 1 2 , 1 1 0 3 5 -> 0 5 0 4 1 5 2 5 3 3 , 1 1 1 1 4 -> 0 4 1 4 3 3 4 3 0 4 , 3 2 1 2 3 4 -> 0 5 3 4 3 2 4 0 3 4 , 3 2 1 2 1 3 -> 4 4 4 5 1 1 3 2 4 3 , 3 2 1 0 3 2 -> 4 4 1 2 2 2 4 3 0 2 , 3 0 2 0 3 1 -> 4 4 0 0 4 4 3 1 5 0 , 2 1 1 1 1 0 -> 2 5 1 2 4 3 3 5 1 4 , 5 3 1 0 4 2 -> 5 0 4 3 0 0 3 2 5 2 , 5 4 3 2 0 1 -> 5 0 5 3 5 3 0 2 4 0 , 5 1 4 1 1 1 -> 5 4 5 2 5 4 4 4 3 1 , 0 1 0 2 1 1 -> 0 5 4 4 2 2 4 3 5 4 , 4 2 0 2 1 3 -> 3 5 5 5 2 2 5 0 2 4 , 4 0 1 3 4 5 -> 4 0 4 0 4 2 0 2 4 5 , 1 3 1 3 4 5 -> 1 4 4 4 4 3 4 4 0 3 , 1 1 2 1 0 3 -> 5 5 3 2 4 0 3 0 0 4 , 1 1 0 5 0 1 -> 2 4 5 4 2 5 5 4 2 1 , 1 1 1 2 0 2 -> 1 2 5 4 4 4 2 0 0 4 , 2 3 4 1 0 1 3 -> 2 3 5 2 5 1 5 3 1 5 , 2 1 2 0 1 1 1 -> 1 2 5 0 3 5 5 3 1 1 , 0 3 2 1 2 0 3 -> 0 3 3 0 2 5 2 1 4 5 , 0 5 4 2 1 1 2 -> 3 1 3 0 4 2 3 0 1 2 , 0 1 1 1 2 4 2 -> 2 4 4 3 3 2 3 2 0 2 , 4 3 1 1 1 1 4 -> 5 2 4 0 1 4 3 2 1 4 , 4 2 1 3 3 2 0 -> 3 5 2 2 2 2 4 1 2 0 , 4 2 1 3 3 2 1 -> 4 0 3 1 0 1 5 2 4 1 , 4 5 0 1 3 1 3 -> 4 4 4 3 3 2 1 5 0 4 , 4 5 1 1 3 5 5 -> 4 5 2 3 3 2 4 1 2 5 , 4 1 1 0 1 1 0 -> 3 2 4 3 2 0 5 4 2 4 , 4 1 1 1 3 4 0 -> 3 0 0 0 5 3 5 0 5 0 , 1 3 1 1 0 1 4 -> 1 0 1 1 3 2 2 5 0 4 , 1 5 1 1 3 3 0 -> 2 4 4 0 2 3 2 0 3 0 , 1 0 1 1 1 0 3 -> 1 4 0 4 1 5 1 1 1 3 , 1 4 1 0 5 1 0 -> 1 4 0 2 2 4 5 3 0 1 , 1 1 3 1 1 3 2 -> 5 0 4 1 4 5 2 5 1 2 , 1 1 3 1 1 1 0 -> 1 3 4 4 3 2 5 0 0 0 , 1 1 5 1 0 1 3 -> 1 5 3 4 3 0 5 0 0 3 , 1 1 1 0 3 4 5 -> 1 1 5 2 1 4 0 4 4 5 , 3 3 3 ->= 2 5 0 4 4 5 0 0 5 5 , 3 3 5 ->= 2 3 0 4 0 2 5 3 3 5 , 4 3 2 ->= 4 4 2 2 4 3 0 4 3 2 , 1 1 3 ->= 3 5 3 0 2 2 2 5 5 5 , 1 0 3 2 ->= 0 4 4 2 4 4 0 5 3 0 , 5 3 3 5 4 ->= 4 4 3 4 0 2 5 4 3 4 , 5 1 1 1 3 ->= 5 1 3 5 0 3 0 3 1 3 , 1 1 1 2 3 ->= 0 0 1 5 4 4 2 5 2 5 , 5 1 0 3 1 3 2 ->= 4 3 4 2 4 3 1 4 5 2 } 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 1 2 3 0 2 2 0 4 3 , 4 4 1 -> 4 4 2 0 5 3 5 0 4 1 , 2 4 3 4 -> 2 4 0 2 2 0 5 3 5 2 , 2 4 1 2 -> 2 2 2 0 4 2 4 2 4 2 , 1 1 1 1 -> 0 2 2 3 5 0 4 4 5 1 , 1 1 1 1 -> 1 0 2 3 3 3 4 4 2 1 , 0 3 0 1 3 -> 5 3 0 5 4 5 2 2 0 3 , 4 1 1 0 5 -> 4 3 4 5 3 5 2 3 4 2 , 1 1 1 1 5 -> 1 3 5 0 4 5 3 1 4 5 , 4 4 4 3 2 -> 5 2 5 3 1 4 3 2 3 2 , 0 1 1 3 2 -> 5 3 1 5 0 4 0 5 3 5 , 1 1 3 0 2 -> 1 3 3 5 0 5 3 0 4 2 , 5 2 5 4 1 -> 5 2 0 4 4 0 5 3 5 1 , 3 1 3 0 1 -> 3 1 3 4 0 4 3 3 5 0 , 5 4 0 1 1 -> 4 4 5 3 5 1 2 0 5 0 , 2 1 1 1 1 -> 2 0 4 2 4 4 2 1 2 0 , 2 4 3 1 3 4 -> 2 4 0 2 3 4 2 4 5 0 , 4 1 3 1 3 4 -> 4 2 3 4 1 1 5 2 2 2 , 3 4 0 1 3 4 -> 3 0 4 2 3 3 3 1 2 2 , 1 4 0 3 0 4 -> 0 5 1 4 2 2 0 0 2 2 , 0 1 1 1 1 3 -> 2 1 5 4 4 2 3 1 5 3 , 3 2 0 1 4 5 -> 3 5 3 4 0 0 4 2 0 5 , 1 0 3 4 2 5 -> 0 2 3 0 4 5 4 5 0 5 , 1 1 1 2 1 5 -> 1 4 2 2 2 5 3 5 2 5 , 1 1 3 0 1 0 -> 2 5 4 2 3 3 2 2 5 0 , 4 1 3 0 3 2 -> 2 3 0 5 3 3 5 5 5 4 , 5 2 4 1 0 2 -> 5 2 3 0 3 2 0 2 0 2 , 5 2 4 1 4 1 -> 4 0 2 2 4 2 2 2 2 1 , 4 0 1 3 1 1 -> 2 0 0 4 0 2 3 4 5 5 , 1 0 5 0 1 1 -> 1 3 2 5 5 3 2 5 2 3 , 3 0 3 1 1 1 -> 2 0 0 3 2 2 2 5 3 1 , 4 1 0 1 2 4 3 -> 5 1 4 5 1 5 3 5 4 3 , 1 1 1 0 3 1 3 -> 1 1 4 5 5 4 0 5 3 1 , 4 0 3 1 3 4 0 -> 5 2 1 3 5 3 0 4 4 0 , 3 1 1 3 2 5 0 -> 3 1 0 4 3 2 0 4 1 4 , 3 2 3 1 1 1 0 -> 3 0 3 4 3 4 4 2 2 3 , 2 1 1 1 1 4 2 -> 2 1 3 4 2 1 0 2 3 5 , 0 3 4 4 1 3 2 -> 0 3 1 2 3 3 3 3 5 4 , 1 3 4 4 1 3 2 -> 1 2 3 5 1 0 1 4 0 2 , 4 1 4 1 0 5 2 -> 2 0 5 1 3 4 4 2 2 2 , 5 5 4 1 1 5 2 -> 5 3 1 2 3 4 4 3 5 2 , 0 1 1 0 1 1 2 -> 2 3 2 5 0 3 4 2 3 4 , 0 2 4 1 1 1 2 -> 0 5 0 5 4 5 0 0 0 4 , 2 1 0 1 1 4 1 -> 2 0 5 3 3 4 1 1 0 1 , 0 4 4 1 1 5 1 -> 0 4 0 3 4 3 0 2 2 3 , 4 0 1 1 1 0 1 -> 4 1 1 1 5 1 2 0 2 1 , 0 1 5 0 1 2 1 -> 1 0 4 5 2 3 3 0 2 1 , 3 4 1 1 4 1 1 -> 3 1 5 3 5 2 1 2 0 5 , 0 1 1 1 4 1 1 -> 0 0 0 5 3 4 2 2 4 1 , 4 1 0 1 5 1 1 -> 4 0 0 5 0 4 2 4 5 1 , 5 2 4 0 1 1 1 -> 5 2 2 0 2 1 3 5 1 1 , 4 4 4 ->= 5 5 0 0 5 2 2 0 5 3 , 5 4 4 ->= 5 4 4 5 3 0 2 0 4 3 , 3 4 2 ->= 3 4 2 0 4 2 3 3 2 2 , 4 1 1 ->= 5 5 5 3 3 3 0 4 5 4 , 3 4 0 1 ->= 0 4 5 0 2 2 3 2 2 0 , 2 5 4 4 5 ->= 2 4 2 5 3 0 2 4 2 2 , 4 1 1 1 5 ->= 4 1 4 0 4 0 5 4 1 5 , 4 3 1 1 1 ->= 5 3 5 3 2 2 5 1 0 0 , 3 4 1 4 0 1 5 ->= 3 5 2 1 4 2 3 2 4 2 } 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, 1]->4, [1, 2]->5, [2, 3]->6, [3, 0]->7, [2, 2]->8, [2, 0]->9, [0, 4]->10, [4, 3]->11, [4, 4]->12, [4, 1]->13, [4, 2]->14, [0, 5]->15, [5, 3]->16, [3, 5]->17, [5, 0]->18, [2, 4]->19, [3, 4]->20, [4, 0]->21, [5, 2]->22, [1, 1]->23, [4, 5]->24, [5, 1]->25, [3, 3]->26, [0, 3]->27, [1, 3]->28, [5, 4]->29, [1, 5]->30, [3, 1]->31, [1, 4]->32, [3, 2]->33, [2, 5]->34, [5, 5]->35 }, it remains to prove termination of the 2160-rule system { 0 1 2 0 -> 3 4 5 6 7 3 8 9 10 11 7 , 10 12 13 2 -> 10 12 14 9 15 16 17 18 10 13 2 , 3 19 11 20 21 -> 3 19 21 3 8 9 15 16 17 22 9 , 3 19 13 5 9 -> 3 8 8 9 10 14 19 14 19 14 9 , 1 23 23 23 2 -> 0 3 8 6 17 18 10 12 24 25 2 , 1 23 23 23 2 -> 1 2 3 6 26 26 20 12 14 4 2 , 0 27 7 1 28 7 -> 15 16 7 15 29 24 22 8 9 27 7 , 10 13 23 2 15 18 -> 10 11 20 24 16 17 22 6 20 14 9 , 1 23 23 23 30 18 -> 1 28 17 18 10 24 16 31 32 24 18 , 10 12 12 11 33 9 -> 15 22 34 16 31 32 11 33 6 33 9 , 0 1 23 28 33 9 -> 15 16 31 30 18 10 21 15 16 17 18 , 1 23 28 7 3 9 -> 1 28 26 17 18 15 16 7 10 14 9 , 15 22 34 29 13 2 -> 15 22 9 10 12 21 15 16 17 25 2 , 27 31 28 7 1 2 -> 27 31 28 20 21 10 11 26 17 18 0 , 15 29 21 1 23 2 -> 10 12 24 16 17 25 5 9 15 18 0 , 3 4 23 23 23 2 -> 3 9 10 14 19 12 14 4 5 9 0 , 3 19 11 31 28 20 21 -> 3 19 21 3 6 20 14 19 24 18 0 , 10 13 28 31 28 20 21 -> 10 14 6 20 13 23 30 22 8 8 9 , 27 20 21 1 28 20 21 -> 27 7 10 14 6 26 26 31 5 8 9 , 1 32 21 27 7 10 21 -> 0 15 25 32 14 8 9 0 3 8 9 , 0 1 23 23 23 28 7 -> 3 4 30 29 12 14 6 31 30 16 7 , 27 33 9 1 32 24 18 -> 27 17 16 20 21 0 10 14 9 15 18 , 1 2 27 20 14 34 18 -> 0 3 6 7 10 24 29 24 18 15 18 , 1 23 23 5 4 30 18 -> 1 32 14 8 8 34 16 17 22 34 18 , 1 23 28 7 1 2 0 -> 3 34 29 14 6 26 33 8 34 18 0 , 10 13 28 7 27 33 9 -> 3 6 7 15 16 26 17 35 35 29 21 , 15 22 19 13 2 3 9 -> 15 22 6 7 27 33 9 3 9 3 9 , 15 22 19 13 32 13 2 -> 10 21 3 8 19 14 8 8 8 4 2 , 10 21 1 28 31 23 2 -> 3 9 0 10 21 3 6 20 24 35 18 , 1 2 15 18 1 23 2 -> 1 28 33 34 35 16 33 34 22 6 7 , 27 7 27 31 23 23 2 -> 3 9 0 27 33 8 8 34 16 31 2 , 10 13 2 1 5 19 11 7 -> 15 25 32 24 25 30 16 17 29 11 7 , 1 23 23 2 27 31 28 7 -> 1 23 32 24 35 29 21 15 16 31 2 , 10 21 27 31 28 20 21 0 -> 15 22 4 28 17 16 7 10 12 21 0 , 27 31 23 28 33 34 18 0 -> 27 31 2 10 11 33 9 10 13 32 21 , 27 33 6 31 23 23 2 0 -> 27 7 27 20 11 20 12 14 8 6 7 , 3 4 23 23 23 32 14 9 -> 3 4 28 20 14 4 2 3 6 17 18 , 0 27 20 12 13 28 33 9 -> 0 27 31 5 6 26 26 26 17 29 21 , 1 28 20 12 13 28 33 9 -> 1 5 6 17 25 2 1 32 21 3 9 , 10 13 32 13 2 15 22 9 -> 3 9 15 25 28 20 12 14 8 8 9 , 15 35 29 13 23 30 22 9 -> 15 16 31 5 6 20 12 11 17 22 9 , 0 1 23 2 1 23 5 9 -> 3 6 33 34 18 27 20 14 6 20 21 , 0 3 19 13 23 23 5 9 -> 0 15 18 15 29 24 18 0 0 10 21 , 3 4 2 1 23 32 13 2 -> 3 9 15 16 26 20 13 23 2 1 2 , 0 10 12 13 23 30 25 2 -> 0 10 21 27 20 11 7 3 8 6 7 , 10 21 1 23 23 2 1 2 -> 10 13 23 23 30 25 5 9 3 4 2 , 0 1 30 18 1 5 4 2 -> 1 2 10 24 22 6 26 7 3 4 2 , 27 20 13 23 32 13 23 2 -> 27 31 30 16 17 22 4 5 9 15 18 , 0 1 23 23 32 13 23 2 -> 0 0 0 15 16 20 14 8 19 13 2 , 10 13 2 1 30 25 23 2 -> 10 21 0 15 18 10 14 19 24 25 2 , 15 22 19 21 1 23 23 2 -> 15 22 8 9 3 4 28 17 25 23 2 , 10 12 12 21 ->= 15 35 18 0 15 22 8 9 15 16 7 , 15 29 12 21 ->= 15 29 12 24 16 7 3 9 10 11 7 , 27 20 14 9 ->= 27 20 14 9 10 14 6 26 33 8 9 , 10 13 23 2 ->= 15 35 35 16 26 26 7 10 24 29 21 , 27 20 21 1 2 ->= 0 10 24 18 3 8 6 33 8 9 0 , 3 34 29 12 24 18 ->= 3 19 14 34 16 7 3 19 14 8 9 , 10 13 23 23 30 18 ->= 10 13 32 21 10 21 15 29 13 30 18 , 10 11 31 23 23 2 ->= 15 16 17 16 33 8 34 25 2 0 0 , 27 20 13 32 21 1 30 18 ->= 27 17 22 4 32 14 6 33 19 14 9 , 0 1 2 1 -> 3 4 5 6 7 3 8 9 10 11 31 , 10 12 13 23 -> 10 12 14 9 15 16 17 18 10 13 23 , 3 19 11 20 13 -> 3 19 21 3 8 9 15 16 17 22 4 , 3 19 13 5 4 -> 3 8 8 9 10 14 19 14 19 14 4 , 1 23 23 23 23 -> 0 3 8 6 17 18 10 12 24 25 23 , 1 23 23 23 23 -> 1 2 3 6 26 26 20 12 14 4 23 , 0 27 7 1 28 31 -> 15 16 7 15 29 24 22 8 9 27 31 , 10 13 23 2 15 25 -> 10 11 20 24 16 17 22 6 20 14 4 , 1 23 23 23 30 25 -> 1 28 17 18 10 24 16 31 32 24 25 , 10 12 12 11 33 4 -> 15 22 34 16 31 32 11 33 6 33 4 , 0 1 23 28 33 4 -> 15 16 31 30 18 10 21 15 16 17 25 , 1 23 28 7 3 4 -> 1 28 26 17 18 15 16 7 10 14 4 , 15 22 34 29 13 23 -> 15 22 9 10 12 21 15 16 17 25 23 , 27 31 28 7 1 23 -> 27 31 28 20 21 10 11 26 17 18 1 , 15 29 21 1 23 23 -> 10 12 24 16 17 25 5 9 15 18 1 , 3 4 23 23 23 23 -> 3 9 10 14 19 12 14 4 5 9 1 , 3 19 11 31 28 20 13 -> 3 19 21 3 6 20 14 19 24 18 1 , 10 13 28 31 28 20 13 -> 10 14 6 20 13 23 30 22 8 8 4 , 27 20 21 1 28 20 13 -> 27 7 10 14 6 26 26 31 5 8 4 , 1 32 21 27 7 10 13 -> 0 15 25 32 14 8 9 0 3 8 4 , 0 1 23 23 23 28 31 -> 3 4 30 29 12 14 6 31 30 16 31 , 27 33 9 1 32 24 25 -> 27 17 16 20 21 0 10 14 9 15 25 , 1 2 27 20 14 34 25 -> 0 3 6 7 10 24 29 24 18 15 25 , 1 23 23 5 4 30 25 -> 1 32 14 8 8 34 16 17 22 34 25 , 1 23 28 7 1 2 1 -> 3 34 29 14 6 26 33 8 34 18 1 , 10 13 28 7 27 33 4 -> 3 6 7 15 16 26 17 35 35 29 13 , 15 22 19 13 2 3 4 -> 15 22 6 7 27 33 9 3 9 3 4 , 15 22 19 13 32 13 23 -> 10 21 3 8 19 14 8 8 8 4 23 , 10 21 1 28 31 23 23 -> 3 9 0 10 21 3 6 20 24 35 25 , 1 2 15 18 1 23 23 -> 1 28 33 34 35 16 33 34 22 6 31 , 27 7 27 31 23 23 23 -> 3 9 0 27 33 8 8 34 16 31 23 , 10 13 2 1 5 19 11 31 -> 15 25 32 24 25 30 16 17 29 11 31 , 1 23 23 2 27 31 28 31 -> 1 23 32 24 35 29 21 15 16 31 23 , 10 21 27 31 28 20 21 1 -> 15 22 4 28 17 16 7 10 12 21 1 , 27 31 23 28 33 34 18 1 -> 27 31 2 10 11 33 9 10 13 32 13 , 27 33 6 31 23 23 2 1 -> 27 7 27 20 11 20 12 14 8 6 31 , 3 4 23 23 23 32 14 4 -> 3 4 28 20 14 4 2 3 6 17 25 , 0 27 20 12 13 28 33 4 -> 0 27 31 5 6 26 26 26 17 29 13 , 1 28 20 12 13 28 33 4 -> 1 5 6 17 25 2 1 32 21 3 4 , 10 13 32 13 2 15 22 4 -> 3 9 15 25 28 20 12 14 8 8 4 , 15 35 29 13 23 30 22 4 -> 15 16 31 5 6 20 12 11 17 22 4 , 0 1 23 2 1 23 5 4 -> 3 6 33 34 18 27 20 14 6 20 13 , 0 3 19 13 23 23 5 4 -> 0 15 18 15 29 24 18 0 0 10 13 , 3 4 2 1 23 32 13 23 -> 3 9 15 16 26 20 13 23 2 1 23 , 0 10 12 13 23 30 25 23 -> 0 10 21 27 20 11 7 3 8 6 31 , 10 21 1 23 23 2 1 23 -> 10 13 23 23 30 25 5 9 3 4 23 , 0 1 30 18 1 5 4 23 -> 1 2 10 24 22 6 26 7 3 4 23 , 27 20 13 23 32 13 23 23 -> 27 31 30 16 17 22 4 5 9 15 25 , 0 1 23 23 32 13 23 23 -> 0 0 0 15 16 20 14 8 19 13 23 , 10 13 2 1 30 25 23 23 -> 10 21 0 15 18 10 14 19 24 25 23 , 15 22 19 21 1 23 23 23 -> 15 22 8 9 3 4 28 17 25 23 23 , 10 12 12 13 ->= 15 35 18 0 15 22 8 9 15 16 31 , 15 29 12 13 ->= 15 29 12 24 16 7 3 9 10 11 31 , 27 20 14 4 ->= 27 20 14 9 10 14 6 26 33 8 4 , 10 13 23 23 ->= 15 35 35 16 26 26 7 10 24 29 13 , 27 20 21 1 23 ->= 0 10 24 18 3 8 6 33 8 9 1 , 3 34 29 12 24 25 ->= 3 19 14 34 16 7 3 19 14 8 4 , 10 13 23 23 30 25 ->= 10 13 32 21 10 21 15 29 13 30 25 , 10 11 31 23 23 23 ->= 15 16 17 16 33 8 34 25 2 0 1 , 27 20 13 32 21 1 30 25 ->= 27 17 22 4 32 14 6 33 19 14 4 , 0 1 2 3 -> 3 4 5 6 7 3 8 9 10 11 33 , 10 12 13 5 -> 10 12 14 9 15 16 17 18 10 13 5 , 3 19 11 20 14 -> 3 19 21 3 8 9 15 16 17 22 8 , 3 19 13 5 8 -> 3 8 8 9 10 14 19 14 19 14 8 , 1 23 23 23 5 -> 0 3 8 6 17 18 10 12 24 25 5 , 1 23 23 23 5 -> 1 2 3 6 26 26 20 12 14 4 5 , 0 27 7 1 28 33 -> 15 16 7 15 29 24 22 8 9 27 33 , 10 13 23 2 15 22 -> 10 11 20 24 16 17 22 6 20 14 8 , 1 23 23 23 30 22 -> 1 28 17 18 10 24 16 31 32 24 22 , 10 12 12 11 33 8 -> 15 22 34 16 31 32 11 33 6 33 8 , 0 1 23 28 33 8 -> 15 16 31 30 18 10 21 15 16 17 22 , 1 23 28 7 3 8 -> 1 28 26 17 18 15 16 7 10 14 8 , 15 22 34 29 13 5 -> 15 22 9 10 12 21 15 16 17 25 5 , 27 31 28 7 1 5 -> 27 31 28 20 21 10 11 26 17 18 3 , 15 29 21 1 23 5 -> 10 12 24 16 17 25 5 9 15 18 3 , 3 4 23 23 23 5 -> 3 9 10 14 19 12 14 4 5 9 3 , 3 19 11 31 28 20 14 -> 3 19 21 3 6 20 14 19 24 18 3 , 10 13 28 31 28 20 14 -> 10 14 6 20 13 23 30 22 8 8 8 , 27 20 21 1 28 20 14 -> 27 7 10 14 6 26 26 31 5 8 8 , 1 32 21 27 7 10 14 -> 0 15 25 32 14 8 9 0 3 8 8 , 0 1 23 23 23 28 33 -> 3 4 30 29 12 14 6 31 30 16 33 , 27 33 9 1 32 24 22 -> 27 17 16 20 21 0 10 14 9 15 22 , 1 2 27 20 14 34 22 -> 0 3 6 7 10 24 29 24 18 15 22 , 1 23 23 5 4 30 22 -> 1 32 14 8 8 34 16 17 22 34 22 , 1 23 28 7 1 2 3 -> 3 34 29 14 6 26 33 8 34 18 3 , 10 13 28 7 27 33 8 -> 3 6 7 15 16 26 17 35 35 29 14 , 15 22 19 13 2 3 8 -> 15 22 6 7 27 33 9 3 9 3 8 , 15 22 19 13 32 13 5 -> 10 21 3 8 19 14 8 8 8 4 5 , 10 21 1 28 31 23 5 -> 3 9 0 10 21 3 6 20 24 35 22 , 1 2 15 18 1 23 5 -> 1 28 33 34 35 16 33 34 22 6 33 , 27 7 27 31 23 23 5 -> 3 9 0 27 33 8 8 34 16 31 5 , 10 13 2 1 5 19 11 33 -> 15 25 32 24 25 30 16 17 29 11 33 , 1 23 23 2 27 31 28 33 -> 1 23 32 24 35 29 21 15 16 31 5 , 10 21 27 31 28 20 21 3 -> 15 22 4 28 17 16 7 10 12 21 3 , 27 31 23 28 33 34 18 3 -> 27 31 2 10 11 33 9 10 13 32 14 , 27 33 6 31 23 23 2 3 -> 27 7 27 20 11 20 12 14 8 6 33 , 3 4 23 23 23 32 14 8 -> 3 4 28 20 14 4 2 3 6 17 22 , 0 27 20 12 13 28 33 8 -> 0 27 31 5 6 26 26 26 17 29 14 , 1 28 20 12 13 28 33 8 -> 1 5 6 17 25 2 1 32 21 3 8 , 10 13 32 13 2 15 22 8 -> 3 9 15 25 28 20 12 14 8 8 8 , 15 35 29 13 23 30 22 8 -> 15 16 31 5 6 20 12 11 17 22 8 , 0 1 23 2 1 23 5 8 -> 3 6 33 34 18 27 20 14 6 20 14 , 0 3 19 13 23 23 5 8 -> 0 15 18 15 29 24 18 0 0 10 14 , 3 4 2 1 23 32 13 5 -> 3 9 15 16 26 20 13 23 2 1 5 , 0 10 12 13 23 30 25 5 -> 0 10 21 27 20 11 7 3 8 6 33 , 10 21 1 23 23 2 1 5 -> 10 13 23 23 30 25 5 9 3 4 5 , 0 1 30 18 1 5 4 5 -> 1 2 10 24 22 6 26 7 3 4 5 , 27 20 13 23 32 13 23 5 -> 27 31 30 16 17 22 4 5 9 15 22 , 0 1 23 23 32 13 23 5 -> 0 0 0 15 16 20 14 8 19 13 5 , 10 13 2 1 30 25 23 5 -> 10 21 0 15 18 10 14 19 24 25 5 , 15 22 19 21 1 23 23 5 -> 15 22 8 9 3 4 28 17 25 23 5 , 10 12 12 14 ->= 15 35 18 0 15 22 8 9 15 16 33 , 15 29 12 14 ->= 15 29 12 24 16 7 3 9 10 11 33 , 27 20 14 8 ->= 27 20 14 9 10 14 6 26 33 8 8 , 10 13 23 5 ->= 15 35 35 16 26 26 7 10 24 29 14 , 27 20 21 1 5 ->= 0 10 24 18 3 8 6 33 8 9 3 , 3 34 29 12 24 22 ->= 3 19 14 34 16 7 3 19 14 8 8 , 10 13 23 23 30 22 ->= 10 13 32 21 10 21 15 29 13 30 22 , 10 11 31 23 23 5 ->= 15 16 17 16 33 8 34 25 2 0 3 , 27 20 13 32 21 1 30 22 ->= 27 17 22 4 32 14 6 33 19 14 8 , 0 1 2 27 -> 3 4 5 6 7 3 8 9 10 11 26 , 10 12 13 28 -> 10 12 14 9 15 16 17 18 10 13 28 , 3 19 11 20 11 -> 3 19 21 3 8 9 15 16 17 22 6 , 3 19 13 5 6 -> 3 8 8 9 10 14 19 14 19 14 6 , 1 23 23 23 28 -> 0 3 8 6 17 18 10 12 24 25 28 , 1 23 23 23 28 -> 1 2 3 6 26 26 20 12 14 4 28 , 0 27 7 1 28 26 -> 15 16 7 15 29 24 22 8 9 27 26 , 10 13 23 2 15 16 -> 10 11 20 24 16 17 22 6 20 14 6 , 1 23 23 23 30 16 -> 1 28 17 18 10 24 16 31 32 24 16 , 10 12 12 11 33 6 -> 15 22 34 16 31 32 11 33 6 33 6 , 0 1 23 28 33 6 -> 15 16 31 30 18 10 21 15 16 17 16 , 1 23 28 7 3 6 -> 1 28 26 17 18 15 16 7 10 14 6 , 15 22 34 29 13 28 -> 15 22 9 10 12 21 15 16 17 25 28 , 27 31 28 7 1 28 -> 27 31 28 20 21 10 11 26 17 18 27 , 15 29 21 1 23 28 -> 10 12 24 16 17 25 5 9 15 18 27 , 3 4 23 23 23 28 -> 3 9 10 14 19 12 14 4 5 9 27 , 3 19 11 31 28 20 11 -> 3 19 21 3 6 20 14 19 24 18 27 , 10 13 28 31 28 20 11 -> 10 14 6 20 13 23 30 22 8 8 6 , 27 20 21 1 28 20 11 -> 27 7 10 14 6 26 26 31 5 8 6 , 1 32 21 27 7 10 11 -> 0 15 25 32 14 8 9 0 3 8 6 , 0 1 23 23 23 28 26 -> 3 4 30 29 12 14 6 31 30 16 26 , 27 33 9 1 32 24 16 -> 27 17 16 20 21 0 10 14 9 15 16 , 1 2 27 20 14 34 16 -> 0 3 6 7 10 24 29 24 18 15 16 , 1 23 23 5 4 30 16 -> 1 32 14 8 8 34 16 17 22 34 16 , 1 23 28 7 1 2 27 -> 3 34 29 14 6 26 33 8 34 18 27 , 10 13 28 7 27 33 6 -> 3 6 7 15 16 26 17 35 35 29 11 , 15 22 19 13 2 3 6 -> 15 22 6 7 27 33 9 3 9 3 6 , 15 22 19 13 32 13 28 -> 10 21 3 8 19 14 8 8 8 4 28 , 10 21 1 28 31 23 28 -> 3 9 0 10 21 3 6 20 24 35 16 , 1 2 15 18 1 23 28 -> 1 28 33 34 35 16 33 34 22 6 26 , 27 7 27 31 23 23 28 -> 3 9 0 27 33 8 8 34 16 31 28 , 10 13 2 1 5 19 11 26 -> 15 25 32 24 25 30 16 17 29 11 26 , 1 23 23 2 27 31 28 26 -> 1 23 32 24 35 29 21 15 16 31 28 , 10 21 27 31 28 20 21 27 -> 15 22 4 28 17 16 7 10 12 21 27 , 27 31 23 28 33 34 18 27 -> 27 31 2 10 11 33 9 10 13 32 11 , 27 33 6 31 23 23 2 27 -> 27 7 27 20 11 20 12 14 8 6 26 , 3 4 23 23 23 32 14 6 -> 3 4 28 20 14 4 2 3 6 17 16 , 0 27 20 12 13 28 33 6 -> 0 27 31 5 6 26 26 26 17 29 11 , 1 28 20 12 13 28 33 6 -> 1 5 6 17 25 2 1 32 21 3 6 , 10 13 32 13 2 15 22 6 -> 3 9 15 25 28 20 12 14 8 8 6 , 15 35 29 13 23 30 22 6 -> 15 16 31 5 6 20 12 11 17 22 6 , 0 1 23 2 1 23 5 6 -> 3 6 33 34 18 27 20 14 6 20 11 , 0 3 19 13 23 23 5 6 -> 0 15 18 15 29 24 18 0 0 10 11 , 3 4 2 1 23 32 13 28 -> 3 9 15 16 26 20 13 23 2 1 28 , 0 10 12 13 23 30 25 28 -> 0 10 21 27 20 11 7 3 8 6 26 , 10 21 1 23 23 2 1 28 -> 10 13 23 23 30 25 5 9 3 4 28 , 0 1 30 18 1 5 4 28 -> 1 2 10 24 22 6 26 7 3 4 28 , 27 20 13 23 32 13 23 28 -> 27 31 30 16 17 22 4 5 9 15 16 , 0 1 23 23 32 13 23 28 -> 0 0 0 15 16 20 14 8 19 13 28 , 10 13 2 1 30 25 23 28 -> 10 21 0 15 18 10 14 19 24 25 28 , 15 22 19 21 1 23 23 28 -> 15 22 8 9 3 4 28 17 25 23 28 , 10 12 12 11 ->= 15 35 18 0 15 22 8 9 15 16 26 , 15 29 12 11 ->= 15 29 12 24 16 7 3 9 10 11 26 , 27 20 14 6 ->= 27 20 14 9 10 14 6 26 33 8 6 , 10 13 23 28 ->= 15 35 35 16 26 26 7 10 24 29 11 , 27 20 21 1 28 ->= 0 10 24 18 3 8 6 33 8 9 27 , 3 34 29 12 24 16 ->= 3 19 14 34 16 7 3 19 14 8 6 , 10 13 23 23 30 16 ->= 10 13 32 21 10 21 15 29 13 30 16 , 10 11 31 23 23 28 ->= 15 16 17 16 33 8 34 25 2 0 27 , 27 20 13 32 21 1 30 16 ->= 27 17 22 4 32 14 6 33 19 14 6 , 0 1 2 10 -> 3 4 5 6 7 3 8 9 10 11 20 , 10 12 13 32 -> 10 12 14 9 15 16 17 18 10 13 32 , 3 19 11 20 12 -> 3 19 21 3 8 9 15 16 17 22 19 , 3 19 13 5 19 -> 3 8 8 9 10 14 19 14 19 14 19 , 1 23 23 23 32 -> 0 3 8 6 17 18 10 12 24 25 32 , 1 23 23 23 32 -> 1 2 3 6 26 26 20 12 14 4 32 , 0 27 7 1 28 20 -> 15 16 7 15 29 24 22 8 9 27 20 , 10 13 23 2 15 29 -> 10 11 20 24 16 17 22 6 20 14 19 , 1 23 23 23 30 29 -> 1 28 17 18 10 24 16 31 32 24 29 , 10 12 12 11 33 19 -> 15 22 34 16 31 32 11 33 6 33 19 , 0 1 23 28 33 19 -> 15 16 31 30 18 10 21 15 16 17 29 , 1 23 28 7 3 19 -> 1 28 26 17 18 15 16 7 10 14 19 , 15 22 34 29 13 32 -> 15 22 9 10 12 21 15 16 17 25 32 , 27 31 28 7 1 32 -> 27 31 28 20 21 10 11 26 17 18 10 , 15 29 21 1 23 32 -> 10 12 24 16 17 25 5 9 15 18 10 , 3 4 23 23 23 32 -> 3 9 10 14 19 12 14 4 5 9 10 , 3 19 11 31 28 20 12 -> 3 19 21 3 6 20 14 19 24 18 10 , 10 13 28 31 28 20 12 -> 10 14 6 20 13 23 30 22 8 8 19 , 27 20 21 1 28 20 12 -> 27 7 10 14 6 26 26 31 5 8 19 , 1 32 21 27 7 10 12 -> 0 15 25 32 14 8 9 0 3 8 19 , 0 1 23 23 23 28 20 -> 3 4 30 29 12 14 6 31 30 16 20 , 27 33 9 1 32 24 29 -> 27 17 16 20 21 0 10 14 9 15 29 , 1 2 27 20 14 34 29 -> 0 3 6 7 10 24 29 24 18 15 29 , 1 23 23 5 4 30 29 -> 1 32 14 8 8 34 16 17 22 34 29 , 1 23 28 7 1 2 10 -> 3 34 29 14 6 26 33 8 34 18 10 , 10 13 28 7 27 33 19 -> 3 6 7 15 16 26 17 35 35 29 12 , 15 22 19 13 2 3 19 -> 15 22 6 7 27 33 9 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27 20 11 7 3 8 6 20 , 10 21 1 23 23 2 1 32 -> 10 13 23 23 30 25 5 9 3 4 32 , 0 1 30 18 1 5 4 32 -> 1 2 10 24 22 6 26 7 3 4 32 , 27 20 13 23 32 13 23 32 -> 27 31 30 16 17 22 4 5 9 15 29 , 0 1 23 23 32 13 23 32 -> 0 0 0 15 16 20 14 8 19 13 32 , 10 13 2 1 30 25 23 32 -> 10 21 0 15 18 10 14 19 24 25 32 , 15 22 19 21 1 23 23 32 -> 15 22 8 9 3 4 28 17 25 23 32 , 10 12 12 12 ->= 15 35 18 0 15 22 8 9 15 16 20 , 15 29 12 12 ->= 15 29 12 24 16 7 3 9 10 11 20 , 27 20 14 19 ->= 27 20 14 9 10 14 6 26 33 8 19 , 10 13 23 32 ->= 15 35 35 16 26 26 7 10 24 29 12 , 27 20 21 1 32 ->= 0 10 24 18 3 8 6 33 8 9 10 , 3 34 29 12 24 29 ->= 3 19 14 34 16 7 3 19 14 8 19 , 10 13 23 23 30 29 ->= 10 13 32 21 10 21 15 29 13 30 29 , 10 11 31 23 23 32 ->= 15 16 17 16 33 8 34 25 2 0 10 , 27 20 13 32 21 1 30 29 ->= 27 17 22 4 32 14 6 33 19 14 19 , 0 1 2 15 -> 3 4 5 6 7 3 8 9 10 11 17 , 10 12 13 30 -> 10 12 14 9 15 16 17 18 10 13 30 , 3 19 11 20 24 -> 3 19 21 3 8 9 15 16 17 22 34 , 3 19 13 5 34 -> 3 8 8 9 10 14 19 14 19 14 34 , 1 23 23 23 30 -> 0 3 8 6 17 18 10 12 24 25 30 , 1 23 23 23 30 -> 1 2 3 6 26 26 20 12 14 4 30 , 0 27 7 1 28 17 -> 15 16 7 15 29 24 22 8 9 27 17 , 10 13 23 2 15 35 -> 10 11 20 24 16 17 22 6 20 14 34 , 1 23 23 23 30 35 -> 1 28 17 18 10 24 16 31 32 24 35 , 10 12 12 11 33 34 -> 15 22 34 16 31 32 11 33 6 33 34 , 0 1 23 28 33 34 -> 15 16 31 30 18 10 21 15 16 17 35 , 1 23 28 7 3 34 -> 1 28 26 17 18 15 16 7 10 14 34 , 15 22 34 29 13 30 -> 15 22 9 10 12 21 15 16 17 25 30 , 27 31 28 7 1 30 -> 27 31 28 20 21 10 11 26 17 18 15 , 15 29 21 1 23 30 -> 10 12 24 16 17 25 5 9 15 18 15 , 3 4 23 23 23 30 -> 3 9 10 14 19 12 14 4 5 9 15 , 3 19 11 31 28 20 24 -> 3 19 21 3 6 20 14 19 24 18 15 , 10 13 28 31 28 20 24 -> 10 14 6 20 13 23 30 22 8 8 34 , 27 20 21 1 28 20 24 -> 27 7 10 14 6 26 26 31 5 8 34 , 1 32 21 27 7 10 24 -> 0 15 25 32 14 8 9 0 3 8 34 , 0 1 23 23 23 28 17 -> 3 4 30 29 12 14 6 31 30 16 17 , 27 33 9 1 32 24 35 -> 27 17 16 20 21 0 10 14 9 15 35 , 1 2 27 20 14 34 35 -> 0 3 6 7 10 24 29 24 18 15 35 , 1 23 23 5 4 30 35 -> 1 32 14 8 8 34 16 17 22 34 35 , 1 23 28 7 1 2 15 -> 3 34 29 14 6 26 33 8 34 18 15 , 10 13 28 7 27 33 34 -> 3 6 7 15 16 26 17 35 35 29 24 , 15 22 19 13 2 3 34 -> 15 22 6 7 27 33 9 3 9 3 34 , 15 22 19 13 32 13 30 -> 10 21 3 8 19 14 8 8 8 4 30 , 10 21 1 28 31 23 30 -> 3 9 0 10 21 3 6 20 24 35 35 , 1 2 15 18 1 23 30 -> 1 28 33 34 35 16 33 34 22 6 17 , 27 7 27 31 23 23 30 -> 3 9 0 27 33 8 8 34 16 31 30 , 10 13 2 1 5 19 11 17 -> 15 25 32 24 25 30 16 17 29 11 17 , 1 23 23 2 27 31 28 17 -> 1 23 32 24 35 29 21 15 16 31 30 , 10 21 27 31 28 20 21 15 -> 15 22 4 28 17 16 7 10 12 21 15 , 27 31 23 28 33 34 18 15 -> 27 31 2 10 11 33 9 10 13 32 24 , 27 33 6 31 23 23 2 15 -> 27 7 27 20 11 20 12 14 8 6 17 , 3 4 23 23 23 32 14 34 -> 3 4 28 20 14 4 2 3 6 17 35 , 0 27 20 12 13 28 33 34 -> 0 27 31 5 6 26 26 26 17 29 24 , 1 28 20 12 13 28 33 34 -> 1 5 6 17 25 2 1 32 21 3 34 , 10 13 32 13 2 15 22 34 -> 3 9 15 25 28 20 12 14 8 8 34 , 15 35 29 13 23 30 22 34 -> 15 16 31 5 6 20 12 11 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27 17 22 4 32 14 6 33 19 14 34 , 2 1 2 0 -> 5 4 5 6 7 3 8 9 10 11 7 , 32 12 13 2 -> 32 12 14 9 15 16 17 18 10 13 2 , 5 19 11 20 21 -> 5 19 21 3 8 9 15 16 17 22 9 , 5 19 13 5 9 -> 5 8 8 9 10 14 19 14 19 14 9 , 23 23 23 23 2 -> 2 3 8 6 17 18 10 12 24 25 2 , 23 23 23 23 2 -> 23 2 3 6 26 26 20 12 14 4 2 , 2 27 7 1 28 7 -> 30 16 7 15 29 24 22 8 9 27 7 , 32 13 23 2 15 18 -> 32 11 20 24 16 17 22 6 20 14 9 , 23 23 23 23 30 18 -> 23 28 17 18 10 24 16 31 32 24 18 , 32 12 12 11 33 9 -> 30 22 34 16 31 32 11 33 6 33 9 , 2 1 23 28 33 9 -> 30 16 31 30 18 10 21 15 16 17 18 , 23 23 28 7 3 9 -> 23 28 26 17 18 15 16 7 10 14 9 , 30 22 34 29 13 2 -> 30 22 9 10 12 21 15 16 17 25 2 , 28 31 28 7 1 2 -> 28 31 28 20 21 10 11 26 17 18 0 , 30 29 21 1 23 2 -> 32 12 24 16 17 25 5 9 15 18 0 , 5 4 23 23 23 2 -> 5 9 10 14 19 12 14 4 5 9 0 , 5 19 11 31 28 20 21 -> 5 19 21 3 6 20 14 19 24 18 0 , 32 13 28 31 28 20 21 -> 32 14 6 20 13 23 30 22 8 8 9 , 28 20 21 1 28 20 21 -> 28 7 10 14 6 26 26 31 5 8 9 , 23 32 21 27 7 10 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9 , 32 13 23 23 30 18 ->= 32 13 32 21 10 21 15 29 13 30 18 , 32 11 31 23 23 2 ->= 30 16 17 16 33 8 34 25 2 0 0 , 28 20 13 32 21 1 30 18 ->= 28 17 22 4 32 14 6 33 19 14 9 , 2 1 2 1 -> 5 4 5 6 7 3 8 9 10 11 31 , 32 12 13 23 -> 32 12 14 9 15 16 17 18 10 13 23 , 5 19 11 20 13 -> 5 19 21 3 8 9 15 16 17 22 4 , 5 19 13 5 4 -> 5 8 8 9 10 14 19 14 19 14 4 , 23 23 23 23 23 -> 2 3 8 6 17 18 10 12 24 25 23 , 23 23 23 23 23 -> 23 2 3 6 26 26 20 12 14 4 23 , 2 27 7 1 28 31 -> 30 16 7 15 29 24 22 8 9 27 31 , 32 13 23 2 15 25 -> 32 11 20 24 16 17 22 6 20 14 4 , 23 23 23 23 30 25 -> 23 28 17 18 10 24 16 31 32 24 25 , 32 12 12 11 33 4 -> 30 22 34 16 31 32 11 33 6 33 4 , 2 1 23 28 33 4 -> 30 16 31 30 18 10 21 15 16 17 25 , 23 23 28 7 3 4 -> 23 28 26 17 18 15 16 7 10 14 4 , 30 22 34 29 13 23 -> 30 22 9 10 12 21 15 16 17 25 23 , 28 31 28 7 1 23 -> 28 31 28 20 21 10 11 26 17 18 1 , 30 29 21 1 23 23 -> 32 12 24 16 17 25 5 9 15 18 1 , 5 4 23 23 23 23 -> 5 9 10 14 19 12 14 4 5 9 1 , 5 19 11 31 28 20 13 -> 5 19 21 3 6 20 14 19 24 18 1 , 32 13 28 31 28 20 13 -> 32 14 6 20 13 23 30 22 8 8 4 , 28 20 21 1 28 20 13 -> 28 7 10 14 6 26 26 31 5 8 4 , 23 32 21 27 7 10 13 -> 2 15 25 32 14 8 9 0 3 8 4 , 2 1 23 23 23 28 31 -> 5 4 30 29 12 14 6 31 30 16 31 , 28 33 9 1 32 24 25 -> 28 17 16 20 21 0 10 14 9 15 25 , 23 2 27 20 14 34 25 -> 2 3 6 7 10 24 29 24 18 15 25 , 23 23 23 5 4 30 25 -> 23 32 14 8 8 34 16 17 22 34 25 , 23 23 28 7 1 2 1 -> 5 34 29 14 6 26 33 8 34 18 1 , 32 13 28 7 27 33 4 -> 5 6 7 15 16 26 17 35 35 29 13 , 30 22 19 13 2 3 4 -> 30 22 6 7 27 33 9 3 9 3 4 , 30 22 19 13 32 13 23 -> 32 21 3 8 19 14 8 8 8 4 23 , 32 21 1 28 31 23 23 -> 5 9 0 10 21 3 6 20 24 35 25 , 23 2 15 18 1 23 23 -> 23 28 33 34 35 16 33 34 22 6 31 , 28 7 27 31 23 23 23 -> 5 9 0 27 33 8 8 34 16 31 23 , 32 13 2 1 5 19 11 31 -> 30 25 32 24 25 30 16 17 29 11 31 , 23 23 23 2 27 31 28 31 -> 23 23 32 24 35 29 21 15 16 31 23 , 32 21 27 31 28 20 21 1 -> 30 22 4 28 17 16 7 10 12 21 1 , 28 31 23 28 33 34 18 1 -> 28 31 2 10 11 33 9 10 13 32 13 , 28 33 6 31 23 23 2 1 -> 28 7 27 20 11 20 12 14 8 6 31 , 5 4 23 23 23 32 14 4 -> 5 4 28 20 14 4 2 3 6 17 25 , 2 27 20 12 13 28 33 4 -> 2 27 31 5 6 26 26 26 17 29 13 , 23 28 20 12 13 28 33 4 -> 23 5 6 17 25 2 1 32 21 3 4 , 32 13 32 13 2 15 22 4 -> 5 9 15 25 28 20 12 14 8 8 4 , 30 35 29 13 23 30 22 4 -> 30 16 31 5 6 20 12 11 17 22 4 , 2 1 23 2 1 23 5 4 -> 5 6 33 34 18 27 20 14 6 20 13 , 2 3 19 13 23 23 5 4 -> 2 15 18 15 29 24 18 0 0 10 13 , 5 4 2 1 23 32 13 23 -> 5 9 15 16 26 20 13 23 2 1 23 , 2 10 12 13 23 30 25 23 -> 2 10 21 27 20 11 7 3 8 6 31 , 32 21 1 23 23 2 1 23 -> 32 13 23 23 30 25 5 9 3 4 23 , 2 1 30 18 1 5 4 23 -> 23 2 10 24 22 6 26 7 3 4 23 , 28 20 13 23 32 13 23 23 -> 28 31 30 16 17 22 4 5 9 15 25 , 2 1 23 23 32 13 23 23 -> 2 0 0 15 16 20 14 8 19 13 23 , 32 13 2 1 30 25 23 23 -> 32 21 0 15 18 10 14 19 24 25 23 , 30 22 19 21 1 23 23 23 -> 30 22 8 9 3 4 28 17 25 23 23 , 32 12 12 13 ->= 30 35 18 0 15 22 8 9 15 16 31 , 30 29 12 13 ->= 30 29 12 24 16 7 3 9 10 11 31 , 28 20 14 4 ->= 28 20 14 9 10 14 6 26 33 8 4 , 32 13 23 23 ->= 30 35 35 16 26 26 7 10 24 29 13 , 28 20 21 1 23 ->= 2 10 24 18 3 8 6 33 8 9 1 , 5 34 29 12 24 25 ->= 5 19 14 34 16 7 3 19 14 8 4 , 32 13 23 23 30 25 ->= 32 13 32 21 10 21 15 29 13 30 25 , 32 11 31 23 23 23 ->= 30 16 17 16 33 8 34 25 2 0 1 , 28 20 13 32 21 1 30 25 ->= 28 17 22 4 32 14 6 33 19 14 4 , 2 1 2 3 -> 5 4 5 6 7 3 8 9 10 11 33 , 32 12 13 5 -> 32 12 14 9 15 16 17 18 10 13 5 , 5 19 11 20 14 -> 5 19 21 3 8 9 15 16 17 22 8 , 5 19 13 5 8 -> 5 8 8 9 10 14 19 14 19 14 8 , 23 23 23 23 5 -> 2 3 8 6 17 18 10 12 24 25 5 , 23 23 23 23 5 -> 23 2 3 6 26 26 20 12 14 4 5 , 2 27 7 1 28 33 -> 30 16 7 15 29 24 22 8 9 27 33 , 32 13 23 2 15 22 -> 32 11 20 24 16 17 22 6 20 14 8 , 23 23 23 23 30 22 -> 23 28 17 18 10 24 16 31 32 24 22 , 32 12 12 11 33 8 -> 30 22 34 16 31 32 11 33 6 33 8 , 2 1 23 28 33 8 -> 30 16 31 30 18 10 21 15 16 17 22 , 23 23 28 7 3 8 -> 23 28 26 17 18 15 16 7 10 14 8 , 30 22 34 29 13 5 -> 30 22 9 10 12 21 15 16 17 25 5 , 28 31 28 7 1 5 -> 28 31 28 20 21 10 11 26 17 18 3 , 30 29 21 1 23 5 -> 32 12 24 16 17 25 5 9 15 18 3 , 5 4 23 23 23 5 -> 5 9 10 14 19 12 14 4 5 9 3 , 5 19 11 31 28 20 14 -> 5 19 21 3 6 20 14 19 24 18 3 , 32 13 28 31 28 20 14 -> 32 14 6 20 13 23 30 22 8 8 8 , 28 20 21 1 28 20 14 -> 28 7 10 14 6 26 26 31 5 8 8 , 23 32 21 27 7 10 14 -> 2 15 25 32 14 8 9 0 3 8 8 , 2 1 23 23 23 28 33 -> 5 4 30 29 12 14 6 31 30 16 33 , 28 33 9 1 32 24 22 -> 28 17 16 20 21 0 10 14 9 15 22 , 23 2 27 20 14 34 22 -> 2 3 6 7 10 24 29 24 18 15 22 , 23 23 23 5 4 30 22 -> 23 32 14 8 8 34 16 17 22 34 22 , 23 23 28 7 1 2 3 -> 5 34 29 14 6 26 33 8 34 18 3 , 32 13 28 7 27 33 8 -> 5 6 7 15 16 26 17 35 35 29 14 , 30 22 19 13 2 3 8 -> 30 22 6 7 27 33 9 3 9 3 8 , 30 22 19 13 32 13 5 -> 32 21 3 8 19 14 8 8 8 4 5 , 32 21 1 28 31 23 5 -> 5 9 0 10 21 3 6 20 24 35 22 , 23 2 15 18 1 23 5 -> 23 28 33 34 35 16 33 34 22 6 33 , 28 7 27 31 23 23 5 -> 5 9 0 27 33 8 8 34 16 31 5 , 32 13 2 1 5 19 11 33 -> 30 25 32 24 25 30 16 17 29 11 33 , 23 23 23 2 27 31 28 33 -> 23 23 32 24 35 29 21 15 16 31 5 , 32 21 27 31 28 20 21 3 -> 30 22 4 28 17 16 7 10 12 21 3 , 28 31 23 28 33 34 18 3 -> 28 31 2 10 11 33 9 10 13 32 14 , 28 33 6 31 23 23 2 3 -> 28 7 27 20 11 20 12 14 8 6 33 , 5 4 23 23 23 32 14 8 -> 5 4 28 20 14 4 2 3 6 17 22 , 2 27 20 12 13 28 33 8 -> 2 27 31 5 6 26 26 26 17 29 14 , 23 28 20 12 13 28 33 8 -> 23 5 6 17 25 2 1 32 21 3 8 , 32 13 32 13 2 15 22 8 -> 5 9 15 25 28 20 12 14 8 8 8 , 30 35 29 13 23 30 22 8 -> 30 16 31 5 6 20 12 11 17 22 8 , 2 1 23 2 1 23 5 8 -> 5 6 33 34 18 27 20 14 6 20 14 , 2 3 19 13 23 23 5 8 -> 2 15 18 15 29 24 18 0 0 10 14 , 5 4 2 1 23 32 13 5 -> 5 9 15 16 26 20 13 23 2 1 5 , 2 10 12 13 23 30 25 5 -> 2 10 21 27 20 11 7 3 8 6 33 , 32 21 1 23 23 2 1 5 -> 32 13 23 23 30 25 5 9 3 4 5 , 2 1 30 18 1 5 4 5 -> 23 2 10 24 22 6 26 7 3 4 5 , 28 20 13 23 32 13 23 5 -> 28 31 30 16 17 22 4 5 9 15 22 , 2 1 23 23 32 13 23 5 -> 2 0 0 15 16 20 14 8 19 13 5 , 32 13 2 1 30 25 23 5 -> 32 21 0 15 18 10 14 19 24 25 5 , 30 22 19 21 1 23 23 5 -> 30 22 8 9 3 4 28 17 25 23 5 , 32 12 12 14 ->= 30 35 18 0 15 22 8 9 15 16 33 , 30 29 12 14 ->= 30 29 12 24 16 7 3 9 10 11 33 , 28 20 14 8 ->= 28 20 14 9 10 14 6 26 33 8 8 , 32 13 23 5 ->= 30 35 35 16 26 26 7 10 24 29 14 , 28 20 21 1 5 ->= 2 10 24 18 3 8 6 33 8 9 3 , 5 34 29 12 24 22 ->= 5 19 14 34 16 7 3 19 14 8 8 , 32 13 23 23 30 22 ->= 32 13 32 21 10 21 15 29 13 30 22 , 32 11 31 23 23 5 ->= 30 16 17 16 33 8 34 25 2 0 3 , 28 20 13 32 21 1 30 22 ->= 28 17 22 4 32 14 6 33 19 14 8 , 2 1 2 27 -> 5 4 5 6 7 3 8 9 10 11 26 , 32 12 13 28 -> 32 12 14 9 15 16 17 18 10 13 28 , 5 19 11 20 11 -> 5 19 21 3 8 9 15 16 17 22 6 , 5 19 13 5 6 -> 5 8 8 9 10 14 19 14 19 14 6 , 23 23 23 23 28 -> 2 3 8 6 17 18 10 12 24 25 28 , 23 23 23 23 28 -> 23 2 3 6 26 26 20 12 14 4 28 , 2 27 7 1 28 26 -> 30 16 7 15 29 24 22 8 9 27 26 , 32 13 23 2 15 16 -> 32 11 20 24 16 17 22 6 20 14 6 , 23 23 23 23 30 16 -> 23 28 17 18 10 24 16 31 32 24 16 , 32 12 12 11 33 6 -> 30 22 34 16 31 32 11 33 6 33 6 , 2 1 23 28 33 6 -> 30 16 31 30 18 10 21 15 16 17 16 , 23 23 28 7 3 6 -> 23 28 26 17 18 15 16 7 10 14 6 , 30 22 34 29 13 28 -> 30 22 9 10 12 21 15 16 17 25 28 , 28 31 28 7 1 28 -> 28 31 28 20 21 10 11 26 17 18 27 , 30 29 21 1 23 28 -> 32 12 24 16 17 25 5 9 15 18 27 , 5 4 23 23 23 28 -> 5 9 10 14 19 12 14 4 5 9 27 , 5 19 11 31 28 20 11 -> 5 19 21 3 6 20 14 19 24 18 27 , 32 13 28 31 28 20 11 -> 32 14 6 20 13 23 30 22 8 8 6 , 28 20 21 1 28 20 11 -> 28 7 10 14 6 26 26 31 5 8 6 , 23 32 21 27 7 10 11 -> 2 15 25 32 14 8 9 0 3 8 6 , 2 1 23 23 23 28 26 -> 5 4 30 29 12 14 6 31 30 16 26 , 28 33 9 1 32 24 16 -> 28 17 16 20 21 0 10 14 9 15 16 , 23 2 27 20 14 34 16 -> 2 3 6 7 10 24 29 24 18 15 16 , 23 23 23 5 4 30 16 -> 23 32 14 8 8 34 16 17 22 34 16 , 23 23 28 7 1 2 27 -> 5 34 29 14 6 26 33 8 34 18 27 , 32 13 28 7 27 33 6 -> 5 6 7 15 16 26 17 35 35 29 11 , 30 22 19 13 2 3 6 -> 30 22 6 7 27 33 9 3 9 3 6 , 30 22 19 13 32 13 28 -> 32 21 3 8 19 14 8 8 8 4 28 , 32 21 1 28 31 23 28 -> 5 9 0 10 21 3 6 20 24 35 16 , 23 2 15 18 1 23 28 -> 23 28 33 34 35 16 33 34 22 6 26 , 28 7 27 31 23 23 28 -> 5 9 0 27 33 8 8 34 16 31 28 , 32 13 2 1 5 19 11 26 -> 30 25 32 24 25 30 16 17 29 11 26 , 23 23 23 2 27 31 28 26 -> 23 23 32 24 35 29 21 15 16 31 28 , 32 21 27 31 28 20 21 27 -> 30 22 4 28 17 16 7 10 12 21 27 , 28 31 23 28 33 34 18 27 -> 28 31 2 10 11 33 9 10 13 32 11 , 28 33 6 31 23 23 2 27 -> 28 7 27 20 11 20 12 14 8 6 26 , 5 4 23 23 23 32 14 6 -> 5 4 28 20 14 4 2 3 6 17 16 , 2 27 20 12 13 28 33 6 -> 2 27 31 5 6 26 26 26 17 29 11 , 23 28 20 12 13 28 33 6 -> 23 5 6 17 25 2 1 32 21 3 6 , 32 13 32 13 2 15 22 6 -> 5 9 15 25 28 20 12 14 8 8 6 , 30 35 29 13 23 30 22 6 -> 30 16 31 5 6 20 12 11 17 22 6 , 2 1 23 2 1 23 5 6 -> 5 6 33 34 18 27 20 14 6 20 11 , 2 3 19 13 23 23 5 6 -> 2 15 18 15 29 24 18 0 0 10 11 , 5 4 2 1 23 32 13 28 -> 5 9 15 16 26 20 13 23 2 1 28 , 2 10 12 13 23 30 25 28 -> 2 10 21 27 20 11 7 3 8 6 26 , 32 21 1 23 23 2 1 28 -> 32 13 23 23 30 25 5 9 3 4 28 , 2 1 30 18 1 5 4 28 -> 23 2 10 24 22 6 26 7 3 4 28 , 28 20 13 23 32 13 23 28 -> 28 31 30 16 17 22 4 5 9 15 16 , 2 1 23 23 32 13 23 28 -> 2 0 0 15 16 20 14 8 19 13 28 , 32 13 2 1 30 25 23 28 -> 32 21 0 15 18 10 14 19 24 25 28 , 30 22 19 21 1 23 23 28 -> 30 22 8 9 3 4 28 17 25 23 28 , 32 12 12 11 ->= 30 35 18 0 15 22 8 9 15 16 26 , 30 29 12 11 ->= 30 29 12 24 16 7 3 9 10 11 26 , 28 20 14 6 ->= 28 20 14 9 10 14 6 26 33 8 6 , 32 13 23 28 ->= 30 35 35 16 26 26 7 10 24 29 11 , 28 20 21 1 28 ->= 2 10 24 18 3 8 6 33 8 9 27 , 5 34 29 12 24 16 ->= 5 19 14 34 16 7 3 19 14 8 6 , 32 13 23 23 30 16 ->= 32 13 32 21 10 21 15 29 13 30 16 , 32 11 31 23 23 28 ->= 30 16 17 16 33 8 34 25 2 0 27 , 28 20 13 32 21 1 30 16 ->= 28 17 22 4 32 14 6 33 19 14 6 , 2 1 2 10 -> 5 4 5 6 7 3 8 9 10 11 20 , 32 12 13 32 -> 32 12 14 9 15 16 17 18 10 13 32 , 5 19 11 20 12 -> 5 19 21 3 8 9 15 16 17 22 19 , 5 19 13 5 19 -> 5 8 8 9 10 14 19 14 19 14 19 , 23 23 23 23 32 -> 2 3 8 6 17 18 10 12 24 25 32 , 23 23 23 23 32 -> 23 2 3 6 26 26 20 12 14 4 32 , 2 27 7 1 28 20 -> 30 16 7 15 29 24 22 8 9 27 20 , 32 13 23 2 15 29 -> 32 11 20 24 16 17 22 6 20 14 19 , 23 23 23 23 30 29 -> 23 28 17 18 10 24 16 31 32 24 29 , 32 12 12 11 33 19 -> 30 22 34 16 31 32 11 33 6 33 19 , 2 1 23 28 33 19 -> 30 16 31 30 18 10 21 15 16 17 29 , 23 23 28 7 3 19 -> 23 28 26 17 18 15 16 7 10 14 19 , 30 22 34 29 13 32 -> 30 22 9 10 12 21 15 16 17 25 32 , 28 31 28 7 1 32 -> 28 31 28 20 21 10 11 26 17 18 10 , 30 29 21 1 23 32 -> 32 12 24 16 17 25 5 9 15 18 10 , 5 4 23 23 23 32 -> 5 9 10 14 19 12 14 4 5 9 10 , 5 19 11 31 28 20 12 -> 5 19 21 3 6 20 14 19 24 18 10 , 32 13 28 31 28 20 12 -> 32 14 6 20 13 23 30 22 8 8 19 , 28 20 21 1 28 20 12 -> 28 7 10 14 6 26 26 31 5 8 19 , 23 32 21 27 7 10 12 -> 2 15 25 32 14 8 9 0 3 8 19 , 2 1 23 23 23 28 20 -> 5 4 30 29 12 14 6 31 30 16 20 , 28 33 9 1 32 24 29 -> 28 17 16 20 21 0 10 14 9 15 29 , 23 2 27 20 14 34 29 -> 2 3 6 7 10 24 29 24 18 15 29 , 23 23 23 5 4 30 29 -> 23 32 14 8 8 34 16 17 22 34 29 , 23 23 28 7 1 2 10 -> 5 34 29 14 6 26 33 8 34 18 10 , 32 13 28 7 27 33 19 -> 5 6 7 15 16 26 17 35 35 29 12 , 30 22 19 13 2 3 19 -> 30 22 6 7 27 33 9 3 9 3 19 , 30 22 19 13 32 13 32 -> 32 21 3 8 19 14 8 8 8 4 32 , 32 21 1 28 31 23 32 -> 5 9 0 10 21 3 6 20 24 35 29 , 23 2 15 18 1 23 32 -> 23 28 33 34 35 16 33 34 22 6 20 , 28 7 27 31 23 23 32 -> 5 9 0 27 33 8 8 34 16 31 32 , 32 13 2 1 5 19 11 20 -> 30 25 32 24 25 30 16 17 29 11 20 , 23 23 23 2 27 31 28 20 -> 23 23 32 24 35 29 21 15 16 31 32 , 32 21 27 31 28 20 21 10 -> 30 22 4 28 17 16 7 10 12 21 10 , 28 31 23 28 33 34 18 10 -> 28 31 2 10 11 33 9 10 13 32 12 , 28 33 6 31 23 23 2 10 -> 28 7 27 20 11 20 12 14 8 6 20 , 5 4 23 23 23 32 14 19 -> 5 4 28 20 14 4 2 3 6 17 29 , 2 27 20 12 13 28 33 19 -> 2 27 31 5 6 26 26 26 17 29 12 , 23 28 20 12 13 28 33 19 -> 23 5 6 17 25 2 1 32 21 3 19 , 32 13 32 13 2 15 22 19 -> 5 9 15 25 28 20 12 14 8 8 19 , 30 35 29 13 23 30 22 19 -> 30 16 31 5 6 20 12 11 17 22 19 , 2 1 23 2 1 23 5 19 -> 5 6 33 34 18 27 20 14 6 20 12 , 2 3 19 13 23 23 5 19 -> 2 15 18 15 29 24 18 0 0 10 12 , 5 4 2 1 23 32 13 32 -> 5 9 15 16 26 20 13 23 2 1 32 , 2 10 12 13 23 30 25 32 -> 2 10 21 27 20 11 7 3 8 6 20 , 32 21 1 23 23 2 1 32 -> 32 13 23 23 30 25 5 9 3 4 32 , 2 1 30 18 1 5 4 32 -> 23 2 10 24 22 6 26 7 3 4 32 , 28 20 13 23 32 13 23 32 -> 28 31 30 16 17 22 4 5 9 15 29 , 2 1 23 23 32 13 23 32 -> 2 0 0 15 16 20 14 8 19 13 32 , 32 13 2 1 30 25 23 32 -> 32 21 0 15 18 10 14 19 24 25 32 , 30 22 19 21 1 23 23 32 -> 30 22 8 9 3 4 28 17 25 23 32 , 32 12 12 12 ->= 30 35 18 0 15 22 8 9 15 16 20 , 30 29 12 12 ->= 30 29 12 24 16 7 3 9 10 11 20 , 28 20 14 19 ->= 28 20 14 9 10 14 6 26 33 8 19 , 32 13 23 32 ->= 30 35 35 16 26 26 7 10 24 29 12 , 28 20 21 1 32 ->= 2 10 24 18 3 8 6 33 8 9 10 , 5 34 29 12 24 29 ->= 5 19 14 34 16 7 3 19 14 8 19 , 32 13 23 23 30 29 ->= 32 13 32 21 10 21 15 29 13 30 29 , 32 11 31 23 23 32 ->= 30 16 17 16 33 8 34 25 2 0 10 , 28 20 13 32 21 1 30 29 ->= 28 17 22 4 32 14 6 33 19 14 19 , 2 1 2 15 -> 5 4 5 6 7 3 8 9 10 11 17 , 32 12 13 30 -> 32 12 14 9 15 16 17 18 10 13 30 , 5 19 11 20 24 -> 5 19 21 3 8 9 15 16 17 22 34 , 5 19 13 5 34 -> 5 8 8 9 10 14 19 14 19 14 34 , 23 23 23 23 30 -> 2 3 8 6 17 18 10 12 24 25 30 , 23 23 23 23 30 -> 23 2 3 6 26 26 20 12 14 4 30 , 2 27 7 1 28 17 -> 30 16 7 15 29 24 22 8 9 27 17 , 32 13 23 2 15 35 -> 32 11 20 24 16 17 22 6 20 14 34 , 23 23 23 23 30 35 -> 23 28 17 18 10 24 16 31 32 24 35 , 32 12 12 11 33 34 -> 30 22 34 16 31 32 11 33 6 33 34 , 2 1 23 28 33 34 -> 30 16 31 30 18 10 21 15 16 17 35 , 23 23 28 7 3 34 -> 23 28 26 17 18 15 16 7 10 14 34 , 30 22 34 29 13 30 -> 30 22 9 10 12 21 15 16 17 25 30 , 28 31 28 7 1 30 -> 28 31 28 20 21 10 11 26 17 18 15 , 30 29 21 1 23 30 -> 32 12 24 16 17 25 5 9 15 18 15 , 5 4 23 23 23 30 -> 5 9 10 14 19 12 14 4 5 9 15 , 5 19 11 31 28 20 24 -> 5 19 21 3 6 20 14 19 24 18 15 , 32 13 28 31 28 20 24 -> 32 14 6 20 13 23 30 22 8 8 34 , 28 20 21 1 28 20 24 -> 28 7 10 14 6 26 26 31 5 8 34 , 23 32 21 27 7 10 24 -> 2 15 25 32 14 8 9 0 3 8 34 , 2 1 23 23 23 28 17 -> 5 4 30 29 12 14 6 31 30 16 17 , 28 33 9 1 32 24 35 -> 28 17 16 20 21 0 10 14 9 15 35 , 23 2 27 20 14 34 35 -> 2 3 6 7 10 24 29 24 18 15 35 , 23 23 23 5 4 30 35 -> 23 32 14 8 8 34 16 17 22 34 35 , 23 23 28 7 1 2 15 -> 5 34 29 14 6 26 33 8 34 18 15 , 32 13 28 7 27 33 34 -> 5 6 7 15 16 26 17 35 35 29 24 , 30 22 19 13 2 3 34 -> 30 22 6 7 27 33 9 3 9 3 34 , 30 22 19 13 32 13 30 -> 32 21 3 8 19 14 8 8 8 4 30 , 32 21 1 28 31 23 30 -> 5 9 0 10 21 3 6 20 24 35 35 , 23 2 15 18 1 23 30 -> 23 28 33 34 35 16 33 34 22 6 17 , 28 7 27 31 23 23 30 -> 5 9 0 27 33 8 8 34 16 31 30 , 32 13 2 1 5 19 11 17 -> 30 25 32 24 25 30 16 17 29 11 17 , 23 23 23 2 27 31 28 17 -> 23 23 32 24 35 29 21 15 16 31 30 , 32 21 27 31 28 20 21 15 -> 30 22 4 28 17 16 7 10 12 21 15 , 28 31 23 28 33 34 18 15 -> 28 31 2 10 11 33 9 10 13 32 24 , 28 33 6 31 23 23 2 15 -> 28 7 27 20 11 20 12 14 8 6 17 , 5 4 23 23 23 32 14 34 -> 5 4 28 20 14 4 2 3 6 17 35 , 2 27 20 12 13 28 33 34 -> 2 27 31 5 6 26 26 26 17 29 24 , 23 28 20 12 13 28 33 34 -> 23 5 6 17 25 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35 ->= 32 13 32 21 10 21 15 29 13 30 35 , 32 11 31 23 23 30 ->= 30 16 17 16 33 8 34 25 2 0 15 , 28 20 13 32 21 1 30 35 ->= 28 17 22 4 32 14 6 33 19 14 34 , 9 1 2 0 -> 8 4 5 6 7 3 8 9 10 11 7 , 19 12 13 2 -> 19 12 14 9 15 16 17 18 10 13 2 , 8 19 11 20 21 -> 8 19 21 3 8 9 15 16 17 22 9 , 8 19 13 5 9 -> 8 8 8 9 10 14 19 14 19 14 9 , 4 23 23 23 2 -> 9 3 8 6 17 18 10 12 24 25 2 , 4 23 23 23 2 -> 4 2 3 6 26 26 20 12 14 4 2 , 9 27 7 1 28 7 -> 34 16 7 15 29 24 22 8 9 27 7 , 19 13 23 2 15 18 -> 19 11 20 24 16 17 22 6 20 14 9 , 4 23 23 23 30 18 -> 4 28 17 18 10 24 16 31 32 24 18 , 19 12 12 11 33 9 -> 34 22 34 16 31 32 11 33 6 33 9 , 9 1 23 28 33 9 -> 34 16 31 30 18 10 21 15 16 17 18 , 4 23 28 7 3 9 -> 4 28 26 17 18 15 16 7 10 14 9 , 34 22 34 29 13 2 -> 34 22 9 10 12 21 15 16 17 25 2 , 6 31 28 7 1 2 -> 6 31 28 20 21 10 11 26 17 18 0 , 34 29 21 1 23 2 -> 19 12 24 16 17 25 5 9 15 18 0 , 8 4 23 23 23 2 -> 8 9 10 14 19 12 14 4 5 9 0 , 8 19 11 31 28 20 21 -> 8 19 21 3 6 20 14 19 24 18 0 , 19 13 28 31 28 20 21 -> 19 14 6 20 13 23 30 22 8 8 9 , 6 20 21 1 28 20 21 -> 6 7 10 14 6 26 26 31 5 8 9 , 4 32 21 27 7 10 21 -> 9 15 25 32 14 8 9 0 3 8 9 , 9 1 23 23 23 28 7 -> 8 4 30 29 12 14 6 31 30 16 7 , 6 33 9 1 32 24 18 -> 6 17 16 20 21 0 10 14 9 15 18 , 4 2 27 20 14 34 18 -> 9 3 6 7 10 24 29 24 18 15 18 , 4 23 23 5 4 30 18 -> 4 32 14 8 8 34 16 17 22 34 18 , 4 23 28 7 1 2 0 -> 8 34 29 14 6 26 33 8 34 18 0 , 19 13 28 7 27 33 9 -> 8 6 7 15 16 26 17 35 35 29 21 , 34 22 19 13 2 3 9 -> 34 22 6 7 27 33 9 3 9 3 9 , 34 22 19 13 32 13 2 -> 19 21 3 8 19 14 8 8 8 4 2 , 19 21 1 28 31 23 2 -> 8 9 0 10 21 3 6 20 24 35 18 , 4 2 15 18 1 23 2 -> 4 28 33 34 35 16 33 34 22 6 7 , 6 7 27 31 23 23 2 -> 8 9 0 27 33 8 8 34 16 31 2 , 19 13 2 1 5 19 11 7 -> 34 25 32 24 25 30 16 17 29 11 7 , 4 23 23 2 27 31 28 7 -> 4 23 32 24 35 29 21 15 16 31 2 , 19 21 27 31 28 20 21 0 -> 34 22 4 28 17 16 7 10 12 21 0 , 6 31 23 28 33 34 18 0 -> 6 31 2 10 11 33 9 10 13 32 21 , 6 33 6 31 23 23 2 0 -> 6 7 27 20 11 20 12 14 8 6 7 , 8 4 23 23 23 32 14 9 -> 8 4 28 20 14 4 2 3 6 17 18 , 9 27 20 12 13 28 33 9 -> 9 27 31 5 6 26 26 26 17 29 21 , 4 28 20 12 13 28 33 9 -> 4 5 6 17 25 2 1 32 21 3 9 , 19 13 32 13 2 15 22 9 -> 8 9 15 25 28 20 12 14 8 8 9 , 34 35 29 13 23 30 22 9 -> 34 16 31 5 6 20 12 11 17 22 9 , 9 1 23 2 1 23 5 9 -> 8 6 33 34 18 27 20 14 6 20 21 , 9 3 19 13 23 23 5 9 -> 9 15 18 15 29 24 18 0 0 10 21 , 8 4 2 1 23 32 13 2 -> 8 9 15 16 26 20 13 23 2 1 2 , 9 10 12 13 23 30 25 2 -> 9 10 21 27 20 11 7 3 8 6 7 , 19 21 1 23 23 2 1 2 -> 19 13 23 23 30 25 5 9 3 4 2 , 9 1 30 18 1 5 4 2 -> 4 2 10 24 22 6 26 7 3 4 2 , 6 20 13 23 32 13 23 2 -> 6 31 30 16 17 22 4 5 9 15 18 , 9 1 23 23 32 13 23 2 -> 9 0 0 15 16 20 14 8 19 13 2 , 19 13 2 1 30 25 23 2 -> 19 21 0 15 18 10 14 19 24 25 2 , 34 22 19 21 1 23 23 2 -> 34 22 8 9 3 4 28 17 25 23 2 , 19 12 12 21 ->= 34 35 18 0 15 22 8 9 15 16 7 , 34 29 12 21 ->= 34 29 12 24 16 7 3 9 10 11 7 , 6 20 14 9 ->= 6 20 14 9 10 14 6 26 33 8 9 , 19 13 23 2 ->= 34 35 35 16 26 26 7 10 24 29 21 , 6 20 21 1 2 ->= 9 10 24 18 3 8 6 33 8 9 0 , 8 34 29 12 24 18 ->= 8 19 14 34 16 7 3 19 14 8 9 , 19 13 23 23 30 18 ->= 19 13 32 21 10 21 15 29 13 30 18 , 19 11 31 23 23 2 ->= 34 16 17 16 33 8 34 25 2 0 0 , 6 20 13 32 21 1 30 18 ->= 6 17 22 4 32 14 6 33 19 14 9 , 9 1 2 1 -> 8 4 5 6 7 3 8 9 10 11 31 , 19 12 13 23 -> 19 12 14 9 15 16 17 18 10 13 23 , 8 19 11 20 13 -> 8 19 21 3 8 9 15 16 17 22 4 , 8 19 13 5 4 -> 8 8 8 9 10 14 19 14 19 14 4 , 4 23 23 23 23 -> 9 3 8 6 17 18 10 12 24 25 23 , 4 23 23 23 23 -> 4 2 3 6 26 26 20 12 14 4 23 , 9 27 7 1 28 31 -> 34 16 7 15 29 24 22 8 9 27 31 , 19 13 23 2 15 25 -> 19 11 20 24 16 17 22 6 20 14 4 , 4 23 23 23 30 25 -> 4 28 17 18 10 24 16 31 32 24 25 , 19 12 12 11 33 4 -> 34 22 34 16 31 32 11 33 6 33 4 , 9 1 23 28 33 4 -> 34 16 31 30 18 10 21 15 16 17 25 , 4 23 28 7 3 4 -> 4 28 26 17 18 15 16 7 10 14 4 , 34 22 34 29 13 23 -> 34 22 9 10 12 21 15 16 17 25 23 , 6 31 28 7 1 23 -> 6 31 28 20 21 10 11 26 17 18 1 , 34 29 21 1 23 23 -> 19 12 24 16 17 25 5 9 15 18 1 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10 12 21 1 , 6 31 23 28 33 34 18 1 -> 6 31 2 10 11 33 9 10 13 32 13 , 6 33 6 31 23 23 2 1 -> 6 7 27 20 11 20 12 14 8 6 31 , 8 4 23 23 23 32 14 4 -> 8 4 28 20 14 4 2 3 6 17 25 , 9 27 20 12 13 28 33 4 -> 9 27 31 5 6 26 26 26 17 29 13 , 4 28 20 12 13 28 33 4 -> 4 5 6 17 25 2 1 32 21 3 4 , 19 13 32 13 2 15 22 4 -> 8 9 15 25 28 20 12 14 8 8 4 , 34 35 29 13 23 30 22 4 -> 34 16 31 5 6 20 12 11 17 22 4 , 9 1 23 2 1 23 5 4 -> 8 6 33 34 18 27 20 14 6 20 13 , 9 3 19 13 23 23 5 4 -> 9 15 18 15 29 24 18 0 0 10 13 , 8 4 2 1 23 32 13 23 -> 8 9 15 16 26 20 13 23 2 1 23 , 9 10 12 13 23 30 25 23 -> 9 10 21 27 20 11 7 3 8 6 31 , 19 21 1 23 23 2 1 23 -> 19 13 23 23 30 25 5 9 3 4 23 , 9 1 30 18 1 5 4 23 -> 4 2 10 24 22 6 26 7 3 4 23 , 6 20 13 23 32 13 23 23 -> 6 31 30 16 17 22 4 5 9 15 25 , 9 1 23 23 32 13 23 23 -> 9 0 0 15 16 20 14 8 19 13 23 , 19 13 2 1 30 25 23 23 -> 19 21 0 15 18 10 14 19 24 25 23 , 34 22 19 21 1 23 23 23 -> 34 22 8 9 3 4 28 17 25 23 23 , 19 12 12 13 ->= 34 35 18 0 15 22 8 9 15 16 31 , 34 29 12 13 ->= 34 29 12 24 16 7 3 9 10 11 31 , 6 20 14 4 ->= 6 20 14 9 10 14 6 26 33 8 4 , 19 13 23 23 ->= 34 35 35 16 26 26 7 10 24 29 13 , 6 20 21 1 23 ->= 9 10 24 18 3 8 6 33 8 9 1 , 8 34 29 12 24 25 ->= 8 19 14 34 16 7 3 19 14 8 4 , 19 13 23 23 30 25 ->= 19 13 32 21 10 21 15 29 13 30 25 , 19 11 31 23 23 23 ->= 34 16 17 16 33 8 34 25 2 0 1 , 6 20 13 32 21 1 30 25 ->= 6 17 22 4 32 14 6 33 19 14 4 , 9 1 2 3 -> 8 4 5 6 7 3 8 9 10 11 33 , 19 12 13 5 -> 19 12 14 9 15 16 17 18 10 13 5 , 8 19 11 20 14 -> 8 19 21 3 8 9 15 16 17 22 8 , 8 19 13 5 8 -> 8 8 8 9 10 14 19 14 19 14 8 , 4 23 23 23 5 -> 9 3 8 6 17 18 10 12 24 25 5 , 4 23 23 23 5 -> 4 2 3 6 26 26 20 12 14 4 5 , 9 27 7 1 28 33 -> 34 16 7 15 29 24 22 8 9 27 33 , 19 13 23 2 15 22 -> 19 11 20 24 16 17 22 6 20 14 8 , 4 23 23 23 30 22 -> 4 28 17 18 10 24 16 31 32 24 22 , 19 12 12 11 33 8 -> 34 22 34 16 31 32 11 33 6 33 8 , 9 1 23 28 33 8 -> 34 16 31 30 18 10 21 15 16 17 22 , 4 23 28 7 3 8 -> 4 28 26 17 18 15 16 7 10 14 8 , 34 22 34 29 13 5 -> 34 22 9 10 12 21 15 16 17 25 5 , 6 31 28 7 1 5 -> 6 31 28 20 21 10 11 26 17 18 3 , 34 29 21 1 23 5 -> 19 12 24 16 17 25 5 9 15 18 3 , 8 4 23 23 23 5 -> 8 9 10 14 19 12 14 4 5 9 3 , 8 19 11 31 28 20 14 -> 8 19 21 3 6 20 14 19 24 18 3 , 19 13 28 31 28 20 14 -> 19 14 6 20 13 23 30 22 8 8 8 , 6 20 21 1 28 20 14 -> 6 7 10 14 6 26 26 31 5 8 8 , 4 32 21 27 7 10 14 -> 9 15 25 32 14 8 9 0 3 8 8 , 9 1 23 23 23 28 33 -> 8 4 30 29 12 14 6 31 30 16 33 , 6 33 9 1 32 24 22 -> 6 17 16 20 21 0 10 14 9 15 22 , 4 2 27 20 14 34 22 -> 9 3 6 7 10 24 29 24 18 15 22 , 4 23 23 5 4 30 22 -> 4 32 14 8 8 34 16 17 22 34 22 , 4 23 28 7 1 2 3 -> 8 34 29 14 6 26 33 8 34 18 3 , 19 13 28 7 27 33 8 -> 8 6 7 15 16 26 17 35 35 29 14 , 34 22 19 13 2 3 8 -> 34 22 6 7 27 33 9 3 9 3 8 , 34 22 19 13 32 13 5 -> 19 21 3 8 19 14 8 8 8 4 5 , 19 21 1 28 31 23 5 -> 8 9 0 10 21 3 6 20 24 35 22 , 4 2 15 18 1 23 5 -> 4 28 33 34 35 16 33 34 22 6 33 , 6 7 27 31 23 23 5 -> 8 9 0 27 33 8 8 34 16 31 5 , 19 13 2 1 5 19 11 33 -> 34 25 32 24 25 30 16 17 29 11 33 , 4 23 23 2 27 31 28 33 -> 4 23 32 24 35 29 21 15 16 31 5 , 19 21 27 31 28 20 21 3 -> 34 22 4 28 17 16 7 10 12 21 3 , 6 31 23 28 33 34 18 3 -> 6 31 2 10 11 33 9 10 13 32 14 , 6 33 6 31 23 23 2 3 -> 6 7 27 20 11 20 12 14 8 6 33 , 8 4 23 23 23 32 14 8 -> 8 4 28 20 14 4 2 3 6 17 22 , 9 27 20 12 13 28 33 8 -> 9 27 31 5 6 26 26 26 17 29 14 , 4 28 20 12 13 28 33 8 -> 4 5 6 17 25 2 1 32 21 3 8 , 19 13 32 13 2 15 22 8 -> 8 9 15 25 28 20 12 14 8 8 8 , 34 35 29 13 23 30 22 8 -> 34 16 31 5 6 20 12 11 17 22 8 , 9 1 23 2 1 23 5 8 -> 8 6 33 34 18 27 20 14 6 20 14 , 9 3 19 13 23 23 5 8 -> 9 15 18 15 29 24 18 0 0 10 14 , 8 4 2 1 23 32 13 5 -> 8 9 15 16 26 20 13 23 2 1 5 , 9 10 12 13 23 30 25 5 -> 9 10 21 27 20 11 7 3 8 6 33 , 19 21 1 23 23 2 1 5 -> 19 13 23 23 30 25 5 9 3 4 5 , 9 1 30 18 1 5 4 5 -> 4 2 10 24 22 6 26 7 3 4 5 , 6 20 13 23 32 13 23 5 -> 6 31 30 16 17 22 4 5 9 15 22 , 9 1 23 23 32 13 23 5 -> 9 0 0 15 16 20 14 8 19 13 5 , 19 13 2 1 30 25 23 5 -> 19 21 0 15 18 10 14 19 24 25 5 , 34 22 19 21 1 23 23 5 -> 34 22 8 9 3 4 28 17 25 23 5 , 19 12 12 14 ->= 34 35 18 0 15 22 8 9 15 16 33 , 34 29 12 14 ->= 34 29 12 24 16 7 3 9 10 11 33 , 6 20 14 8 ->= 6 20 14 9 10 14 6 26 33 8 8 , 19 13 23 5 ->= 34 35 35 16 26 26 7 10 24 29 14 , 6 20 21 1 5 ->= 9 10 24 18 3 8 6 33 8 9 3 , 8 34 29 12 24 22 ->= 8 19 14 34 16 7 3 19 14 8 8 , 19 13 23 23 30 22 ->= 19 13 32 21 10 21 15 29 13 30 22 , 19 11 31 23 23 5 ->= 34 16 17 16 33 8 34 25 2 0 3 , 6 20 13 32 21 1 30 22 ->= 6 17 22 4 32 14 6 33 19 14 8 , 9 1 2 27 -> 8 4 5 6 7 3 8 9 10 11 26 , 19 12 13 28 -> 19 12 14 9 15 16 17 18 10 13 28 , 8 19 11 20 11 -> 8 19 21 3 8 9 15 16 17 22 6 , 8 19 13 5 6 -> 8 8 8 9 10 14 19 14 19 14 6 , 4 23 23 23 28 -> 9 3 8 6 17 18 10 12 24 25 28 , 4 23 23 23 28 -> 4 2 3 6 26 26 20 12 14 4 28 , 9 27 7 1 28 26 -> 34 16 7 15 29 24 22 8 9 27 26 , 19 13 23 2 15 16 -> 19 11 20 24 16 17 22 6 20 14 6 , 4 23 23 23 30 16 -> 4 28 17 18 10 24 16 31 32 24 16 , 19 12 12 11 33 6 -> 34 22 34 16 31 32 11 33 6 33 6 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2 15 18 1 23 28 -> 4 28 33 34 35 16 33 34 22 6 26 , 6 7 27 31 23 23 28 -> 8 9 0 27 33 8 8 34 16 31 28 , 19 13 2 1 5 19 11 26 -> 34 25 32 24 25 30 16 17 29 11 26 , 4 23 23 2 27 31 28 26 -> 4 23 32 24 35 29 21 15 16 31 28 , 19 21 27 31 28 20 21 27 -> 34 22 4 28 17 16 7 10 12 21 27 , 6 31 23 28 33 34 18 27 -> 6 31 2 10 11 33 9 10 13 32 11 , 6 33 6 31 23 23 2 27 -> 6 7 27 20 11 20 12 14 8 6 26 , 8 4 23 23 23 32 14 6 -> 8 4 28 20 14 4 2 3 6 17 16 , 9 27 20 12 13 28 33 6 -> 9 27 31 5 6 26 26 26 17 29 11 , 4 28 20 12 13 28 33 6 -> 4 5 6 17 25 2 1 32 21 3 6 , 19 13 32 13 2 15 22 6 -> 8 9 15 25 28 20 12 14 8 8 6 , 34 35 29 13 23 30 22 6 -> 34 16 31 5 6 20 12 11 17 22 6 , 9 1 23 2 1 23 5 6 -> 8 6 33 34 18 27 20 14 6 20 11 , 9 3 19 13 23 23 5 6 -> 9 15 18 15 29 24 18 0 0 10 11 , 8 4 2 1 23 32 13 28 -> 8 9 15 16 26 20 13 23 2 1 28 , 9 10 12 13 23 30 25 28 -> 9 10 21 27 20 11 7 3 8 6 26 , 19 21 1 23 23 2 1 28 -> 19 13 23 23 30 25 5 9 3 4 28 , 9 1 30 18 1 5 4 28 -> 4 2 10 24 22 6 26 7 3 4 28 , 6 20 13 23 32 13 23 28 -> 6 31 30 16 17 22 4 5 9 15 16 , 9 1 23 23 32 13 23 28 -> 9 0 0 15 16 20 14 8 19 13 28 , 19 13 2 1 30 25 23 28 -> 19 21 0 15 18 10 14 19 24 25 28 , 34 22 19 21 1 23 23 28 -> 34 22 8 9 3 4 28 17 25 23 28 , 19 12 12 11 ->= 34 35 18 0 15 22 8 9 15 16 26 , 34 29 12 11 ->= 34 29 12 24 16 7 3 9 10 11 26 , 6 20 14 6 ->= 6 20 14 9 10 14 6 26 33 8 6 , 19 13 23 28 ->= 34 35 35 16 26 26 7 10 24 29 11 , 6 20 21 1 28 ->= 9 10 24 18 3 8 6 33 8 9 27 , 8 34 29 12 24 16 ->= 8 19 14 34 16 7 3 19 14 8 6 , 19 13 23 23 30 16 ->= 19 13 32 21 10 21 15 29 13 30 16 , 19 11 31 23 23 28 ->= 34 16 17 16 33 8 34 25 2 0 27 , 6 20 13 32 21 1 30 16 ->= 6 17 22 4 32 14 6 33 19 14 6 , 9 1 2 10 -> 8 4 5 6 7 3 8 9 10 11 20 , 19 12 13 32 -> 19 12 14 9 15 16 17 18 10 13 32 , 8 19 11 20 12 -> 8 19 21 3 8 9 15 16 17 22 19 , 8 19 13 5 19 -> 8 8 8 9 10 14 19 14 19 14 19 , 4 23 23 23 32 -> 9 3 8 6 17 18 10 12 24 25 32 , 4 23 23 23 32 -> 4 2 3 6 26 26 20 12 14 4 32 , 9 27 7 1 28 20 -> 34 16 7 15 29 24 22 8 9 27 20 , 19 13 23 2 15 29 -> 19 11 20 24 16 17 22 6 20 14 19 , 4 23 23 23 30 29 -> 4 28 17 18 10 24 16 31 32 24 29 , 19 12 12 11 33 19 -> 34 22 34 16 31 32 11 33 6 33 19 , 9 1 23 28 33 19 -> 34 16 31 30 18 10 21 15 16 17 29 , 4 23 28 7 3 19 -> 4 28 26 17 18 15 16 7 10 14 19 , 34 22 34 29 13 32 -> 34 22 9 10 12 21 15 16 17 25 32 , 6 31 28 7 1 32 -> 6 31 28 20 21 10 11 26 17 18 10 , 34 29 21 1 23 32 -> 19 12 24 16 17 25 5 9 15 18 10 , 8 4 23 23 23 32 -> 8 9 10 14 19 12 14 4 5 9 10 , 8 19 11 31 28 20 12 -> 8 19 21 3 6 20 14 19 24 18 10 , 19 13 28 31 28 20 12 -> 19 14 6 20 13 23 30 22 8 8 19 , 6 20 21 1 28 20 12 -> 6 7 10 14 6 26 26 31 5 8 19 , 4 32 21 27 7 10 12 -> 9 15 25 32 14 8 9 0 3 8 19 , 9 1 23 23 23 28 20 -> 8 4 30 29 12 14 6 31 30 16 20 , 6 33 9 1 32 24 29 -> 6 17 16 20 21 0 10 14 9 15 29 , 4 2 27 20 14 34 29 -> 9 3 6 7 10 24 29 24 18 15 29 , 4 23 23 5 4 30 29 -> 4 32 14 8 8 34 16 17 22 34 29 , 4 23 28 7 1 2 10 -> 8 34 29 14 6 26 33 8 34 18 10 , 19 13 28 7 27 33 19 -> 8 6 7 15 16 26 17 35 35 29 12 , 34 22 19 13 2 3 19 -> 34 22 6 7 27 33 9 3 9 3 19 , 34 22 19 13 32 13 32 -> 19 21 3 8 19 14 8 8 8 4 32 , 19 21 1 28 31 23 32 -> 8 9 0 10 21 3 6 20 24 35 29 , 4 2 15 18 1 23 32 -> 4 28 33 34 35 16 33 34 22 6 20 , 6 7 27 31 23 23 32 -> 8 9 0 27 33 8 8 34 16 31 32 , 19 13 2 1 5 19 11 20 -> 34 25 32 24 25 30 16 17 29 11 20 , 4 23 23 2 27 31 28 20 -> 4 23 32 24 35 29 21 15 16 31 32 , 19 21 27 31 28 20 21 10 -> 34 22 4 28 17 16 7 10 12 21 10 , 6 31 23 28 33 34 18 10 -> 6 31 2 10 11 33 9 10 13 32 12 , 6 33 6 31 23 23 2 10 -> 6 7 27 20 11 20 12 14 8 6 20 , 8 4 23 23 23 32 14 19 -> 8 4 28 20 14 4 2 3 6 17 29 , 9 27 20 12 13 28 33 19 -> 9 27 31 5 6 26 26 26 17 29 12 , 4 28 20 12 13 28 33 19 -> 4 5 6 17 25 2 1 32 21 3 19 , 19 13 32 13 2 15 22 19 -> 8 9 15 25 28 20 12 14 8 8 19 , 34 35 29 13 23 30 22 19 -> 34 16 31 5 6 20 12 11 17 22 19 , 9 1 23 2 1 23 5 19 -> 8 6 33 34 18 27 20 14 6 20 12 , 9 3 19 13 23 23 5 19 -> 9 15 18 15 29 24 18 0 0 10 12 , 8 4 2 1 23 32 13 32 -> 8 9 15 16 26 20 13 23 2 1 32 , 9 10 12 13 23 30 25 32 -> 9 10 21 27 20 11 7 3 8 6 20 , 19 21 1 23 23 2 1 32 -> 19 13 23 23 30 25 5 9 3 4 32 , 9 1 30 18 1 5 4 32 -> 4 2 10 24 22 6 26 7 3 4 32 , 6 20 13 23 32 13 23 32 -> 6 31 30 16 17 22 4 5 9 15 29 , 9 1 23 23 32 13 23 32 -> 9 0 0 15 16 20 14 8 19 13 32 , 19 13 2 1 30 25 23 32 -> 19 21 0 15 18 10 14 19 24 25 32 , 34 22 19 21 1 23 23 32 -> 34 22 8 9 3 4 28 17 25 23 32 , 19 12 12 12 ->= 34 35 18 0 15 22 8 9 15 16 20 , 34 29 12 12 ->= 34 29 12 24 16 7 3 9 10 11 20 , 6 20 14 19 ->= 6 20 14 9 10 14 6 26 33 8 19 , 19 13 23 32 ->= 34 35 35 16 26 26 7 10 24 29 12 , 6 20 21 1 32 ->= 9 10 24 18 3 8 6 33 8 9 10 , 8 34 29 12 24 29 ->= 8 19 14 34 16 7 3 19 14 8 19 , 19 13 23 23 30 29 ->= 19 13 32 21 10 21 15 29 13 30 29 , 19 11 31 23 23 32 ->= 34 16 17 16 33 8 34 25 2 0 10 , 6 20 13 32 21 1 30 29 ->= 6 17 22 4 32 14 6 33 19 14 19 , 9 1 2 15 -> 8 4 5 6 7 3 8 9 10 11 17 , 19 12 13 30 -> 19 12 14 9 15 16 17 18 10 13 30 , 8 19 11 20 24 -> 8 19 21 3 8 9 15 16 17 22 34 , 8 19 13 5 34 -> 8 8 8 9 10 14 19 14 19 14 34 , 4 23 23 23 30 -> 9 3 8 6 17 18 10 12 24 25 30 , 4 23 23 23 30 -> 4 2 3 6 26 26 20 12 14 4 30 , 9 27 7 1 28 17 -> 34 16 7 15 29 24 22 8 9 27 17 , 19 13 23 2 15 35 -> 19 11 20 24 16 17 22 6 20 14 34 , 4 23 23 23 30 35 -> 4 28 17 18 10 24 16 31 32 24 35 , 19 12 12 11 33 34 -> 34 22 34 16 31 32 11 33 6 33 34 , 9 1 23 28 33 34 -> 34 16 31 30 18 10 21 15 16 17 35 , 4 23 28 7 3 34 -> 4 28 26 17 18 15 16 7 10 14 34 , 34 22 34 29 13 30 -> 34 22 9 10 12 21 15 16 17 25 30 , 6 31 28 7 1 30 -> 6 31 28 20 21 10 11 26 17 18 15 , 34 29 21 1 23 30 -> 19 12 24 16 17 25 5 9 15 18 15 , 8 4 23 23 23 30 -> 8 9 10 14 19 12 14 4 5 9 15 , 8 19 11 31 28 20 24 -> 8 19 21 3 6 20 14 19 24 18 15 , 19 13 28 31 28 20 24 -> 19 14 6 20 13 23 30 22 8 8 34 , 6 20 21 1 28 20 24 -> 6 7 10 14 6 26 26 31 5 8 34 , 4 32 21 27 7 10 24 -> 9 15 25 32 14 8 9 0 3 8 34 , 9 1 23 23 23 28 17 -> 8 4 30 29 12 14 6 31 30 16 17 , 6 33 9 1 32 24 35 -> 6 17 16 20 21 0 10 14 9 15 35 , 4 2 27 20 14 34 35 -> 9 3 6 7 10 24 29 24 18 15 35 , 4 23 23 5 4 30 35 -> 4 32 14 8 8 34 16 17 22 34 35 , 4 23 28 7 1 2 15 -> 8 34 29 14 6 26 33 8 34 18 15 , 19 13 28 7 27 33 34 -> 8 6 7 15 16 26 17 35 35 29 24 , 34 22 19 13 2 3 34 -> 34 22 6 7 27 33 9 3 9 3 34 , 34 22 19 13 32 13 30 -> 19 21 3 8 19 14 8 8 8 4 30 , 19 21 1 28 31 23 30 -> 8 9 0 10 21 3 6 20 24 35 35 , 4 2 15 18 1 23 30 -> 4 28 33 34 35 16 33 34 22 6 17 , 6 7 27 31 23 23 30 -> 8 9 0 27 33 8 8 34 16 31 30 , 19 13 2 1 5 19 11 17 -> 34 25 32 24 25 30 16 17 29 11 17 , 4 23 23 2 27 31 28 17 -> 4 23 32 24 35 29 21 15 16 31 30 , 19 21 27 31 28 20 21 15 -> 34 22 4 28 17 16 7 10 12 21 15 , 6 31 23 28 33 34 18 15 -> 6 31 2 10 11 33 9 10 13 32 24 , 6 33 6 31 23 23 2 15 -> 6 7 27 20 11 20 12 14 8 6 17 , 8 4 23 23 23 32 14 34 -> 8 4 28 20 14 4 2 3 6 17 35 , 9 27 20 12 13 28 33 34 -> 9 27 31 5 6 26 26 26 17 29 24 , 4 28 20 12 13 28 33 34 -> 4 5 6 17 25 2 1 32 21 3 34 , 19 13 32 13 2 15 22 34 -> 8 9 15 25 28 20 12 14 8 8 34 , 34 35 29 13 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14 6 26 26 31 5 8 9 , 31 32 21 27 7 10 21 -> 7 15 25 32 14 8 9 0 3 8 9 , 7 1 23 23 23 28 7 -> 33 4 30 29 12 14 6 31 30 16 7 , 26 33 9 1 32 24 18 -> 26 17 16 20 21 0 10 14 9 15 18 , 31 2 27 20 14 34 18 -> 7 3 6 7 10 24 29 24 18 15 18 , 31 23 23 5 4 30 18 -> 31 32 14 8 8 34 16 17 22 34 18 , 31 23 28 7 1 2 0 -> 33 34 29 14 6 26 33 8 34 18 0 , 20 13 28 7 27 33 9 -> 33 6 7 15 16 26 17 35 35 29 21 , 17 22 19 13 2 3 9 -> 17 22 6 7 27 33 9 3 9 3 9 , 17 22 19 13 32 13 2 -> 20 21 3 8 19 14 8 8 8 4 2 , 20 21 1 28 31 23 2 -> 33 9 0 10 21 3 6 20 24 35 18 , 31 2 15 18 1 23 2 -> 31 28 33 34 35 16 33 34 22 6 7 , 26 7 27 31 23 23 2 -> 33 9 0 27 33 8 8 34 16 31 2 , 20 13 2 1 5 19 11 7 -> 17 25 32 24 25 30 16 17 29 11 7 , 31 23 23 2 27 31 28 7 -> 31 23 32 24 35 29 21 15 16 31 2 , 20 21 27 31 28 20 21 0 -> 17 22 4 28 17 16 7 10 12 21 0 , 26 31 23 28 33 34 18 0 -> 26 31 2 10 11 33 9 10 13 32 21 , 26 33 6 31 23 23 2 0 -> 26 7 27 20 11 20 12 14 8 6 7 , 33 4 23 23 23 32 14 9 -> 33 4 28 20 14 4 2 3 6 17 18 , 7 27 20 12 13 28 33 9 -> 7 27 31 5 6 26 26 26 17 29 21 , 31 28 20 12 13 28 33 9 -> 31 5 6 17 25 2 1 32 21 3 9 , 20 13 32 13 2 15 22 9 -> 33 9 15 25 28 20 12 14 8 8 9 , 17 35 29 13 23 30 22 9 -> 17 16 31 5 6 20 12 11 17 22 9 , 7 1 23 2 1 23 5 9 -> 33 6 33 34 18 27 20 14 6 20 21 , 7 3 19 13 23 23 5 9 -> 7 15 18 15 29 24 18 0 0 10 21 , 33 4 2 1 23 32 13 2 -> 33 9 15 16 26 20 13 23 2 1 2 , 7 10 12 13 23 30 25 2 -> 7 10 21 27 20 11 7 3 8 6 7 , 20 21 1 23 23 2 1 2 -> 20 13 23 23 30 25 5 9 3 4 2 , 7 1 30 18 1 5 4 2 -> 31 2 10 24 22 6 26 7 3 4 2 , 26 20 13 23 32 13 23 2 -> 26 31 30 16 17 22 4 5 9 15 18 , 7 1 23 23 32 13 23 2 -> 7 0 0 15 16 20 14 8 19 13 2 , 20 13 2 1 30 25 23 2 -> 20 21 0 15 18 10 14 19 24 25 2 , 17 22 19 21 1 23 23 2 -> 17 22 8 9 3 4 28 17 25 23 2 , 20 12 12 21 ->= 17 35 18 0 15 22 8 9 15 16 7 , 17 29 12 21 ->= 17 29 12 24 16 7 3 9 10 11 7 , 26 20 14 9 ->= 26 20 14 9 10 14 6 26 33 8 9 , 20 13 23 2 ->= 17 35 35 16 26 26 7 10 24 29 21 , 26 20 21 1 2 ->= 7 10 24 18 3 8 6 33 8 9 0 , 33 34 29 12 24 18 ->= 33 19 14 34 16 7 3 19 14 8 9 , 20 13 23 23 30 18 ->= 20 13 32 21 10 21 15 29 13 30 18 , 20 11 31 23 23 2 ->= 17 16 17 16 33 8 34 25 2 0 0 , 26 20 13 32 21 1 30 18 ->= 26 17 22 4 32 14 6 33 19 14 9 , 7 1 2 1 -> 33 4 5 6 7 3 8 9 10 11 31 , 20 12 13 23 -> 20 12 14 9 15 16 17 18 10 13 23 , 33 19 11 20 13 -> 33 19 21 3 8 9 15 16 17 22 4 , 33 19 13 5 4 -> 33 8 8 9 10 14 19 14 19 14 4 , 31 23 23 23 23 -> 7 3 8 6 17 18 10 12 24 25 23 , 31 23 23 23 23 -> 31 2 3 6 26 26 20 12 14 4 23 , 7 27 7 1 28 31 -> 17 16 7 15 29 24 22 8 9 27 31 , 20 13 23 2 15 25 -> 20 11 20 24 16 17 22 6 20 14 4 , 31 23 23 23 30 25 -> 31 28 17 18 10 24 16 31 32 24 25 , 20 12 12 11 33 4 -> 17 22 34 16 31 32 11 33 6 33 4 , 7 1 23 28 33 4 -> 17 16 31 30 18 10 21 15 16 17 25 , 31 23 28 7 3 4 -> 31 28 26 17 18 15 16 7 10 14 4 , 17 22 34 29 13 23 -> 17 22 9 10 12 21 15 16 17 25 23 , 26 31 28 7 1 23 -> 26 31 28 20 21 10 11 26 17 18 1 , 17 29 21 1 23 23 -> 20 12 24 16 17 25 5 9 15 18 1 , 33 4 23 23 23 23 -> 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7 10 12 21 1 , 26 31 23 28 33 34 18 1 -> 26 31 2 10 11 33 9 10 13 32 13 , 26 33 6 31 23 23 2 1 -> 26 7 27 20 11 20 12 14 8 6 31 , 33 4 23 23 23 32 14 4 -> 33 4 28 20 14 4 2 3 6 17 25 , 7 27 20 12 13 28 33 4 -> 7 27 31 5 6 26 26 26 17 29 13 , 31 28 20 12 13 28 33 4 -> 31 5 6 17 25 2 1 32 21 3 4 , 20 13 32 13 2 15 22 4 -> 33 9 15 25 28 20 12 14 8 8 4 , 17 35 29 13 23 30 22 4 -> 17 16 31 5 6 20 12 11 17 22 4 , 7 1 23 2 1 23 5 4 -> 33 6 33 34 18 27 20 14 6 20 13 , 7 3 19 13 23 23 5 4 -> 7 15 18 15 29 24 18 0 0 10 13 , 33 4 2 1 23 32 13 23 -> 33 9 15 16 26 20 13 23 2 1 23 , 7 10 12 13 23 30 25 23 -> 7 10 21 27 20 11 7 3 8 6 31 , 20 21 1 23 23 2 1 23 -> 20 13 23 23 30 25 5 9 3 4 23 , 7 1 30 18 1 5 4 23 -> 31 2 10 24 22 6 26 7 3 4 23 , 26 20 13 23 32 13 23 23 -> 26 31 30 16 17 22 4 5 9 15 25 , 7 1 23 23 32 13 23 23 -> 7 0 0 15 16 20 14 8 19 13 23 , 20 13 2 1 30 25 23 23 -> 20 21 0 15 18 10 14 19 24 25 23 , 17 22 19 21 1 23 23 23 -> 17 22 8 9 3 4 28 17 25 23 23 , 20 12 12 13 ->= 17 35 18 0 15 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9 0 27 33 8 8 34 16 31 5 , 20 13 2 1 5 19 11 33 -> 17 25 32 24 25 30 16 17 29 11 33 , 31 23 23 2 27 31 28 33 -> 31 23 32 24 35 29 21 15 16 31 5 , 20 21 27 31 28 20 21 3 -> 17 22 4 28 17 16 7 10 12 21 3 , 26 31 23 28 33 34 18 3 -> 26 31 2 10 11 33 9 10 13 32 14 , 26 33 6 31 23 23 2 3 -> 26 7 27 20 11 20 12 14 8 6 33 , 33 4 23 23 23 32 14 8 -> 33 4 28 20 14 4 2 3 6 17 22 , 7 27 20 12 13 28 33 8 -> 7 27 31 5 6 26 26 26 17 29 14 , 31 28 20 12 13 28 33 8 -> 31 5 6 17 25 2 1 32 21 3 8 , 20 13 32 13 2 15 22 8 -> 33 9 15 25 28 20 12 14 8 8 8 , 17 35 29 13 23 30 22 8 -> 17 16 31 5 6 20 12 11 17 22 8 , 7 1 23 2 1 23 5 8 -> 33 6 33 34 18 27 20 14 6 20 14 , 7 3 19 13 23 23 5 8 -> 7 15 18 15 29 24 18 0 0 10 14 , 33 4 2 1 23 32 13 5 -> 33 9 15 16 26 20 13 23 2 1 5 , 7 10 12 13 23 30 25 5 -> 7 10 21 27 20 11 7 3 8 6 33 , 20 21 1 23 23 2 1 5 -> 20 13 23 23 30 25 5 9 3 4 5 , 7 1 30 18 1 5 4 5 -> 31 2 10 24 22 6 26 7 3 4 5 , 26 20 13 23 32 13 23 5 -> 26 31 30 16 17 22 4 5 9 15 22 , 7 1 23 23 32 13 23 5 -> 7 0 0 15 16 20 14 8 19 13 5 , 20 13 2 1 30 25 23 5 -> 20 21 0 15 18 10 14 19 24 25 5 , 17 22 19 21 1 23 23 5 -> 17 22 8 9 3 4 28 17 25 23 5 , 20 12 12 14 ->= 17 35 18 0 15 22 8 9 15 16 33 , 17 29 12 14 ->= 17 29 12 24 16 7 3 9 10 11 33 , 26 20 14 8 ->= 26 20 14 9 10 14 6 26 33 8 8 , 20 13 23 5 ->= 17 35 35 16 26 26 7 10 24 29 14 , 26 20 21 1 5 ->= 7 10 24 18 3 8 6 33 8 9 3 , 33 34 29 12 24 22 ->= 33 19 14 34 16 7 3 19 14 8 8 , 20 13 23 23 30 22 ->= 20 13 32 21 10 21 15 29 13 30 22 , 20 11 31 23 23 5 ->= 17 16 17 16 33 8 34 25 2 0 3 , 26 20 13 32 21 1 30 22 ->= 26 17 22 4 32 14 6 33 19 14 8 , 7 1 2 27 -> 33 4 5 6 7 3 8 9 10 11 26 , 20 12 13 28 -> 20 12 14 9 15 16 17 18 10 13 28 , 33 19 11 20 11 -> 33 19 21 3 8 9 15 16 17 22 6 , 33 19 13 5 6 -> 33 8 8 9 10 14 19 14 19 14 6 , 31 23 23 23 28 -> 7 3 8 6 17 18 10 12 24 25 28 , 31 23 23 23 28 -> 31 2 3 6 26 26 20 12 14 4 28 , 7 27 7 1 28 26 -> 17 16 7 15 29 24 22 8 9 27 26 , 20 13 23 2 15 16 -> 20 11 20 24 16 17 22 6 20 14 6 , 31 23 23 23 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27 20 11 7 3 8 6 26 , 20 21 1 23 23 2 1 28 -> 20 13 23 23 30 25 5 9 3 4 28 , 7 1 30 18 1 5 4 28 -> 31 2 10 24 22 6 26 7 3 4 28 , 26 20 13 23 32 13 23 28 -> 26 31 30 16 17 22 4 5 9 15 16 , 7 1 23 23 32 13 23 28 -> 7 0 0 15 16 20 14 8 19 13 28 , 20 13 2 1 30 25 23 28 -> 20 21 0 15 18 10 14 19 24 25 28 , 17 22 19 21 1 23 23 28 -> 17 22 8 9 3 4 28 17 25 23 28 , 20 12 12 11 ->= 17 35 18 0 15 22 8 9 15 16 26 , 17 29 12 11 ->= 17 29 12 24 16 7 3 9 10 11 26 , 26 20 14 6 ->= 26 20 14 9 10 14 6 26 33 8 6 , 20 13 23 28 ->= 17 35 35 16 26 26 7 10 24 29 11 , 26 20 21 1 28 ->= 7 10 24 18 3 8 6 33 8 9 27 , 33 34 29 12 24 16 ->= 33 19 14 34 16 7 3 19 14 8 6 , 20 13 23 23 30 16 ->= 20 13 32 21 10 21 15 29 13 30 16 , 20 11 31 23 23 28 ->= 17 16 17 16 33 8 34 25 2 0 27 , 26 20 13 32 21 1 30 16 ->= 26 17 22 4 32 14 6 33 19 14 6 , 7 1 2 10 -> 33 4 5 6 7 3 8 9 10 11 20 , 20 12 13 32 -> 20 12 14 9 15 16 17 18 10 13 32 , 33 19 11 20 12 -> 33 19 21 3 8 9 15 16 17 22 19 , 33 19 13 5 19 -> 33 8 8 9 10 14 19 14 19 14 19 , 31 23 23 23 32 -> 7 3 8 6 17 18 10 12 24 25 32 , 31 23 23 23 32 -> 31 2 3 6 26 26 20 12 14 4 32 , 7 27 7 1 28 20 -> 17 16 7 15 29 24 22 8 9 27 20 , 20 13 23 2 15 29 -> 20 11 20 24 16 17 22 6 20 14 19 , 31 23 23 23 30 29 -> 31 28 17 18 10 24 16 31 32 24 29 , 20 12 12 11 33 19 -> 17 22 34 16 31 32 11 33 6 33 19 , 7 1 23 28 33 19 -> 17 16 31 30 18 10 21 15 16 17 29 , 31 23 28 7 3 19 -> 31 28 26 17 18 15 16 7 10 14 19 , 17 22 34 29 13 32 -> 17 22 9 10 12 21 15 16 17 25 32 , 26 31 28 7 1 32 -> 26 31 28 20 21 10 11 26 17 18 10 , 17 29 21 1 23 32 -> 20 12 24 16 17 25 5 9 15 18 10 , 33 4 23 23 23 32 -> 33 9 10 14 19 12 14 4 5 9 10 , 33 19 11 31 28 20 12 -> 33 19 21 3 6 20 14 19 24 18 10 , 20 13 28 31 28 20 12 -> 20 14 6 20 13 23 30 22 8 8 19 , 26 20 21 1 28 20 12 -> 26 7 10 14 6 26 26 31 5 8 19 , 31 32 21 27 7 10 12 -> 7 15 25 32 14 8 9 0 3 8 19 , 7 1 23 23 23 28 20 -> 33 4 30 29 12 14 6 31 30 16 20 , 26 33 9 1 32 24 29 -> 26 17 16 20 21 0 10 14 9 15 29 , 31 2 27 20 14 34 29 -> 7 3 6 7 10 24 29 24 18 15 29 , 31 23 23 5 4 30 29 -> 31 32 14 8 8 34 16 17 22 34 29 , 31 23 28 7 1 2 10 -> 33 34 29 14 6 26 33 8 34 18 10 , 20 13 28 7 27 33 19 -> 33 6 7 15 16 26 17 35 35 29 12 , 17 22 19 13 2 3 19 -> 17 22 6 7 27 33 9 3 9 3 19 , 17 22 19 13 32 13 32 -> 20 21 3 8 19 14 8 8 8 4 32 , 20 21 1 28 31 23 32 -> 33 9 0 10 21 3 6 20 24 35 29 , 31 2 15 18 1 23 32 -> 31 28 33 34 35 16 33 34 22 6 20 , 26 7 27 31 23 23 32 -> 33 9 0 27 33 8 8 34 16 31 32 , 20 13 2 1 5 19 11 20 -> 17 25 32 24 25 30 16 17 29 11 20 , 31 23 23 2 27 31 28 20 -> 31 23 32 24 35 29 21 15 16 31 32 , 20 21 27 31 28 20 21 10 -> 17 22 4 28 17 16 7 10 12 21 10 , 26 31 23 28 33 34 18 10 -> 26 31 2 10 11 33 9 10 13 32 12 , 26 33 6 31 23 23 2 10 -> 26 7 27 20 11 20 12 14 8 6 20 , 33 4 23 23 23 32 14 19 -> 33 4 28 20 14 4 2 3 6 17 29 , 7 27 20 12 13 28 33 19 -> 7 27 31 5 6 26 26 26 17 29 12 , 31 28 20 12 13 28 33 19 -> 31 5 6 17 25 2 1 32 21 3 19 , 20 13 32 13 2 15 22 19 -> 33 9 15 25 28 20 12 14 8 8 19 , 17 35 29 13 23 30 22 19 -> 17 16 31 5 6 20 12 11 17 22 19 , 7 1 23 2 1 23 5 19 -> 33 6 33 34 18 27 20 14 6 20 12 , 7 3 19 13 23 23 5 19 -> 7 15 18 15 29 24 18 0 0 10 12 , 33 4 2 1 23 32 13 32 -> 33 9 15 16 26 20 13 23 2 1 32 , 7 10 12 13 23 30 25 32 -> 7 10 21 27 20 11 7 3 8 6 20 , 20 21 1 23 23 2 1 32 -> 20 13 23 23 30 25 5 9 3 4 32 , 7 1 30 18 1 5 4 32 -> 31 2 10 24 22 6 26 7 3 4 32 , 26 20 13 23 32 13 23 32 -> 26 31 30 16 17 22 4 5 9 15 29 , 7 1 23 23 32 13 23 32 -> 7 0 0 15 16 20 14 8 19 13 32 , 20 13 2 1 30 25 23 32 -> 20 21 0 15 18 10 14 19 24 25 32 , 17 22 19 21 1 23 23 32 -> 17 22 8 9 3 4 28 17 25 23 32 , 20 12 12 12 ->= 17 35 18 0 15 22 8 9 15 16 20 , 17 29 12 12 ->= 17 29 12 24 16 7 3 9 10 11 20 , 26 20 14 19 ->= 26 20 14 9 10 14 6 26 33 8 19 , 20 13 23 32 ->= 17 35 35 16 26 26 7 10 24 29 12 , 26 20 21 1 32 ->= 7 10 24 18 3 8 6 33 8 9 10 , 33 34 29 12 24 29 ->= 33 19 14 34 16 7 3 19 14 8 19 , 20 13 23 23 30 29 ->= 20 13 32 21 10 21 15 29 13 30 29 , 20 11 31 23 23 32 ->= 17 16 17 16 33 8 34 25 2 0 10 , 26 20 13 32 21 1 30 29 ->= 26 17 22 4 32 14 6 33 19 14 19 , 7 1 2 15 -> 33 4 5 6 7 3 8 9 10 11 17 , 20 12 13 30 -> 20 12 14 9 15 16 17 18 10 13 30 , 33 19 11 20 24 -> 33 19 21 3 8 9 15 16 17 22 34 , 33 19 13 5 34 -> 33 8 8 9 10 14 19 14 19 14 34 , 31 23 23 23 30 -> 7 3 8 6 17 18 10 12 24 25 30 , 31 23 23 23 30 -> 31 2 3 6 26 26 20 12 14 4 30 , 7 27 7 1 28 17 -> 17 16 7 15 29 24 22 8 9 27 17 , 20 13 23 2 15 35 -> 20 11 20 24 16 17 22 6 20 14 34 , 31 23 23 23 30 35 -> 31 28 17 18 10 24 16 31 32 24 35 , 20 12 12 11 33 34 -> 17 22 34 16 31 32 11 33 6 33 34 , 7 1 23 28 33 34 -> 17 16 31 30 18 10 21 15 16 17 35 , 31 23 28 7 3 34 -> 31 28 26 17 18 15 16 7 10 14 34 , 17 22 34 29 13 30 -> 17 22 9 10 12 21 15 16 17 25 30 , 26 31 28 7 1 30 -> 26 31 28 20 21 10 11 26 17 18 15 , 17 29 21 1 23 30 -> 20 12 24 16 17 25 5 9 15 18 15 , 33 4 23 23 23 30 -> 33 9 10 14 19 12 14 4 5 9 15 , 33 19 11 31 28 20 24 -> 33 19 21 3 6 20 14 19 24 18 15 , 20 13 28 31 28 20 24 -> 20 14 6 20 13 23 30 22 8 8 34 , 26 20 21 1 28 20 24 -> 26 7 10 14 6 26 26 31 5 8 34 , 31 32 21 27 7 10 24 -> 7 15 25 32 14 8 9 0 3 8 34 , 7 1 23 23 23 28 17 -> 33 4 30 29 12 14 6 31 30 16 17 , 26 33 9 1 32 24 35 -> 26 17 16 20 21 0 10 14 9 15 35 , 31 2 27 20 14 34 35 -> 7 3 6 7 10 24 29 24 18 15 35 , 31 23 23 5 4 30 35 -> 31 32 14 8 8 34 16 17 22 34 35 , 31 23 28 7 1 2 15 -> 33 34 29 14 6 26 33 8 34 18 15 , 20 13 28 7 27 33 34 -> 33 6 7 15 16 26 17 35 35 29 24 , 17 22 19 13 2 3 34 -> 17 22 6 7 27 33 9 3 9 3 34 , 17 22 19 13 32 13 30 -> 20 21 3 8 19 14 8 8 8 4 30 , 20 21 1 28 31 23 30 -> 33 9 0 10 21 3 6 20 24 35 35 , 31 2 15 18 1 23 30 -> 31 28 33 34 35 16 33 34 22 6 17 , 26 7 27 31 23 23 30 -> 33 9 0 27 33 8 8 34 16 31 30 , 20 13 2 1 5 19 11 17 -> 17 25 32 24 25 30 16 17 29 11 17 , 31 23 23 2 27 31 28 17 -> 31 23 32 24 35 29 21 15 16 31 30 , 20 21 27 31 28 20 21 15 -> 17 22 4 28 17 16 7 10 12 21 15 , 26 31 23 28 33 34 18 15 -> 26 31 2 10 11 33 9 10 13 32 24 , 26 33 6 31 23 23 2 15 -> 26 7 27 20 11 20 12 14 8 6 17 , 33 4 23 23 23 32 14 34 -> 33 4 28 20 14 4 2 3 6 17 35 , 7 27 20 12 13 28 33 34 -> 7 27 31 5 6 26 26 26 17 29 24 , 31 28 20 12 13 28 33 34 -> 31 5 6 17 25 2 1 32 21 3 34 , 20 13 32 13 2 15 22 34 -> 33 9 15 25 28 20 12 14 8 8 34 , 17 35 29 13 23 30 22 34 -> 17 16 31 5 6 20 12 11 17 22 34 , 7 1 23 2 1 23 5 34 -> 33 6 33 34 18 27 20 14 6 20 24 , 7 3 19 13 23 23 5 34 -> 7 15 18 15 29 24 18 0 0 10 24 , 33 4 2 1 23 32 13 30 -> 33 9 15 16 26 20 13 23 2 1 30 , 7 10 12 13 23 30 25 30 -> 7 10 21 27 20 11 7 3 8 6 17 , 20 21 1 23 23 2 1 30 -> 20 13 23 23 30 25 5 9 3 4 30 , 7 1 30 18 1 5 4 30 -> 31 2 10 24 22 6 26 7 3 4 30 , 26 20 13 23 32 13 23 30 -> 26 31 30 16 17 22 4 5 9 15 35 , 7 1 23 23 32 13 23 30 -> 7 0 0 15 16 20 14 8 19 13 30 , 20 13 2 1 30 25 23 30 -> 20 21 0 15 18 10 14 19 24 25 30 , 17 22 19 21 1 23 23 30 -> 17 22 8 9 3 4 28 17 25 23 30 , 20 12 12 24 ->= 17 35 18 0 15 22 8 9 15 16 17 , 17 29 12 24 ->= 17 29 12 24 16 7 3 9 10 11 17 , 26 20 14 34 ->= 26 20 14 9 10 14 6 26 33 8 34 , 20 13 23 30 ->= 17 35 35 16 26 26 7 10 24 29 24 , 26 20 21 1 30 ->= 7 10 24 18 3 8 6 33 8 9 15 , 33 34 29 12 24 35 ->= 33 19 14 34 16 7 3 19 14 8 34 , 20 13 23 23 30 35 ->= 20 13 32 21 10 21 15 29 13 30 35 , 20 11 31 23 23 30 ->= 17 16 17 16 33 8 34 25 2 0 15 , 26 20 13 32 21 1 30 35 ->= 26 17 22 4 32 14 6 33 19 14 34 , 21 1 2 0 -> 14 4 5 6 7 3 8 9 10 11 7 , 12 12 13 2 -> 12 12 14 9 15 16 17 18 10 13 2 , 14 19 11 20 21 -> 14 19 21 3 8 9 15 16 17 22 9 , 14 19 13 5 9 -> 14 8 8 9 10 14 19 14 19 14 9 , 13 23 23 23 2 -> 21 3 8 6 17 18 10 12 24 25 2 , 13 23 23 23 2 -> 13 2 3 6 26 26 20 12 14 4 2 , 21 27 7 1 28 7 -> 24 16 7 15 29 24 22 8 9 27 7 , 12 13 23 2 15 18 -> 12 11 20 24 16 17 22 6 20 14 9 , 13 23 23 23 30 18 -> 13 28 17 18 10 24 16 31 32 24 18 , 12 12 12 11 33 9 -> 24 22 34 16 31 32 11 33 6 33 9 , 21 1 23 28 33 9 -> 24 16 31 30 18 10 21 15 16 17 18 , 13 23 28 7 3 9 -> 13 28 26 17 18 15 16 7 10 14 9 , 24 22 34 29 13 2 -> 24 22 9 10 12 21 15 16 17 25 2 , 11 31 28 7 1 2 -> 11 31 28 20 21 10 11 26 17 18 0 , 24 29 21 1 23 2 -> 12 12 24 16 17 25 5 9 15 18 0 , 14 4 23 23 23 2 -> 14 9 10 14 19 12 14 4 5 9 0 , 14 19 11 31 28 20 21 -> 14 19 21 3 6 20 14 19 24 18 0 , 12 13 28 31 28 20 21 -> 12 14 6 20 13 23 30 22 8 8 9 , 11 20 21 1 28 20 21 -> 11 7 10 14 6 26 26 31 5 8 9 , 13 32 21 27 7 10 21 -> 21 15 25 32 14 8 9 0 3 8 9 , 21 1 23 23 23 28 7 -> 14 4 30 29 12 14 6 31 30 16 7 , 11 33 9 1 32 24 18 -> 11 17 16 20 21 0 10 14 9 15 18 , 13 2 27 20 14 34 18 -> 21 3 6 7 10 24 29 24 18 15 18 , 13 23 23 5 4 30 18 -> 13 32 14 8 8 34 16 17 22 34 18 , 13 23 28 7 1 2 0 -> 14 34 29 14 6 26 33 8 34 18 0 , 12 13 28 7 27 33 9 -> 14 6 7 15 16 26 17 35 35 29 21 , 24 22 19 13 2 3 9 -> 24 22 6 7 27 33 9 3 9 3 9 , 24 22 19 13 32 13 2 -> 12 21 3 8 19 14 8 8 8 4 2 , 12 21 1 28 31 23 2 -> 14 9 0 10 21 3 6 20 24 35 18 , 13 2 15 18 1 23 2 -> 13 28 33 34 35 16 33 34 22 6 7 , 11 7 27 31 23 23 2 -> 14 9 0 27 33 8 8 34 16 31 2 , 12 13 2 1 5 19 11 7 -> 24 25 32 24 25 30 16 17 29 11 7 , 13 23 23 2 27 31 28 7 -> 13 23 32 24 35 29 21 15 16 31 2 , 12 21 27 31 28 20 21 0 -> 24 22 4 28 17 16 7 10 12 21 0 , 11 31 23 28 33 34 18 0 -> 11 31 2 10 11 33 9 10 13 32 21 , 11 33 6 31 23 23 2 0 -> 11 7 27 20 11 20 12 14 8 6 7 , 14 4 23 23 23 32 14 9 -> 14 4 28 20 14 4 2 3 6 17 18 , 21 27 20 12 13 28 33 9 -> 21 27 31 5 6 26 26 26 17 29 21 , 13 28 20 12 13 28 33 9 -> 13 5 6 17 25 2 1 32 21 3 9 , 12 13 32 13 2 15 22 9 -> 14 9 15 25 28 20 12 14 8 8 9 , 24 35 29 13 23 30 22 9 -> 24 16 31 5 6 20 12 11 17 22 9 , 21 1 23 2 1 23 5 9 -> 14 6 33 34 18 27 20 14 6 20 21 , 21 3 19 13 23 23 5 9 -> 21 15 18 15 29 24 18 0 0 10 21 , 14 4 2 1 23 32 13 2 -> 14 9 15 16 26 20 13 23 2 1 2 , 21 10 12 13 23 30 25 2 -> 21 10 21 27 20 11 7 3 8 6 7 , 12 21 1 23 23 2 1 2 -> 12 13 23 23 30 25 5 9 3 4 2 , 21 1 30 18 1 5 4 2 -> 13 2 10 24 22 6 26 7 3 4 2 , 11 20 13 23 32 13 23 2 -> 11 31 30 16 17 22 4 5 9 15 18 , 21 1 23 23 32 13 23 2 -> 21 0 0 15 16 20 14 8 19 13 2 , 12 13 2 1 30 25 23 2 -> 12 21 0 15 18 10 14 19 24 25 2 , 24 22 19 21 1 23 23 2 -> 24 22 8 9 3 4 28 17 25 23 2 , 12 12 12 21 ->= 24 35 18 0 15 22 8 9 15 16 7 , 24 29 12 21 ->= 24 29 12 24 16 7 3 9 10 11 7 , 11 20 14 9 ->= 11 20 14 9 10 14 6 26 33 8 9 , 12 13 23 2 ->= 24 35 35 16 26 26 7 10 24 29 21 , 11 20 21 1 2 ->= 21 10 24 18 3 8 6 33 8 9 0 , 14 34 29 12 24 18 ->= 14 19 14 34 16 7 3 19 14 8 9 , 12 13 23 23 30 18 ->= 12 13 32 21 10 21 15 29 13 30 18 , 12 11 31 23 23 2 ->= 24 16 17 16 33 8 34 25 2 0 0 , 11 20 13 32 21 1 30 18 ->= 11 17 22 4 32 14 6 33 19 14 9 , 21 1 2 1 -> 14 4 5 6 7 3 8 9 10 11 31 , 12 12 13 23 -> 12 12 14 9 15 16 17 18 10 13 23 , 14 19 11 20 13 -> 14 19 21 3 8 9 15 16 17 22 4 , 14 19 13 5 4 -> 14 8 8 9 10 14 19 14 19 14 4 , 13 23 23 23 23 -> 21 3 8 6 17 18 10 12 24 25 23 , 13 23 23 23 23 -> 13 2 3 6 26 26 20 12 14 4 23 , 21 27 7 1 28 31 -> 24 16 7 15 29 24 22 8 9 27 31 , 12 13 23 2 15 25 -> 12 11 20 24 16 17 22 6 20 14 4 , 13 23 23 23 30 25 -> 13 28 17 18 10 24 16 31 32 24 25 , 12 12 12 11 33 4 -> 24 22 34 16 31 32 11 33 6 33 4 , 21 1 23 28 33 4 -> 24 16 31 30 18 10 21 15 16 17 25 , 13 23 28 7 3 4 -> 13 28 26 17 18 15 16 7 10 14 4 , 24 22 34 29 13 23 -> 24 22 9 10 12 21 15 16 17 25 23 , 11 31 28 7 1 23 -> 11 31 28 20 21 10 11 26 17 18 1 , 24 29 21 1 23 23 -> 12 12 24 16 17 25 5 9 15 18 1 , 14 4 23 23 23 23 -> 14 9 10 14 19 12 14 4 5 9 1 , 14 19 11 31 28 20 13 -> 14 19 21 3 6 20 14 19 24 18 1 , 12 13 28 31 28 20 13 -> 12 14 6 20 13 23 30 22 8 8 4 , 11 20 21 1 28 20 13 -> 11 7 10 14 6 26 26 31 5 8 4 , 13 32 21 27 7 10 13 -> 21 15 25 32 14 8 9 0 3 8 4 , 21 1 23 23 23 28 31 -> 14 4 30 29 12 14 6 31 30 16 31 , 11 33 9 1 32 24 25 -> 11 17 16 20 21 0 10 14 9 15 25 , 13 2 27 20 14 34 25 -> 21 3 6 7 10 24 29 24 18 15 25 , 13 23 23 5 4 30 25 -> 13 32 14 8 8 34 16 17 22 34 25 , 13 23 28 7 1 2 1 -> 14 34 29 14 6 26 33 8 34 18 1 , 12 13 28 7 27 33 4 -> 14 6 7 15 16 26 17 35 35 29 13 , 24 22 19 13 2 3 4 -> 24 22 6 7 27 33 9 3 9 3 4 , 24 22 19 13 32 13 23 -> 12 21 3 8 19 14 8 8 8 4 23 , 12 21 1 28 31 23 23 -> 14 9 0 10 21 3 6 20 24 35 25 , 13 2 15 18 1 23 23 -> 13 28 33 34 35 16 33 34 22 6 31 , 11 7 27 31 23 23 23 -> 14 9 0 27 33 8 8 34 16 31 23 , 12 13 2 1 5 19 11 31 -> 24 25 32 24 25 30 16 17 29 11 31 , 13 23 23 2 27 31 28 31 -> 13 23 32 24 35 29 21 15 16 31 23 , 12 21 27 31 28 20 21 1 -> 24 22 4 28 17 16 7 10 12 21 1 , 11 31 23 28 33 34 18 1 -> 11 31 2 10 11 33 9 10 13 32 13 , 11 33 6 31 23 23 2 1 -> 11 7 27 20 11 20 12 14 8 6 31 , 14 4 23 23 23 32 14 4 -> 14 4 28 20 14 4 2 3 6 17 25 , 21 27 20 12 13 28 33 4 -> 21 27 31 5 6 26 26 26 17 29 13 , 13 28 20 12 13 28 33 4 -> 13 5 6 17 25 2 1 32 21 3 4 , 12 13 32 13 2 15 22 4 -> 14 9 15 25 28 20 12 14 8 8 4 , 24 35 29 13 23 30 22 4 -> 24 16 31 5 6 20 12 11 17 22 4 , 21 1 23 2 1 23 5 4 -> 14 6 33 34 18 27 20 14 6 20 13 , 21 3 19 13 23 23 5 4 -> 21 15 18 15 29 24 18 0 0 10 13 , 14 4 2 1 23 32 13 23 -> 14 9 15 16 26 20 13 23 2 1 23 , 21 10 12 13 23 30 25 23 -> 21 10 21 27 20 11 7 3 8 6 31 , 12 21 1 23 23 2 1 23 -> 12 13 23 23 30 25 5 9 3 4 23 , 21 1 30 18 1 5 4 23 -> 13 2 10 24 22 6 26 7 3 4 23 , 11 20 13 23 32 13 23 23 -> 11 31 30 16 17 22 4 5 9 15 25 , 21 1 23 23 32 13 23 23 -> 21 0 0 15 16 20 14 8 19 13 23 , 12 13 2 1 30 25 23 23 -> 12 21 0 15 18 10 14 19 24 25 23 , 24 22 19 21 1 23 23 23 -> 24 22 8 9 3 4 28 17 25 23 23 , 12 12 12 13 ->= 24 35 18 0 15 22 8 9 15 16 31 , 24 29 12 13 ->= 24 29 12 24 16 7 3 9 10 11 31 , 11 20 14 4 ->= 11 20 14 9 10 14 6 26 33 8 4 , 12 13 23 23 ->= 24 35 35 16 26 26 7 10 24 29 13 , 11 20 21 1 23 ->= 21 10 24 18 3 8 6 33 8 9 1 , 14 34 29 12 24 25 ->= 14 19 14 34 16 7 3 19 14 8 4 , 12 13 23 23 30 25 ->= 12 13 32 21 10 21 15 29 13 30 25 , 12 11 31 23 23 23 ->= 24 16 17 16 33 8 34 25 2 0 1 , 11 20 13 32 21 1 30 25 ->= 11 17 22 4 32 14 6 33 19 14 4 , 21 1 2 3 -> 14 4 5 6 7 3 8 9 10 11 33 , 12 12 13 5 -> 12 12 14 9 15 16 17 18 10 13 5 , 14 19 11 20 14 -> 14 19 21 3 8 9 15 16 17 22 8 , 14 19 13 5 8 -> 14 8 8 9 10 14 19 14 19 14 8 , 13 23 23 23 5 -> 21 3 8 6 17 18 10 12 24 25 5 , 13 23 23 23 5 -> 13 2 3 6 26 26 20 12 14 4 5 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33 8 34 18 3 , 12 13 28 7 27 33 8 -> 14 6 7 15 16 26 17 35 35 29 14 , 24 22 19 13 2 3 8 -> 24 22 6 7 27 33 9 3 9 3 8 , 24 22 19 13 32 13 5 -> 12 21 3 8 19 14 8 8 8 4 5 , 12 21 1 28 31 23 5 -> 14 9 0 10 21 3 6 20 24 35 22 , 13 2 15 18 1 23 5 -> 13 28 33 34 35 16 33 34 22 6 33 , 11 7 27 31 23 23 5 -> 14 9 0 27 33 8 8 34 16 31 5 , 12 13 2 1 5 19 11 33 -> 24 25 32 24 25 30 16 17 29 11 33 , 13 23 23 2 27 31 28 33 -> 13 23 32 24 35 29 21 15 16 31 5 , 12 21 27 31 28 20 21 3 -> 24 22 4 28 17 16 7 10 12 21 3 , 11 31 23 28 33 34 18 3 -> 11 31 2 10 11 33 9 10 13 32 14 , 11 33 6 31 23 23 2 3 -> 11 7 27 20 11 20 12 14 8 6 33 , 14 4 23 23 23 32 14 8 -> 14 4 28 20 14 4 2 3 6 17 22 , 21 27 20 12 13 28 33 8 -> 21 27 31 5 6 26 26 26 17 29 14 , 13 28 20 12 13 28 33 8 -> 13 5 6 17 25 2 1 32 21 3 8 , 12 13 32 13 2 15 22 8 -> 14 9 15 25 28 20 12 14 8 8 8 , 24 35 29 13 23 30 22 8 -> 24 16 31 5 6 20 12 11 17 22 8 , 21 1 23 2 1 23 5 8 -> 14 6 33 34 18 27 20 14 6 20 14 , 21 3 19 13 23 23 5 8 -> 21 15 18 15 29 24 18 0 0 10 14 , 14 4 2 1 23 32 13 5 -> 14 9 15 16 26 20 13 23 2 1 5 , 21 10 12 13 23 30 25 5 -> 21 10 21 27 20 11 7 3 8 6 33 , 12 21 1 23 23 2 1 5 -> 12 13 23 23 30 25 5 9 3 4 5 , 21 1 30 18 1 5 4 5 -> 13 2 10 24 22 6 26 7 3 4 5 , 11 20 13 23 32 13 23 5 -> 11 31 30 16 17 22 4 5 9 15 22 , 21 1 23 23 32 13 23 5 -> 21 0 0 15 16 20 14 8 19 13 5 , 12 13 2 1 30 25 23 5 -> 12 21 0 15 18 10 14 19 24 25 5 , 24 22 19 21 1 23 23 5 -> 24 22 8 9 3 4 28 17 25 23 5 , 12 12 12 14 ->= 24 35 18 0 15 22 8 9 15 16 33 , 24 29 12 14 ->= 24 29 12 24 16 7 3 9 10 11 33 , 11 20 14 8 ->= 11 20 14 9 10 14 6 26 33 8 8 , 12 13 23 5 ->= 24 35 35 16 26 26 7 10 24 29 14 , 11 20 21 1 5 ->= 21 10 24 18 3 8 6 33 8 9 3 , 14 34 29 12 24 22 ->= 14 19 14 34 16 7 3 19 14 8 8 , 12 13 23 23 30 22 ->= 12 13 32 21 10 21 15 29 13 30 22 , 12 11 31 23 23 5 ->= 24 16 17 16 33 8 34 25 2 0 3 , 11 20 13 32 21 1 30 22 ->= 11 17 22 4 32 14 6 33 19 14 8 , 21 1 2 27 -> 14 4 5 6 7 3 8 9 10 11 26 , 12 12 13 28 -> 12 12 14 9 15 16 17 18 10 13 28 , 14 19 11 20 11 -> 14 19 21 3 8 9 15 16 17 22 6 , 14 19 13 5 6 -> 14 8 8 9 10 14 19 14 19 14 6 , 13 23 23 23 28 -> 21 3 8 6 17 18 10 12 24 25 28 , 13 23 23 23 28 -> 13 2 3 6 26 26 20 12 14 4 28 , 21 27 7 1 28 26 -> 24 16 7 15 29 24 22 8 9 27 26 , 12 13 23 2 15 16 -> 12 11 20 24 16 17 22 6 20 14 6 , 13 23 23 23 30 16 -> 13 28 17 18 10 24 16 31 32 24 16 , 12 12 12 11 33 6 -> 24 22 34 16 31 32 11 33 6 33 6 , 21 1 23 28 33 6 -> 24 16 31 30 18 10 21 15 16 17 16 , 13 23 28 7 3 6 -> 13 28 26 17 18 15 16 7 10 14 6 , 24 22 34 29 13 28 -> 24 22 9 10 12 21 15 16 17 25 28 , 11 31 28 7 1 28 -> 11 31 28 20 21 10 11 26 17 18 27 , 24 29 21 1 23 28 -> 12 12 24 16 17 25 5 9 15 18 27 , 14 4 23 23 23 28 -> 14 9 10 14 19 12 14 4 5 9 27 , 14 19 11 31 28 20 11 -> 14 19 21 3 6 20 14 19 24 18 27 , 12 13 28 31 28 20 11 -> 12 14 6 20 13 23 30 22 8 8 6 , 11 20 21 1 28 20 11 -> 11 7 10 14 6 26 26 31 5 8 6 , 13 32 21 27 7 10 11 -> 21 15 25 32 14 8 9 0 3 8 6 , 21 1 23 23 23 28 26 -> 14 4 30 29 12 14 6 31 30 16 26 , 11 33 9 1 32 24 16 -> 11 17 16 20 21 0 10 14 9 15 16 , 13 2 27 20 14 34 16 -> 21 3 6 7 10 24 29 24 18 15 16 , 13 23 23 5 4 30 16 -> 13 32 14 8 8 34 16 17 22 34 16 , 13 23 28 7 1 2 27 -> 14 34 29 14 6 26 33 8 34 18 27 , 12 13 28 7 27 33 6 -> 14 6 7 15 16 26 17 35 35 29 11 , 24 22 19 13 2 3 6 -> 24 22 6 7 27 33 9 3 9 3 6 , 24 22 19 13 32 13 28 -> 12 21 3 8 19 14 8 8 8 4 28 , 12 21 1 28 31 23 28 -> 14 9 0 10 21 3 6 20 24 35 16 , 13 2 15 18 1 23 28 -> 13 28 33 34 35 16 33 34 22 6 26 , 11 7 27 31 23 23 28 -> 14 9 0 27 33 8 8 34 16 31 28 , 12 13 2 1 5 19 11 26 -> 24 25 32 24 25 30 16 17 29 11 26 , 13 23 23 2 27 31 28 26 -> 13 23 32 24 35 29 21 15 16 31 28 , 12 21 27 31 28 20 21 27 -> 24 22 4 28 17 16 7 10 12 21 27 , 11 31 23 28 33 34 18 27 -> 11 31 2 10 11 33 9 10 13 32 11 , 11 33 6 31 23 23 2 27 -> 11 7 27 20 11 20 12 14 8 6 26 , 14 4 23 23 23 32 14 6 -> 14 4 28 20 14 4 2 3 6 17 16 , 21 27 20 12 13 28 33 6 -> 21 27 31 5 6 26 26 26 17 29 11 , 13 28 20 12 13 28 33 6 -> 13 5 6 17 25 2 1 32 21 3 6 , 12 13 32 13 2 15 22 6 -> 14 9 15 25 28 20 12 14 8 8 6 , 24 35 29 13 23 30 22 6 -> 24 16 31 5 6 20 12 11 17 22 6 , 21 1 23 2 1 23 5 6 -> 14 6 33 34 18 27 20 14 6 20 11 , 21 3 19 13 23 23 5 6 -> 21 15 18 15 29 24 18 0 0 10 11 , 14 4 2 1 23 32 13 28 -> 14 9 15 16 26 20 13 23 2 1 28 , 21 10 12 13 23 30 25 28 -> 21 10 21 27 20 11 7 3 8 6 26 , 12 21 1 23 23 2 1 28 -> 12 13 23 23 30 25 5 9 3 4 28 , 21 1 30 18 1 5 4 28 -> 13 2 10 24 22 6 26 7 3 4 28 , 11 20 13 23 32 13 23 28 -> 11 31 30 16 17 22 4 5 9 15 16 , 21 1 23 23 32 13 23 28 -> 21 0 0 15 16 20 14 8 19 13 28 , 12 13 2 1 30 25 23 28 -> 12 21 0 15 18 10 14 19 24 25 28 , 24 22 19 21 1 23 23 28 -> 24 22 8 9 3 4 28 17 25 23 28 , 12 12 12 11 ->= 24 35 18 0 15 22 8 9 15 16 26 , 24 29 12 11 ->= 24 29 12 24 16 7 3 9 10 11 26 , 11 20 14 6 ->= 11 20 14 9 10 14 6 26 33 8 6 , 12 13 23 28 ->= 24 35 35 16 26 26 7 10 24 29 11 , 11 20 21 1 28 ->= 21 10 24 18 3 8 6 33 8 9 27 , 14 34 29 12 24 16 ->= 14 19 14 34 16 7 3 19 14 8 6 , 12 13 23 23 30 16 ->= 12 13 32 21 10 21 15 29 13 30 16 , 12 11 31 23 23 28 ->= 24 16 17 16 33 8 34 25 2 0 27 , 11 20 13 32 21 1 30 16 ->= 11 17 22 4 32 14 6 33 19 14 6 , 21 1 2 10 -> 14 4 5 6 7 3 8 9 10 11 20 , 12 12 13 32 -> 12 12 14 9 15 16 17 18 10 13 32 , 14 19 11 20 12 -> 14 19 21 3 8 9 15 16 17 22 19 , 14 19 13 5 19 -> 14 8 8 9 10 14 19 14 19 14 19 , 13 23 23 23 32 -> 21 3 8 6 17 18 10 12 24 25 32 , 13 23 23 23 32 -> 13 2 3 6 26 26 20 12 14 4 32 , 21 27 7 1 28 20 -> 24 16 7 15 29 24 22 8 9 27 20 , 12 13 23 2 15 29 -> 12 11 20 24 16 17 22 6 20 14 19 , 13 23 23 23 30 29 -> 13 28 17 18 10 24 16 31 32 24 29 , 12 12 12 11 33 19 -> 24 22 34 16 31 32 11 33 6 33 19 , 21 1 23 28 33 19 -> 24 16 31 30 18 10 21 15 16 17 29 , 13 23 28 7 3 19 -> 13 28 26 17 18 15 16 7 10 14 19 , 24 22 34 29 13 32 -> 24 22 9 10 12 21 15 16 17 25 32 , 11 31 28 7 1 32 -> 11 31 28 20 21 10 11 26 17 18 10 , 24 29 21 1 23 32 -> 12 12 24 16 17 25 5 9 15 18 10 , 14 4 23 23 23 32 -> 14 9 10 14 19 12 14 4 5 9 10 , 14 19 11 31 28 20 12 -> 14 19 21 3 6 20 14 19 24 18 10 , 12 13 28 31 28 20 12 -> 12 14 6 20 13 23 30 22 8 8 19 , 11 20 21 1 28 20 12 -> 11 7 10 14 6 26 26 31 5 8 19 , 13 32 21 27 7 10 12 -> 21 15 25 32 14 8 9 0 3 8 19 , 21 1 23 23 23 28 20 -> 14 4 30 29 12 14 6 31 30 16 20 , 11 33 9 1 32 24 29 -> 11 17 16 20 21 0 10 14 9 15 29 , 13 2 27 20 14 34 29 -> 21 3 6 7 10 24 29 24 18 15 29 , 13 23 23 5 4 30 29 -> 13 32 14 8 8 34 16 17 22 34 29 , 13 23 28 7 1 2 10 -> 14 34 29 14 6 26 33 8 34 18 10 , 12 13 28 7 27 33 19 -> 14 6 7 15 16 26 17 35 35 29 12 , 24 22 19 13 2 3 19 -> 24 22 6 7 27 33 9 3 9 3 19 , 24 22 19 13 32 13 32 -> 12 21 3 8 19 14 8 8 8 4 32 , 12 21 1 28 31 23 32 -> 14 9 0 10 21 3 6 20 24 35 29 , 13 2 15 18 1 23 32 -> 13 28 33 34 35 16 33 34 22 6 20 , 11 7 27 31 23 23 32 -> 14 9 0 27 33 8 8 34 16 31 32 , 12 13 2 1 5 19 11 20 -> 24 25 32 24 25 30 16 17 29 11 20 , 13 23 23 2 27 31 28 20 -> 13 23 32 24 35 29 21 15 16 31 32 , 12 21 27 31 28 20 21 10 -> 24 22 4 28 17 16 7 10 12 21 10 , 11 31 23 28 33 34 18 10 -> 11 31 2 10 11 33 9 10 13 32 12 , 11 33 6 31 23 23 2 10 -> 11 7 27 20 11 20 12 14 8 6 20 , 14 4 23 23 23 32 14 19 -> 14 4 28 20 14 4 2 3 6 17 29 , 21 27 20 12 13 28 33 19 -> 21 27 31 5 6 26 26 26 17 29 12 , 13 28 20 12 13 28 33 19 -> 13 5 6 17 25 2 1 32 21 3 19 , 12 13 32 13 2 15 22 19 -> 14 9 15 25 28 20 12 14 8 8 19 , 24 35 29 13 23 30 22 19 -> 24 16 31 5 6 20 12 11 17 22 19 , 21 1 23 2 1 23 5 19 -> 14 6 33 34 18 27 20 14 6 20 12 , 21 3 19 13 23 23 5 19 -> 21 15 18 15 29 24 18 0 0 10 12 , 14 4 2 1 23 32 13 32 -> 14 9 15 16 26 20 13 23 2 1 32 , 21 10 12 13 23 30 25 32 -> 21 10 21 27 20 11 7 3 8 6 20 , 12 21 1 23 23 2 1 32 -> 12 13 23 23 30 25 5 9 3 4 32 , 21 1 30 18 1 5 4 32 -> 13 2 10 24 22 6 26 7 3 4 32 , 11 20 13 23 32 13 23 32 -> 11 31 30 16 17 22 4 5 9 15 29 , 21 1 23 23 32 13 23 32 -> 21 0 0 15 16 20 14 8 19 13 32 , 12 13 2 1 30 25 23 32 -> 12 21 0 15 18 10 14 19 24 25 32 , 24 22 19 21 1 23 23 32 -> 24 22 8 9 3 4 28 17 25 23 32 , 12 12 12 12 ->= 24 35 18 0 15 22 8 9 15 16 20 , 24 29 12 12 ->= 24 29 12 24 16 7 3 9 10 11 20 , 11 20 14 19 ->= 11 20 14 9 10 14 6 26 33 8 19 , 12 13 23 32 ->= 24 35 35 16 26 26 7 10 24 29 12 , 11 20 21 1 32 ->= 21 10 24 18 3 8 6 33 8 9 10 , 14 34 29 12 24 29 ->= 14 19 14 34 16 7 3 19 14 8 19 , 12 13 23 23 30 29 ->= 12 13 32 21 10 21 15 29 13 30 29 , 12 11 31 23 23 32 ->= 24 16 17 16 33 8 34 25 2 0 10 , 11 20 13 32 21 1 30 29 ->= 11 17 22 4 32 14 6 33 19 14 19 , 21 1 2 15 -> 14 4 5 6 7 3 8 9 10 11 17 , 12 12 13 30 -> 12 12 14 9 15 16 17 18 10 13 30 , 14 19 11 20 24 -> 14 19 21 3 8 9 15 16 17 22 34 , 14 19 13 5 34 -> 14 8 8 9 10 14 19 14 19 14 34 , 13 23 23 23 30 -> 21 3 8 6 17 18 10 12 24 25 30 , 13 23 23 23 30 -> 13 2 3 6 26 26 20 12 14 4 30 , 21 27 7 1 28 17 -> 24 16 7 15 29 24 22 8 9 27 17 , 12 13 23 2 15 35 -> 12 11 20 24 16 17 22 6 20 14 34 , 13 23 23 23 30 35 -> 13 28 17 18 10 24 16 31 32 24 35 , 12 12 12 11 33 34 -> 24 22 34 16 31 32 11 33 6 33 34 , 21 1 23 28 33 34 -> 24 16 31 30 18 10 21 15 16 17 35 , 13 23 28 7 3 34 -> 13 28 26 17 18 15 16 7 10 14 34 , 24 22 34 29 13 30 -> 24 22 9 10 12 21 15 16 17 25 30 , 11 31 28 7 1 30 -> 11 31 28 20 21 10 11 26 17 18 15 , 24 29 21 1 23 30 -> 12 12 24 16 17 25 5 9 15 18 15 , 14 4 23 23 23 30 -> 14 9 10 14 19 12 14 4 5 9 15 , 14 19 11 31 28 20 24 -> 14 19 21 3 6 20 14 19 24 18 15 , 12 13 28 31 28 20 24 -> 12 14 6 20 13 23 30 22 8 8 34 , 11 20 21 1 28 20 24 -> 11 7 10 14 6 26 26 31 5 8 34 , 13 32 21 27 7 10 24 -> 21 15 25 32 14 8 9 0 3 8 34 , 21 1 23 23 23 28 17 -> 14 4 30 29 12 14 6 31 30 16 17 , 11 33 9 1 32 24 35 -> 11 17 16 20 21 0 10 14 9 15 35 , 13 2 27 20 14 34 35 -> 21 3 6 7 10 24 29 24 18 15 35 , 13 23 23 5 4 30 35 -> 13 32 14 8 8 34 16 17 22 34 35 , 13 23 28 7 1 2 15 -> 14 34 29 14 6 26 33 8 34 18 15 , 12 13 28 7 27 33 34 -> 14 6 7 15 16 26 17 35 35 29 24 , 24 22 19 13 2 3 34 -> 24 22 6 7 27 33 9 3 9 3 34 , 24 22 19 13 32 13 30 -> 12 21 3 8 19 14 8 8 8 4 30 , 12 21 1 28 31 23 30 -> 14 9 0 10 21 3 6 20 24 35 35 , 13 2 15 18 1 23 30 -> 13 28 33 34 35 16 33 34 22 6 17 , 11 7 27 31 23 23 30 -> 14 9 0 27 33 8 8 34 16 31 30 , 12 13 2 1 5 19 11 17 -> 24 25 32 24 25 30 16 17 29 11 17 , 13 23 23 2 27 31 28 17 -> 13 23 32 24 35 29 21 15 16 31 30 , 12 21 27 31 28 20 21 15 -> 24 22 4 28 17 16 7 10 12 21 15 , 11 31 23 28 33 34 18 15 -> 11 31 2 10 11 33 9 10 13 32 24 , 11 33 6 31 23 23 2 15 -> 11 7 27 20 11 20 12 14 8 6 17 , 14 4 23 23 23 32 14 34 -> 14 4 28 20 14 4 2 3 6 17 35 , 21 27 20 12 13 28 33 34 -> 21 27 31 5 6 26 26 26 17 29 24 , 13 28 20 12 13 28 33 34 -> 13 5 6 17 25 2 1 32 21 3 34 , 12 13 32 13 2 15 22 34 -> 14 9 15 25 28 20 12 14 8 8 34 , 24 35 29 13 23 30 22 34 -> 24 16 31 5 6 20 12 11 17 22 34 , 21 1 23 2 1 23 5 34 -> 14 6 33 34 18 27 20 14 6 20 24 , 21 3 19 13 23 23 5 34 -> 21 15 18 15 29 24 18 0 0 10 24 , 14 4 2 1 23 32 13 30 -> 14 9 15 16 26 20 13 23 2 1 30 , 21 10 12 13 23 30 25 30 -> 21 10 21 27 20 11 7 3 8 6 17 , 12 21 1 23 23 2 1 30 -> 12 13 23 23 30 25 5 9 3 4 30 , 21 1 30 18 1 5 4 30 -> 13 2 10 24 22 6 26 7 3 4 30 , 11 20 13 23 32 13 23 30 -> 11 31 30 16 17 22 4 5 9 15 35 , 21 1 23 23 32 13 23 30 -> 21 0 0 15 16 20 14 8 19 13 30 , 12 13 2 1 30 25 23 30 -> 12 21 0 15 18 10 14 19 24 25 30 , 24 22 19 21 1 23 23 30 -> 24 22 8 9 3 4 28 17 25 23 30 , 12 12 12 24 ->= 24 35 18 0 15 22 8 9 15 16 17 , 24 29 12 24 ->= 24 29 12 24 16 7 3 9 10 11 17 , 11 20 14 34 ->= 11 20 14 9 10 14 6 26 33 8 34 , 12 13 23 30 ->= 24 35 35 16 26 26 7 10 24 29 24 , 11 20 21 1 30 ->= 21 10 24 18 3 8 6 33 8 9 15 , 14 34 29 12 24 35 ->= 14 19 14 34 16 7 3 19 14 8 34 , 12 13 23 23 30 35 ->= 12 13 32 21 10 21 15 29 13 30 35 , 12 11 31 23 23 30 ->= 24 16 17 16 33 8 34 25 2 0 15 , 11 20 13 32 21 1 30 35 ->= 11 17 22 4 32 14 6 33 19 14 34 , 18 1 2 0 -> 22 4 5 6 7 3 8 9 10 11 7 , 29 12 13 2 -> 29 12 14 9 15 16 17 18 10 13 2 , 22 19 11 20 21 -> 22 19 21 3 8 9 15 16 17 22 9 , 22 19 13 5 9 -> 22 8 8 9 10 14 19 14 19 14 9 , 25 23 23 23 2 -> 18 3 8 6 17 18 10 12 24 25 2 , 25 23 23 23 2 -> 25 2 3 6 26 26 20 12 14 4 2 , 18 27 7 1 28 7 -> 35 16 7 15 29 24 22 8 9 27 7 , 29 13 23 2 15 18 -> 29 11 20 24 16 17 22 6 20 14 9 , 25 23 23 23 30 18 -> 25 28 17 18 10 24 16 31 32 24 18 , 29 12 12 11 33 9 -> 35 22 34 16 31 32 11 33 6 33 9 , 18 1 23 28 33 9 -> 35 16 31 30 18 10 21 15 16 17 18 , 25 23 28 7 3 9 -> 25 28 26 17 18 15 16 7 10 14 9 , 35 22 34 29 13 2 -> 35 22 9 10 12 21 15 16 17 25 2 , 16 31 28 7 1 2 -> 16 31 28 20 21 10 11 26 17 18 0 , 35 29 21 1 23 2 -> 29 12 24 16 17 25 5 9 15 18 0 , 22 4 23 23 23 2 -> 22 9 10 14 19 12 14 4 5 9 0 , 22 19 11 31 28 20 21 -> 22 19 21 3 6 20 14 19 24 18 0 , 29 13 28 31 28 20 21 -> 29 14 6 20 13 23 30 22 8 8 9 , 16 20 21 1 28 20 21 -> 16 7 10 14 6 26 26 31 5 8 9 , 25 32 21 27 7 10 21 -> 18 15 25 32 14 8 9 0 3 8 9 , 18 1 23 23 23 28 7 -> 22 4 30 29 12 14 6 31 30 16 7 , 16 33 9 1 32 24 18 -> 16 17 16 20 21 0 10 14 9 15 18 , 25 2 27 20 14 34 18 -> 18 3 6 7 10 24 29 24 18 15 18 , 25 23 23 5 4 30 18 -> 25 32 14 8 8 34 16 17 22 34 18 , 25 23 28 7 1 2 0 -> 22 34 29 14 6 26 33 8 34 18 0 , 29 13 28 7 27 33 9 -> 22 6 7 15 16 26 17 35 35 29 21 , 35 22 19 13 2 3 9 -> 35 22 6 7 27 33 9 3 9 3 9 , 35 22 19 13 32 13 2 -> 29 21 3 8 19 14 8 8 8 4 2 , 29 21 1 28 31 23 2 -> 22 9 0 10 21 3 6 20 24 35 18 , 25 2 15 18 1 23 2 -> 25 28 33 34 35 16 33 34 22 6 7 , 16 7 27 31 23 23 2 -> 22 9 0 27 33 8 8 34 16 31 2 , 29 13 2 1 5 19 11 7 -> 35 25 32 24 25 30 16 17 29 11 7 , 25 23 23 2 27 31 28 7 -> 25 23 32 24 35 29 21 15 16 31 2 , 29 21 27 31 28 20 21 0 -> 35 22 4 28 17 16 7 10 12 21 0 , 16 31 23 28 33 34 18 0 -> 16 31 2 10 11 33 9 10 13 32 21 , 16 33 6 31 23 23 2 0 -> 16 7 27 20 11 20 12 14 8 6 7 , 22 4 23 23 23 32 14 9 -> 22 4 28 20 14 4 2 3 6 17 18 , 18 27 20 12 13 28 33 9 -> 18 27 31 5 6 26 26 26 17 29 21 , 25 28 20 12 13 28 33 9 -> 25 5 6 17 25 2 1 32 21 3 9 , 29 13 32 13 2 15 22 9 -> 22 9 15 25 28 20 12 14 8 8 9 , 35 35 29 13 23 30 22 9 -> 35 16 31 5 6 20 12 11 17 22 9 , 18 1 23 2 1 23 5 9 -> 22 6 33 34 18 27 20 14 6 20 21 , 18 3 19 13 23 23 5 9 -> 18 15 18 15 29 24 18 0 0 10 21 , 22 4 2 1 23 32 13 2 -> 22 9 15 16 26 20 13 23 2 1 2 , 18 10 12 13 23 30 25 2 -> 18 10 21 27 20 11 7 3 8 6 7 , 29 21 1 23 23 2 1 2 -> 29 13 23 23 30 25 5 9 3 4 2 , 18 1 30 18 1 5 4 2 -> 25 2 10 24 22 6 26 7 3 4 2 , 16 20 13 23 32 13 23 2 -> 16 31 30 16 17 22 4 5 9 15 18 , 18 1 23 23 32 13 23 2 -> 18 0 0 15 16 20 14 8 19 13 2 , 29 13 2 1 30 25 23 2 -> 29 21 0 15 18 10 14 19 24 25 2 , 35 22 19 21 1 23 23 2 -> 35 22 8 9 3 4 28 17 25 23 2 , 29 12 12 21 ->= 35 35 18 0 15 22 8 9 15 16 7 , 35 29 12 21 ->= 35 29 12 24 16 7 3 9 10 11 7 , 16 20 14 9 ->= 16 20 14 9 10 14 6 26 33 8 9 , 29 13 23 2 ->= 35 35 35 16 26 26 7 10 24 29 21 , 16 20 21 1 2 ->= 18 10 24 18 3 8 6 33 8 9 0 , 22 34 29 12 24 18 ->= 22 19 14 34 16 7 3 19 14 8 9 , 29 13 23 23 30 18 ->= 29 13 32 21 10 21 15 29 13 30 18 , 29 11 31 23 23 2 ->= 35 16 17 16 33 8 34 25 2 0 0 , 16 20 13 32 21 1 30 18 ->= 16 17 22 4 32 14 6 33 19 14 9 , 18 1 2 1 -> 22 4 5 6 7 3 8 9 10 11 31 , 29 12 13 23 -> 29 12 14 9 15 16 17 18 10 13 23 , 22 19 11 20 13 -> 22 19 21 3 8 9 15 16 17 22 4 , 22 19 13 5 4 -> 22 8 8 9 10 14 19 14 19 14 4 , 25 23 23 23 23 -> 18 3 8 6 17 18 10 12 24 25 23 , 25 23 23 23 23 -> 25 2 3 6 26 26 20 12 14 4 23 , 18 27 7 1 28 31 -> 35 16 7 15 29 24 22 8 9 27 31 , 29 13 23 2 15 25 -> 29 11 20 24 16 17 22 6 20 14 4 , 25 23 23 23 30 25 -> 25 28 17 18 10 24 16 31 32 24 25 , 29 12 12 11 33 4 -> 35 22 34 16 31 32 11 33 6 33 4 , 18 1 23 28 33 4 -> 35 16 31 30 18 10 21 15 16 17 25 , 25 23 28 7 3 4 -> 25 28 26 17 18 15 16 7 10 14 4 , 35 22 34 29 13 23 -> 35 22 9 10 12 21 15 16 17 25 23 , 16 31 28 7 1 23 -> 16 31 28 20 21 10 11 26 17 18 1 , 35 29 21 1 23 23 -> 29 12 24 16 17 25 5 9 15 18 1 , 22 4 23 23 23 23 -> 22 9 10 14 19 12 14 4 5 9 1 , 22 19 11 31 28 20 13 -> 22 19 21 3 6 20 14 19 24 18 1 , 29 13 28 31 28 20 13 -> 29 14 6 20 13 23 30 22 8 8 4 , 16 20 21 1 28 20 13 -> 16 7 10 14 6 26 26 31 5 8 4 , 25 32 21 27 7 10 13 -> 18 15 25 32 14 8 9 0 3 8 4 , 18 1 23 23 23 28 31 -> 22 4 30 29 12 14 6 31 30 16 31 , 16 33 9 1 32 24 25 -> 16 17 16 20 21 0 10 14 9 15 25 , 25 2 27 20 14 34 25 -> 18 3 6 7 10 24 29 24 18 15 25 , 25 23 23 5 4 30 25 -> 25 32 14 8 8 34 16 17 22 34 25 , 25 23 28 7 1 2 1 -> 22 34 29 14 6 26 33 8 34 18 1 , 29 13 28 7 27 33 4 -> 22 6 7 15 16 26 17 35 35 29 13 , 35 22 19 13 2 3 4 -> 35 22 6 7 27 33 9 3 9 3 4 , 35 22 19 13 32 13 23 -> 29 21 3 8 19 14 8 8 8 4 23 , 29 21 1 28 31 23 23 -> 22 9 0 10 21 3 6 20 24 35 25 , 25 2 15 18 1 23 23 -> 25 28 33 34 35 16 33 34 22 6 31 , 16 7 27 31 23 23 23 -> 22 9 0 27 33 8 8 34 16 31 23 , 29 13 2 1 5 19 11 31 -> 35 25 32 24 25 30 16 17 29 11 31 , 25 23 23 2 27 31 28 31 -> 25 23 32 24 35 29 21 15 16 31 23 , 29 21 27 31 28 20 21 1 -> 35 22 4 28 17 16 7 10 12 21 1 , 16 31 23 28 33 34 18 1 -> 16 31 2 10 11 33 9 10 13 32 13 , 16 33 6 31 23 23 2 1 -> 16 7 27 20 11 20 12 14 8 6 31 , 22 4 23 23 23 32 14 4 -> 22 4 28 20 14 4 2 3 6 17 25 , 18 27 20 12 13 28 33 4 -> 18 27 31 5 6 26 26 26 17 29 13 , 25 28 20 12 13 28 33 4 -> 25 5 6 17 25 2 1 32 21 3 4 , 29 13 32 13 2 15 22 4 -> 22 9 15 25 28 20 12 14 8 8 4 , 35 35 29 13 23 30 22 4 -> 35 16 31 5 6 20 12 11 17 22 4 , 18 1 23 2 1 23 5 4 -> 22 6 33 34 18 27 20 14 6 20 13 , 18 3 19 13 23 23 5 4 -> 18 15 18 15 29 24 18 0 0 10 13 , 22 4 2 1 23 32 13 23 -> 22 9 15 16 26 20 13 23 2 1 23 , 18 10 12 13 23 30 25 23 -> 18 10 21 27 20 11 7 3 8 6 31 , 29 21 1 23 23 2 1 23 -> 29 13 23 23 30 25 5 9 3 4 23 , 18 1 30 18 1 5 4 23 -> 25 2 10 24 22 6 26 7 3 4 23 , 16 20 13 23 32 13 23 23 -> 16 31 30 16 17 22 4 5 9 15 25 , 18 1 23 23 32 13 23 23 -> 18 0 0 15 16 20 14 8 19 13 23 , 29 13 2 1 30 25 23 23 -> 29 21 0 15 18 10 14 19 24 25 23 , 35 22 19 21 1 23 23 23 -> 35 22 8 9 3 4 28 17 25 23 23 , 29 12 12 13 ->= 35 35 18 0 15 22 8 9 15 16 31 , 35 29 12 13 ->= 35 29 12 24 16 7 3 9 10 11 31 , 16 20 14 4 ->= 16 20 14 9 10 14 6 26 33 8 4 , 29 13 23 23 ->= 35 35 35 16 26 26 7 10 24 29 13 , 16 20 21 1 23 ->= 18 10 24 18 3 8 6 33 8 9 1 , 22 34 29 12 24 25 ->= 22 19 14 34 16 7 3 19 14 8 4 , 29 13 23 23 30 25 ->= 29 13 32 21 10 21 15 29 13 30 25 , 29 11 31 23 23 23 ->= 35 16 17 16 33 8 34 25 2 0 1 , 16 20 13 32 21 1 30 25 ->= 16 17 22 4 32 14 6 33 19 14 4 , 18 1 2 3 -> 22 4 5 6 7 3 8 9 10 11 33 , 29 12 13 5 -> 29 12 14 9 15 16 17 18 10 13 5 , 22 19 11 20 14 -> 22 19 21 3 8 9 15 16 17 22 8 , 22 19 13 5 8 -> 22 8 8 9 10 14 19 14 19 14 8 , 25 23 23 23 5 -> 18 3 8 6 17 18 10 12 24 25 5 , 25 23 23 23 5 -> 25 2 3 6 26 26 20 12 14 4 5 , 18 27 7 1 28 33 -> 35 16 7 15 29 24 22 8 9 27 33 , 29 13 23 2 15 22 -> 29 11 20 24 16 17 22 6 20 14 8 , 25 23 23 23 30 22 -> 25 28 17 18 10 24 16 31 32 24 22 , 29 12 12 11 33 8 -> 35 22 34 16 31 32 11 33 6 33 8 , 18 1 23 28 33 8 -> 35 16 31 30 18 10 21 15 16 17 22 , 25 23 28 7 3 8 -> 25 28 26 17 18 15 16 7 10 14 8 , 35 22 34 29 13 5 -> 35 22 9 10 12 21 15 16 17 25 5 , 16 31 28 7 1 5 -> 16 31 28 20 21 10 11 26 17 18 3 , 35 29 21 1 23 5 -> 29 12 24 16 17 25 5 9 15 18 3 , 22 4 23 23 23 5 -> 22 9 10 14 19 12 14 4 5 9 3 , 22 19 11 31 28 20 14 -> 22 19 21 3 6 20 14 19 24 18 3 , 29 13 28 31 28 20 14 -> 29 14 6 20 13 23 30 22 8 8 8 , 16 20 21 1 28 20 14 -> 16 7 10 14 6 26 26 31 5 8 8 , 25 32 21 27 7 10 14 -> 18 15 25 32 14 8 9 0 3 8 8 , 18 1 23 23 23 28 33 -> 22 4 30 29 12 14 6 31 30 16 33 , 16 33 9 1 32 24 22 -> 16 17 16 20 21 0 10 14 9 15 22 , 25 2 27 20 14 34 22 -> 18 3 6 7 10 24 29 24 18 15 22 , 25 23 23 5 4 30 22 -> 25 32 14 8 8 34 16 17 22 34 22 , 25 23 28 7 1 2 3 -> 22 34 29 14 6 26 33 8 34 18 3 , 29 13 28 7 27 33 8 -> 22 6 7 15 16 26 17 35 35 29 14 , 35 22 19 13 2 3 8 -> 35 22 6 7 27 33 9 3 9 3 8 , 35 22 19 13 32 13 5 -> 29 21 3 8 19 14 8 8 8 4 5 , 29 21 1 28 31 23 5 -> 22 9 0 10 21 3 6 20 24 35 22 , 25 2 15 18 1 23 5 -> 25 28 33 34 35 16 33 34 22 6 33 , 16 7 27 31 23 23 5 -> 22 9 0 27 33 8 8 34 16 31 5 , 29 13 2 1 5 19 11 33 -> 35 25 32 24 25 30 16 17 29 11 33 , 25 23 23 2 27 31 28 33 -> 25 23 32 24 35 29 21 15 16 31 5 , 29 21 27 31 28 20 21 3 -> 35 22 4 28 17 16 7 10 12 21 3 , 16 31 23 28 33 34 18 3 -> 16 31 2 10 11 33 9 10 13 32 14 , 16 33 6 31 23 23 2 3 -> 16 7 27 20 11 20 12 14 8 6 33 , 22 4 23 23 23 32 14 8 -> 22 4 28 20 14 4 2 3 6 17 22 , 18 27 20 12 13 28 33 8 -> 18 27 31 5 6 26 26 26 17 29 14 , 25 28 20 12 13 28 33 8 -> 25 5 6 17 25 2 1 32 21 3 8 , 29 13 32 13 2 15 22 8 -> 22 9 15 25 28 20 12 14 8 8 8 , 35 35 29 13 23 30 22 8 -> 35 16 31 5 6 20 12 11 17 22 8 , 18 1 23 2 1 23 5 8 -> 22 6 33 34 18 27 20 14 6 20 14 , 18 3 19 13 23 23 5 8 -> 18 15 18 15 29 24 18 0 0 10 14 , 22 4 2 1 23 32 13 5 -> 22 9 15 16 26 20 13 23 2 1 5 , 18 10 12 13 23 30 25 5 -> 18 10 21 27 20 11 7 3 8 6 33 , 29 21 1 23 23 2 1 5 -> 29 13 23 23 30 25 5 9 3 4 5 , 18 1 30 18 1 5 4 5 -> 25 2 10 24 22 6 26 7 3 4 5 , 16 20 13 23 32 13 23 5 -> 16 31 30 16 17 22 4 5 9 15 22 , 18 1 23 23 32 13 23 5 -> 18 0 0 15 16 20 14 8 19 13 5 , 29 13 2 1 30 25 23 5 -> 29 21 0 15 18 10 14 19 24 25 5 , 35 22 19 21 1 23 23 5 -> 35 22 8 9 3 4 28 17 25 23 5 , 29 12 12 14 ->= 35 35 18 0 15 22 8 9 15 16 33 , 35 29 12 14 ->= 35 29 12 24 16 7 3 9 10 11 33 , 16 20 14 8 ->= 16 20 14 9 10 14 6 26 33 8 8 , 29 13 23 5 ->= 35 35 35 16 26 26 7 10 24 29 14 , 16 20 21 1 5 ->= 18 10 24 18 3 8 6 33 8 9 3 , 22 34 29 12 24 22 ->= 22 19 14 34 16 7 3 19 14 8 8 , 29 13 23 23 30 22 ->= 29 13 32 21 10 21 15 29 13 30 22 , 29 11 31 23 23 5 ->= 35 16 17 16 33 8 34 25 2 0 3 , 16 20 13 32 21 1 30 22 ->= 16 17 22 4 32 14 6 33 19 14 8 , 18 1 2 27 -> 22 4 5 6 7 3 8 9 10 11 26 , 29 12 13 28 -> 29 12 14 9 15 16 17 18 10 13 28 , 22 19 11 20 11 -> 22 19 21 3 8 9 15 16 17 22 6 , 22 19 13 5 6 -> 22 8 8 9 10 14 19 14 19 14 6 , 25 23 23 23 28 -> 18 3 8 6 17 18 10 12 24 25 28 , 25 23 23 23 28 -> 25 2 3 6 26 26 20 12 14 4 28 , 18 27 7 1 28 26 -> 35 16 7 15 29 24 22 8 9 27 26 , 29 13 23 2 15 16 -> 29 11 20 24 16 17 22 6 20 14 6 , 25 23 23 23 30 16 -> 25 28 17 18 10 24 16 31 32 24 16 , 29 12 12 11 33 6 -> 35 22 34 16 31 32 11 33 6 33 6 , 18 1 23 28 33 6 -> 35 16 31 30 18 10 21 15 16 17 16 , 25 23 28 7 3 6 -> 25 28 26 17 18 15 16 7 10 14 6 , 35 22 34 29 13 28 -> 35 22 9 10 12 21 15 16 17 25 28 , 16 31 28 7 1 28 -> 16 31 28 20 21 10 11 26 17 18 27 , 35 29 21 1 23 28 -> 29 12 24 16 17 25 5 9 15 18 27 , 22 4 23 23 23 28 -> 22 9 10 14 19 12 14 4 5 9 27 , 22 19 11 31 28 20 11 -> 22 19 21 3 6 20 14 19 24 18 27 , 29 13 28 31 28 20 11 -> 29 14 6 20 13 23 30 22 8 8 6 , 16 20 21 1 28 20 11 -> 16 7 10 14 6 26 26 31 5 8 6 , 25 32 21 27 7 10 11 -> 18 15 25 32 14 8 9 0 3 8 6 , 18 1 23 23 23 28 26 -> 22 4 30 29 12 14 6 31 30 16 26 , 16 33 9 1 32 24 16 -> 16 17 16 20 21 0 10 14 9 15 16 , 25 2 27 20 14 34 16 -> 18 3 6 7 10 24 29 24 18 15 16 , 25 23 23 5 4 30 16 -> 25 32 14 8 8 34 16 17 22 34 16 , 25 23 28 7 1 2 27 -> 22 34 29 14 6 26 33 8 34 18 27 , 29 13 28 7 27 33 6 -> 22 6 7 15 16 26 17 35 35 29 11 , 35 22 19 13 2 3 6 -> 35 22 6 7 27 33 9 3 9 3 6 , 35 22 19 13 32 13 28 -> 29 21 3 8 19 14 8 8 8 4 28 , 29 21 1 28 31 23 28 -> 22 9 0 10 21 3 6 20 24 35 16 , 25 2 15 18 1 23 28 -> 25 28 33 34 35 16 33 34 22 6 26 , 16 7 27 31 23 23 28 -> 22 9 0 27 33 8 8 34 16 31 28 , 29 13 2 1 5 19 11 26 -> 35 25 32 24 25 30 16 17 29 11 26 , 25 23 23 2 27 31 28 26 -> 25 23 32 24 35 29 21 15 16 31 28 , 29 21 27 31 28 20 21 27 -> 35 22 4 28 17 16 7 10 12 21 27 , 16 31 23 28 33 34 18 27 -> 16 31 2 10 11 33 9 10 13 32 11 , 16 33 6 31 23 23 2 27 -> 16 7 27 20 11 20 12 14 8 6 26 , 22 4 23 23 23 32 14 6 -> 22 4 28 20 14 4 2 3 6 17 16 , 18 27 20 12 13 28 33 6 -> 18 27 31 5 6 26 26 26 17 29 11 , 25 28 20 12 13 28 33 6 -> 25 5 6 17 25 2 1 32 21 3 6 , 29 13 32 13 2 15 22 6 -> 22 9 15 25 28 20 12 14 8 8 6 , 35 35 29 13 23 30 22 6 -> 35 16 31 5 6 20 12 11 17 22 6 , 18 1 23 2 1 23 5 6 -> 22 6 33 34 18 27 20 14 6 20 11 , 18 3 19 13 23 23 5 6 -> 18 15 18 15 29 24 18 0 0 10 11 , 22 4 2 1 23 32 13 28 -> 22 9 15 16 26 20 13 23 2 1 28 , 18 10 12 13 23 30 25 28 -> 18 10 21 27 20 11 7 3 8 6 26 , 29 21 1 23 23 2 1 28 -> 29 13 23 23 30 25 5 9 3 4 28 , 18 1 30 18 1 5 4 28 -> 25 2 10 24 22 6 26 7 3 4 28 , 16 20 13 23 32 13 23 28 -> 16 31 30 16 17 22 4 5 9 15 16 , 18 1 23 23 32 13 23 28 -> 18 0 0 15 16 20 14 8 19 13 28 , 29 13 2 1 30 25 23 28 -> 29 21 0 15 18 10 14 19 24 25 28 , 35 22 19 21 1 23 23 28 -> 35 22 8 9 3 4 28 17 25 23 28 , 29 12 12 11 ->= 35 35 18 0 15 22 8 9 15 16 26 , 35 29 12 11 ->= 35 29 12 24 16 7 3 9 10 11 26 , 16 20 14 6 ->= 16 20 14 9 10 14 6 26 33 8 6 , 29 13 23 28 ->= 35 35 35 16 26 26 7 10 24 29 11 , 16 20 21 1 28 ->= 18 10 24 18 3 8 6 33 8 9 27 , 22 34 29 12 24 16 ->= 22 19 14 34 16 7 3 19 14 8 6 , 29 13 23 23 30 16 ->= 29 13 32 21 10 21 15 29 13 30 16 , 29 11 31 23 23 28 ->= 35 16 17 16 33 8 34 25 2 0 27 , 16 20 13 32 21 1 30 16 ->= 16 17 22 4 32 14 6 33 19 14 6 , 18 1 2 10 -> 22 4 5 6 7 3 8 9 10 11 20 , 29 12 13 32 -> 29 12 14 9 15 16 17 18 10 13 32 , 22 19 11 20 12 -> 22 19 21 3 8 9 15 16 17 22 19 , 22 19 13 5 19 -> 22 8 8 9 10 14 19 14 19 14 19 , 25 23 23 23 32 -> 18 3 8 6 17 18 10 12 24 25 32 , 25 23 23 23 32 -> 25 2 3 6 26 26 20 12 14 4 32 , 18 27 7 1 28 20 -> 35 16 7 15 29 24 22 8 9 27 20 , 29 13 23 2 15 29 -> 29 11 20 24 16 17 22 6 20 14 19 , 25 23 23 23 30 29 -> 25 28 17 18 10 24 16 31 32 24 29 , 29 12 12 11 33 19 -> 35 22 34 16 31 32 11 33 6 33 19 , 18 1 23 28 33 19 -> 35 16 31 30 18 10 21 15 16 17 29 , 25 23 28 7 3 19 -> 25 28 26 17 18 15 16 7 10 14 19 , 35 22 34 29 13 32 -> 35 22 9 10 12 21 15 16 17 25 32 , 16 31 28 7 1 32 -> 16 31 28 20 21 10 11 26 17 18 10 , 35 29 21 1 23 32 -> 29 12 24 16 17 25 5 9 15 18 10 , 22 4 23 23 23 32 -> 22 9 10 14 19 12 14 4 5 9 10 , 22 19 11 31 28 20 12 -> 22 19 21 3 6 20 14 19 24 18 10 , 29 13 28 31 28 20 12 -> 29 14 6 20 13 23 30 22 8 8 19 , 16 20 21 1 28 20 12 -> 16 7 10 14 6 26 26 31 5 8 19 , 25 32 21 27 7 10 12 -> 18 15 25 32 14 8 9 0 3 8 19 , 18 1 23 23 23 28 20 -> 22 4 30 29 12 14 6 31 30 16 20 , 16 33 9 1 32 24 29 -> 16 17 16 20 21 0 10 14 9 15 29 , 25 2 27 20 14 34 29 -> 18 3 6 7 10 24 29 24 18 15 29 , 25 23 23 5 4 30 29 -> 25 32 14 8 8 34 16 17 22 34 29 , 25 23 28 7 1 2 10 -> 22 34 29 14 6 26 33 8 34 18 10 , 29 13 28 7 27 33 19 -> 22 6 7 15 16 26 17 35 35 29 12 , 35 22 19 13 2 3 19 -> 35 22 6 7 27 33 9 3 9 3 19 , 35 22 19 13 32 13 32 -> 29 21 3 8 19 14 8 8 8 4 32 , 29 21 1 28 31 23 32 -> 22 9 0 10 21 3 6 20 24 35 29 , 25 2 15 18 1 23 32 -> 25 28 33 34 35 16 33 34 22 6 20 , 16 7 27 31 23 23 32 -> 22 9 0 27 33 8 8 34 16 31 32 , 29 13 2 1 5 19 11 20 -> 35 25 32 24 25 30 16 17 29 11 20 , 25 23 23 2 27 31 28 20 -> 25 23 32 24 35 29 21 15 16 31 32 , 29 21 27 31 28 20 21 10 -> 35 22 4 28 17 16 7 10 12 21 10 , 16 31 23 28 33 34 18 10 -> 16 31 2 10 11 33 9 10 13 32 12 , 16 33 6 31 23 23 2 10 -> 16 7 27 20 11 20 12 14 8 6 20 , 22 4 23 23 23 32 14 19 -> 22 4 28 20 14 4 2 3 6 17 29 , 18 27 20 12 13 28 33 19 -> 18 27 31 5 6 26 26 26 17 29 12 , 25 28 20 12 13 28 33 19 -> 25 5 6 17 25 2 1 32 21 3 19 , 29 13 32 13 2 15 22 19 -> 22 9 15 25 28 20 12 14 8 8 19 , 35 35 29 13 23 30 22 19 -> 35 16 31 5 6 20 12 11 17 22 19 , 18 1 23 2 1 23 5 19 -> 22 6 33 34 18 27 20 14 6 20 12 , 18 3 19 13 23 23 5 19 -> 18 15 18 15 29 24 18 0 0 10 12 , 22 4 2 1 23 32 13 32 -> 22 9 15 16 26 20 13 23 2 1 32 , 18 10 12 13 23 30 25 32 -> 18 10 21 27 20 11 7 3 8 6 20 , 29 21 1 23 23 2 1 32 -> 29 13 23 23 30 25 5 9 3 4 32 , 18 1 30 18 1 5 4 32 -> 25 2 10 24 22 6 26 7 3 4 32 , 16 20 13 23 32 13 23 32 -> 16 31 30 16 17 22 4 5 9 15 29 , 18 1 23 23 32 13 23 32 -> 18 0 0 15 16 20 14 8 19 13 32 , 29 13 2 1 30 25 23 32 -> 29 21 0 15 18 10 14 19 24 25 32 , 35 22 19 21 1 23 23 32 -> 35 22 8 9 3 4 28 17 25 23 32 , 29 12 12 12 ->= 35 35 18 0 15 22 8 9 15 16 20 , 35 29 12 12 ->= 35 29 12 24 16 7 3 9 10 11 20 , 16 20 14 19 ->= 16 20 14 9 10 14 6 26 33 8 19 , 29 13 23 32 ->= 35 35 35 16 26 26 7 10 24 29 12 , 16 20 21 1 32 ->= 18 10 24 18 3 8 6 33 8 9 10 , 22 34 29 12 24 29 ->= 22 19 14 34 16 7 3 19 14 8 19 , 29 13 23 23 30 29 ->= 29 13 32 21 10 21 15 29 13 30 29 , 29 11 31 23 23 32 ->= 35 16 17 16 33 8 34 25 2 0 10 , 16 20 13 32 21 1 30 29 ->= 16 17 22 4 32 14 6 33 19 14 19 , 18 1 2 15 -> 22 4 5 6 7 3 8 9 10 11 17 , 29 12 13 30 -> 29 12 14 9 15 16 17 18 10 13 30 , 22 19 11 20 24 -> 22 19 21 3 8 9 15 16 17 22 34 , 22 19 13 5 34 -> 22 8 8 9 10 14 19 14 19 14 34 , 25 23 23 23 30 -> 18 3 8 6 17 18 10 12 24 25 30 , 25 23 23 23 30 -> 25 2 3 6 26 26 20 12 14 4 30 , 18 27 7 1 28 17 -> 35 16 7 15 29 24 22 8 9 27 17 , 29 13 23 2 15 35 -> 29 11 20 24 16 17 22 6 20 14 34 , 25 23 23 23 30 35 -> 25 28 17 18 10 24 16 31 32 24 35 , 29 12 12 11 33 34 -> 35 22 34 16 31 32 11 33 6 33 34 , 18 1 23 28 33 34 -> 35 16 31 30 18 10 21 15 16 17 35 , 25 23 28 7 3 34 -> 25 28 26 17 18 15 16 7 10 14 34 , 35 22 34 29 13 30 -> 35 22 9 10 12 21 15 16 17 25 30 , 16 31 28 7 1 30 -> 16 31 28 20 21 10 11 26 17 18 15 , 35 29 21 1 23 30 -> 29 12 24 16 17 25 5 9 15 18 15 , 22 4 23 23 23 30 -> 22 9 10 14 19 12 14 4 5 9 15 , 22 19 11 31 28 20 24 -> 22 19 21 3 6 20 14 19 24 18 15 , 29 13 28 31 28 20 24 -> 29 14 6 20 13 23 30 22 8 8 34 , 16 20 21 1 28 20 24 -> 16 7 10 14 6 26 26 31 5 8 34 , 25 32 21 27 7 10 24 -> 18 15 25 32 14 8 9 0 3 8 34 , 18 1 23 23 23 28 17 -> 22 4 30 29 12 14 6 31 30 16 17 , 16 33 9 1 32 24 35 -> 16 17 16 20 21 0 10 14 9 15 35 , 25 2 27 20 14 34 35 -> 18 3 6 7 10 24 29 24 18 15 35 , 25 23 23 5 4 30 35 -> 25 32 14 8 8 34 16 17 22 34 35 , 25 23 28 7 1 2 15 -> 22 34 29 14 6 26 33 8 34 18 15 , 29 13 28 7 27 33 34 -> 22 6 7 15 16 26 17 35 35 29 24 , 35 22 19 13 2 3 34 -> 35 22 6 7 27 33 9 3 9 3 34 , 35 22 19 13 32 13 30 -> 29 21 3 8 19 14 8 8 8 4 30 , 29 21 1 28 31 23 30 -> 22 9 0 10 21 3 6 20 24 35 35 , 25 2 15 18 1 23 30 -> 25 28 33 34 35 16 33 34 22 6 17 , 16 7 27 31 23 23 30 -> 22 9 0 27 33 8 8 34 16 31 30 , 29 13 2 1 5 19 11 17 -> 35 25 32 24 25 30 16 17 29 11 17 , 25 23 23 2 27 31 28 17 -> 25 23 32 24 35 29 21 15 16 31 30 , 29 21 27 31 28 20 21 15 -> 35 22 4 28 17 16 7 10 12 21 15 , 16 31 23 28 33 34 18 15 -> 16 31 2 10 11 33 9 10 13 32 24 , 16 33 6 31 23 23 2 15 -> 16 7 27 20 11 20 12 14 8 6 17 , 22 4 23 23 23 32 14 34 -> 22 4 28 20 14 4 2 3 6 17 35 , 18 27 20 12 13 28 33 34 -> 18 27 31 5 6 26 26 26 17 29 24 , 25 28 20 12 13 28 33 34 -> 25 5 6 17 25 2 1 32 21 3 34 , 29 13 32 13 2 15 22 34 -> 22 9 15 25 28 20 12 14 8 8 34 , 35 35 29 13 23 30 22 34 -> 35 16 31 5 6 20 12 11 17 22 34 , 18 1 23 2 1 23 5 34 -> 22 6 33 34 18 27 20 14 6 20 24 , 18 3 19 13 23 23 5 34 -> 18 15 18 15 29 24 18 0 0 10 24 , 22 4 2 1 23 32 13 30 -> 22 9 15 16 26 20 13 23 2 1 30 , 18 10 12 13 23 30 25 30 -> 18 10 21 27 20 11 7 3 8 6 17 , 29 21 1 23 23 2 1 30 -> 29 13 23 23 30 25 5 9 3 4 30 , 18 1 30 18 1 5 4 30 -> 25 2 10 24 22 6 26 7 3 4 30 , 16 20 13 23 32 13 23 30 -> 16 31 30 16 17 22 4 5 9 15 35 , 18 1 23 23 32 13 23 30 -> 18 0 0 15 16 20 14 8 19 13 30 , 29 13 2 1 30 25 23 30 -> 29 21 0 15 18 10 14 19 24 25 30 , 35 22 19 21 1 23 23 30 -> 35 22 8 9 3 4 28 17 25 23 30 , 29 12 12 24 ->= 35 35 18 0 15 22 8 9 15 16 17 , 35 29 12 24 ->= 35 29 12 24 16 7 3 9 10 11 17 , 16 20 14 34 ->= 16 20 14 9 10 14 6 26 33 8 34 , 29 13 23 30 ->= 35 35 35 16 26 26 7 10 24 29 24 , 16 20 21 1 30 ->= 18 10 24 18 3 8 6 33 8 9 15 , 22 34 29 12 24 35 ->= 22 19 14 34 16 7 3 19 14 8 34 , 29 13 23 23 30 35 ->= 29 13 32 21 10 21 15 29 13 30 35 , 29 11 31 23 23 30 ->= 35 16 17 16 33 8 34 25 2 0 15 , 16 20 13 32 21 1 30 35 ->= 16 17 22 4 32 14 6 33 19 14 34 } 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 4 | | 0 1 | \ / 2 is interpreted by / \ | 1 3 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 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 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 3 | | 0 1 | \ / 13 is interpreted by / \ | 1 5 | | 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 2 | | 0 1 | \ / 21 is interpreted by / \ | 1 1 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 6 | | 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 4 | | 0 1 | \ / 28 is interpreted by / \ | 1 6 | | 0 1 | \ / 29 is interpreted by / \ | 1 1 | | 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 | \ / 35 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 10->0, 12->1, 13->2, 2->3, 14->4, 9->5, 15->6, 16->7, 17->8, 18->9, 27->10, 20->11, 6->12, 26->13, 33->14, 8->15, 23->16, 4->17, 5->18, 29->19, 24->20, 7->21, 3->22, 11->23, 28->24, 32->25, 19->26, 30->27, 34->28, 35->29 }, it remains to prove termination of the 90-rule system { 0 1 2 3 -> 0 1 4 5 6 7 8 9 0 2 3 , 10 11 4 5 ->= 10 11 4 5 0 4 12 13 14 15 5 , 0 1 2 16 -> 0 1 4 5 6 7 8 9 0 2 16 , 10 11 4 17 ->= 10 11 4 5 0 4 12 13 14 15 17 , 0 1 2 18 -> 0 1 4 5 6 7 8 9 0 2 18 , 6 19 1 4 ->= 6 19 1 20 7 21 22 5 0 23 14 , 10 11 4 15 ->= 10 11 4 5 0 4 12 13 14 15 15 , 0 1 2 24 -> 0 1 4 5 6 7 8 9 0 2 24 , 6 19 1 23 ->= 6 19 1 20 7 21 22 5 0 23 13 , 10 11 4 12 ->= 10 11 4 5 0 4 12 13 14 15 12 , 0 1 2 25 -> 0 1 4 5 6 7 8 9 0 2 25 , 10 11 4 26 ->= 10 11 4 5 0 4 12 13 14 15 26 , 0 1 2 27 -> 0 1 4 5 6 7 8 9 0 2 27 , 6 19 1 20 ->= 6 19 1 20 7 21 22 5 0 23 8 , 10 11 4 28 ->= 10 11 4 5 0 4 12 13 14 15 28 , 25 1 2 3 -> 25 1 4 5 6 7 8 9 0 2 3 , 24 11 4 5 ->= 24 11 4 5 0 4 12 13 14 15 5 , 25 1 2 16 -> 25 1 4 5 6 7 8 9 0 2 16 , 24 11 4 17 ->= 24 11 4 5 0 4 12 13 14 15 17 , 25 1 2 18 -> 25 1 4 5 6 7 8 9 0 2 18 , 27 19 1 4 ->= 27 19 1 20 7 21 22 5 0 23 14 , 24 11 4 15 ->= 24 11 4 5 0 4 12 13 14 15 15 , 25 1 2 24 -> 25 1 4 5 6 7 8 9 0 2 24 , 27 19 1 23 ->= 27 19 1 20 7 21 22 5 0 23 13 , 24 11 4 12 ->= 24 11 4 5 0 4 12 13 14 15 12 , 25 1 2 25 -> 25 1 4 5 6 7 8 9 0 2 25 , 24 11 4 26 ->= 24 11 4 5 0 4 12 13 14 15 26 , 25 1 2 27 -> 25 1 4 5 6 7 8 9 0 2 27 , 27 19 1 20 ->= 27 19 1 20 7 21 22 5 0 23 8 , 24 11 4 28 ->= 24 11 4 5 0 4 12 13 14 15 28 , 26 1 2 3 -> 26 1 4 5 6 7 8 9 0 2 3 , 12 11 4 5 ->= 12 11 4 5 0 4 12 13 14 15 5 , 26 1 2 16 -> 26 1 4 5 6 7 8 9 0 2 16 , 12 11 4 17 ->= 12 11 4 5 0 4 12 13 14 15 17 , 26 1 2 18 -> 26 1 4 5 6 7 8 9 0 2 18 , 28 19 1 4 ->= 28 19 1 20 7 21 22 5 0 23 14 , 12 11 4 15 ->= 12 11 4 5 0 4 12 13 14 15 15 , 26 1 2 24 -> 26 1 4 5 6 7 8 9 0 2 24 , 28 19 1 23 ->= 28 19 1 20 7 21 22 5 0 23 13 , 12 11 4 12 ->= 12 11 4 5 0 4 12 13 14 15 12 , 26 1 2 25 -> 26 1 4 5 6 7 8 9 0 2 25 , 12 11 4 26 ->= 12 11 4 5 0 4 12 13 14 15 26 , 26 1 2 27 -> 26 1 4 5 6 7 8 9 0 2 27 , 28 19 1 20 ->= 28 19 1 20 7 21 22 5 0 23 8 , 12 11 4 28 ->= 12 11 4 5 0 4 12 13 14 15 28 , 11 1 2 3 -> 11 1 4 5 6 7 8 9 0 2 3 , 13 11 4 5 ->= 13 11 4 5 0 4 12 13 14 15 5 , 11 1 2 16 -> 11 1 4 5 6 7 8 9 0 2 16 , 13 11 4 17 ->= 13 11 4 5 0 4 12 13 14 15 17 , 11 1 2 18 -> 11 1 4 5 6 7 8 9 0 2 18 , 8 19 1 4 ->= 8 19 1 20 7 21 22 5 0 23 14 , 13 11 4 15 ->= 13 11 4 5 0 4 12 13 14 15 15 , 11 1 2 24 -> 11 1 4 5 6 7 8 9 0 2 24 , 8 19 1 23 ->= 8 19 1 20 7 21 22 5 0 23 13 , 13 11 4 12 ->= 13 11 4 5 0 4 12 13 14 15 12 , 11 1 2 25 -> 11 1 4 5 6 7 8 9 0 2 25 , 13 11 4 26 ->= 13 11 4 5 0 4 12 13 14 15 26 , 11 1 2 27 -> 11 1 4 5 6 7 8 9 0 2 27 , 8 19 1 20 ->= 8 19 1 20 7 21 22 5 0 23 8 , 13 11 4 28 ->= 13 11 4 5 0 4 12 13 14 15 28 , 1 1 2 3 -> 1 1 4 5 6 7 8 9 0 2 3 , 23 11 4 5 ->= 23 11 4 5 0 4 12 13 14 15 5 , 1 1 2 16 -> 1 1 4 5 6 7 8 9 0 2 16 , 23 11 4 17 ->= 23 11 4 5 0 4 12 13 14 15 17 , 1 1 2 18 -> 1 1 4 5 6 7 8 9 0 2 18 , 20 19 1 4 ->= 20 19 1 20 7 21 22 5 0 23 14 , 23 11 4 15 ->= 23 11 4 5 0 4 12 13 14 15 15 , 1 1 2 24 -> 1 1 4 5 6 7 8 9 0 2 24 , 20 19 1 23 ->= 20 19 1 20 7 21 22 5 0 23 13 , 23 11 4 12 ->= 23 11 4 5 0 4 12 13 14 15 12 , 1 1 2 25 -> 1 1 4 5 6 7 8 9 0 2 25 , 23 11 4 26 ->= 23 11 4 5 0 4 12 13 14 15 26 , 1 1 2 27 -> 1 1 4 5 6 7 8 9 0 2 27 , 20 19 1 20 ->= 20 19 1 20 7 21 22 5 0 23 8 , 23 11 4 28 ->= 23 11 4 5 0 4 12 13 14 15 28 , 19 1 2 3 -> 19 1 4 5 6 7 8 9 0 2 3 , 7 11 4 5 ->= 7 11 4 5 0 4 12 13 14 15 5 , 19 1 2 16 -> 19 1 4 5 6 7 8 9 0 2 16 , 7 11 4 17 ->= 7 11 4 5 0 4 12 13 14 15 17 , 19 1 2 18 -> 19 1 4 5 6 7 8 9 0 2 18 , 29 19 1 4 ->= 29 19 1 20 7 21 22 5 0 23 14 , 7 11 4 15 ->= 7 11 4 5 0 4 12 13 14 15 15 , 19 1 2 24 -> 19 1 4 5 6 7 8 9 0 2 24 , 29 19 1 23 ->= 29 19 1 20 7 21 22 5 0 23 13 , 7 11 4 12 ->= 7 11 4 5 0 4 12 13 14 15 12 , 19 1 2 25 -> 19 1 4 5 6 7 8 9 0 2 25 , 7 11 4 26 ->= 7 11 4 5 0 4 12 13 14 15 26 , 19 1 2 27 -> 19 1 4 5 6 7 8 9 0 2 27 , 29 19 1 20 ->= 29 19 1 20 7 21 22 5 0 23 8 , 7 11 4 28 ->= 7 11 4 5 0 4 12 13 14 15 28 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 10->0, 11->1, 4->2, 5->3, 0->4, 12->5, 13->6, 14->7, 15->8, 1->9, 2->10, 16->11, 6->12, 7->13, 8->14, 9->15, 17->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 3->28, 29->29 }, it remains to prove termination of the 89-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 4 9 10 11 -> 4 9 2 3 12 13 14 15 4 10 11 , 0 1 2 16 ->= 0 1 2 3 4 2 5 6 7 8 16 , 4 9 10 17 -> 4 9 2 3 12 13 14 15 4 10 17 , 12 18 9 2 ->= 12 18 9 19 13 20 21 3 4 22 7 , 0 1 2 8 ->= 0 1 2 3 4 2 5 6 7 8 8 , 4 9 10 23 -> 4 9 2 3 12 13 14 15 4 10 23 , 12 18 9 22 ->= 12 18 9 19 13 20 21 3 4 22 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 9 10 24 -> 4 9 2 3 12 13 14 15 4 10 24 , 0 1 2 25 ->= 0 1 2 3 4 2 5 6 7 8 25 , 4 9 10 26 -> 4 9 2 3 12 13 14 15 4 10 26 , 12 18 9 19 ->= 12 18 9 19 13 20 21 3 4 22 14 , 0 1 2 27 ->= 0 1 2 3 4 2 5 6 7 8 27 , 24 9 10 28 -> 24 9 2 3 12 13 14 15 4 10 28 , 23 1 2 3 ->= 23 1 2 3 4 2 5 6 7 8 3 , 24 9 10 11 -> 24 9 2 3 12 13 14 15 4 10 11 , 23 1 2 16 ->= 23 1 2 3 4 2 5 6 7 8 16 , 24 9 10 17 -> 24 9 2 3 12 13 14 15 4 10 17 , 26 18 9 2 ->= 26 18 9 19 13 20 21 3 4 22 7 , 23 1 2 8 ->= 23 1 2 3 4 2 5 6 7 8 8 , 24 9 10 23 -> 24 9 2 3 12 13 14 15 4 10 23 , 26 18 9 22 ->= 26 18 9 19 13 20 21 3 4 22 6 , 23 1 2 5 ->= 23 1 2 3 4 2 5 6 7 8 5 , 24 9 10 24 -> 24 9 2 3 12 13 14 15 4 10 24 , 23 1 2 25 ->= 23 1 2 3 4 2 5 6 7 8 25 , 24 9 10 26 -> 24 9 2 3 12 13 14 15 4 10 26 , 26 18 9 19 ->= 26 18 9 19 13 20 21 3 4 22 14 , 23 1 2 27 ->= 23 1 2 3 4 2 5 6 7 8 27 , 25 9 10 28 -> 25 9 2 3 12 13 14 15 4 10 28 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 25 9 10 11 -> 25 9 2 3 12 13 14 15 4 10 11 , 5 1 2 16 ->= 5 1 2 3 4 2 5 6 7 8 16 , 25 9 10 17 -> 25 9 2 3 12 13 14 15 4 10 17 , 27 18 9 2 ->= 27 18 9 19 13 20 21 3 4 22 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 25 9 10 23 -> 25 9 2 3 12 13 14 15 4 10 23 , 27 18 9 22 ->= 27 18 9 19 13 20 21 3 4 22 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 25 9 10 24 -> 25 9 2 3 12 13 14 15 4 10 24 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 25 9 10 26 -> 25 9 2 3 12 13 14 15 4 10 26 , 27 18 9 19 ->= 27 18 9 19 13 20 21 3 4 22 14 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 1 9 10 28 -> 1 9 2 3 12 13 14 15 4 10 28 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 9 10 11 -> 1 9 2 3 12 13 14 15 4 10 11 , 6 1 2 16 ->= 6 1 2 3 4 2 5 6 7 8 16 , 1 9 10 17 -> 1 9 2 3 12 13 14 15 4 10 17 , 14 18 9 2 ->= 14 18 9 19 13 20 21 3 4 22 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 9 10 23 -> 1 9 2 3 12 13 14 15 4 10 23 , 14 18 9 22 ->= 14 18 9 19 13 20 21 3 4 22 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 9 10 24 -> 1 9 2 3 12 13 14 15 4 10 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 9 10 26 -> 1 9 2 3 12 13 14 15 4 10 26 , 14 18 9 19 ->= 14 18 9 19 13 20 21 3 4 22 14 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 9 9 10 28 -> 9 9 2 3 12 13 14 15 4 10 28 , 22 1 2 3 ->= 22 1 2 3 4 2 5 6 7 8 3 , 9 9 10 11 -> 9 9 2 3 12 13 14 15 4 10 11 , 22 1 2 16 ->= 22 1 2 3 4 2 5 6 7 8 16 , 9 9 10 17 -> 9 9 2 3 12 13 14 15 4 10 17 , 19 18 9 2 ->= 19 18 9 19 13 20 21 3 4 22 7 , 22 1 2 8 ->= 22 1 2 3 4 2 5 6 7 8 8 , 9 9 10 23 -> 9 9 2 3 12 13 14 15 4 10 23 , 19 18 9 22 ->= 19 18 9 19 13 20 21 3 4 22 6 , 22 1 2 5 ->= 22 1 2 3 4 2 5 6 7 8 5 , 9 9 10 24 -> 9 9 2 3 12 13 14 15 4 10 24 , 22 1 2 25 ->= 22 1 2 3 4 2 5 6 7 8 25 , 9 9 10 26 -> 9 9 2 3 12 13 14 15 4 10 26 , 19 18 9 19 ->= 19 18 9 19 13 20 21 3 4 22 14 , 22 1 2 27 ->= 22 1 2 3 4 2 5 6 7 8 27 , 18 9 10 28 -> 18 9 2 3 12 13 14 15 4 10 28 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 18 9 10 11 -> 18 9 2 3 12 13 14 15 4 10 11 , 13 1 2 16 ->= 13 1 2 3 4 2 5 6 7 8 16 , 18 9 10 17 -> 18 9 2 3 12 13 14 15 4 10 17 , 29 18 9 2 ->= 29 18 9 19 13 20 21 3 4 22 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 18 9 10 23 -> 18 9 2 3 12 13 14 15 4 10 23 , 29 18 9 22 ->= 29 18 9 19 13 20 21 3 4 22 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 18 9 10 24 -> 18 9 2 3 12 13 14 15 4 10 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 18 9 10 26 -> 18 9 2 3 12 13 14 15 4 10 26 , 29 18 9 19 ->= 29 18 9 19 13 20 21 3 4 22 14 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 16->9, 9->10, 10->11, 17->12, 12->13, 13->14, 14->15, 15->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 11->28, 29->29 }, it remains to prove termination of the 88-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 0 1 2 9 ->= 0 1 2 3 4 2 5 6 7 8 9 , 4 10 11 12 -> 4 10 2 3 13 14 15 16 4 11 12 , 13 17 10 2 ->= 13 17 10 18 14 19 20 3 4 21 7 , 0 1 2 8 ->= 0 1 2 3 4 2 5 6 7 8 8 , 4 10 11 22 -> 4 10 2 3 13 14 15 16 4 11 22 , 13 17 10 21 ->= 13 17 10 18 14 19 20 3 4 21 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 10 11 23 -> 4 10 2 3 13 14 15 16 4 11 23 , 0 1 2 24 ->= 0 1 2 3 4 2 5 6 7 8 24 , 4 10 11 25 -> 4 10 2 3 13 14 15 16 4 11 25 , 13 17 10 18 ->= 13 17 10 18 14 19 20 3 4 21 15 , 0 1 2 26 ->= 0 1 2 3 4 2 5 6 7 8 26 , 23 10 11 27 -> 23 10 2 3 13 14 15 16 4 11 27 , 22 1 2 3 ->= 22 1 2 3 4 2 5 6 7 8 3 , 23 10 11 28 -> 23 10 2 3 13 14 15 16 4 11 28 , 22 1 2 9 ->= 22 1 2 3 4 2 5 6 7 8 9 , 23 10 11 12 -> 23 10 2 3 13 14 15 16 4 11 12 , 25 17 10 2 ->= 25 17 10 18 14 19 20 3 4 21 7 , 22 1 2 8 ->= 22 1 2 3 4 2 5 6 7 8 8 , 23 10 11 22 -> 23 10 2 3 13 14 15 16 4 11 22 , 25 17 10 21 ->= 25 17 10 18 14 19 20 3 4 21 6 , 22 1 2 5 ->= 22 1 2 3 4 2 5 6 7 8 5 , 23 10 11 23 -> 23 10 2 3 13 14 15 16 4 11 23 , 22 1 2 24 ->= 22 1 2 3 4 2 5 6 7 8 24 , 23 10 11 25 -> 23 10 2 3 13 14 15 16 4 11 25 , 25 17 10 18 ->= 25 17 10 18 14 19 20 3 4 21 15 , 22 1 2 26 ->= 22 1 2 3 4 2 5 6 7 8 26 , 24 10 11 27 -> 24 10 2 3 13 14 15 16 4 11 27 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 24 10 11 28 -> 24 10 2 3 13 14 15 16 4 11 28 , 5 1 2 9 ->= 5 1 2 3 4 2 5 6 7 8 9 , 24 10 11 12 -> 24 10 2 3 13 14 15 16 4 11 12 , 26 17 10 2 ->= 26 17 10 18 14 19 20 3 4 21 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 24 10 11 22 -> 24 10 2 3 13 14 15 16 4 11 22 , 26 17 10 21 ->= 26 17 10 18 14 19 20 3 4 21 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 24 10 11 23 -> 24 10 2 3 13 14 15 16 4 11 23 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 24 10 11 25 -> 24 10 2 3 13 14 15 16 4 11 25 , 26 17 10 18 ->= 26 17 10 18 14 19 20 3 4 21 15 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 1 10 11 27 -> 1 10 2 3 13 14 15 16 4 11 27 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 10 11 28 -> 1 10 2 3 13 14 15 16 4 11 28 , 6 1 2 9 ->= 6 1 2 3 4 2 5 6 7 8 9 , 1 10 11 12 -> 1 10 2 3 13 14 15 16 4 11 12 , 15 17 10 2 ->= 15 17 10 18 14 19 20 3 4 21 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 10 11 22 -> 1 10 2 3 13 14 15 16 4 11 22 , 15 17 10 21 ->= 15 17 10 18 14 19 20 3 4 21 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 10 11 23 -> 1 10 2 3 13 14 15 16 4 11 23 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 10 11 25 -> 1 10 2 3 13 14 15 16 4 11 25 , 15 17 10 18 ->= 15 17 10 18 14 19 20 3 4 21 15 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 10 10 11 27 -> 10 10 2 3 13 14 15 16 4 11 27 , 21 1 2 3 ->= 21 1 2 3 4 2 5 6 7 8 3 , 10 10 11 28 -> 10 10 2 3 13 14 15 16 4 11 28 , 21 1 2 9 ->= 21 1 2 3 4 2 5 6 7 8 9 , 10 10 11 12 -> 10 10 2 3 13 14 15 16 4 11 12 , 18 17 10 2 ->= 18 17 10 18 14 19 20 3 4 21 7 , 21 1 2 8 ->= 21 1 2 3 4 2 5 6 7 8 8 , 10 10 11 22 -> 10 10 2 3 13 14 15 16 4 11 22 , 18 17 10 21 ->= 18 17 10 18 14 19 20 3 4 21 6 , 21 1 2 5 ->= 21 1 2 3 4 2 5 6 7 8 5 , 10 10 11 23 -> 10 10 2 3 13 14 15 16 4 11 23 , 21 1 2 24 ->= 21 1 2 3 4 2 5 6 7 8 24 , 10 10 11 25 -> 10 10 2 3 13 14 15 16 4 11 25 , 18 17 10 18 ->= 18 17 10 18 14 19 20 3 4 21 15 , 21 1 2 26 ->= 21 1 2 3 4 2 5 6 7 8 26 , 17 10 11 27 -> 17 10 2 3 13 14 15 16 4 11 27 , 14 1 2 3 ->= 14 1 2 3 4 2 5 6 7 8 3 , 17 10 11 28 -> 17 10 2 3 13 14 15 16 4 11 28 , 14 1 2 9 ->= 14 1 2 3 4 2 5 6 7 8 9 , 17 10 11 12 -> 17 10 2 3 13 14 15 16 4 11 12 , 29 17 10 2 ->= 29 17 10 18 14 19 20 3 4 21 7 , 14 1 2 8 ->= 14 1 2 3 4 2 5 6 7 8 8 , 17 10 11 22 -> 17 10 2 3 13 14 15 16 4 11 22 , 29 17 10 21 ->= 29 17 10 18 14 19 20 3 4 21 6 , 14 1 2 5 ->= 14 1 2 3 4 2 5 6 7 8 5 , 17 10 11 23 -> 17 10 2 3 13 14 15 16 4 11 23 , 14 1 2 24 ->= 14 1 2 3 4 2 5 6 7 8 24 , 17 10 11 25 -> 17 10 2 3 13 14 15 16 4 11 25 , 29 17 10 18 ->= 29 17 10 18 14 19 20 3 4 21 15 , 14 1 2 26 ->= 14 1 2 3 4 2 5 6 7 8 26 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 10->9, 11->10, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 9->28, 29->29 }, it remains to prove termination of the 87-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 4 9 10 11 -> 4 9 2 3 12 13 14 15 4 10 11 , 12 16 9 2 ->= 12 16 9 17 13 18 19 3 4 20 7 , 0 1 2 8 ->= 0 1 2 3 4 2 5 6 7 8 8 , 4 9 10 21 -> 4 9 2 3 12 13 14 15 4 10 21 , 12 16 9 20 ->= 12 16 9 17 13 18 19 3 4 20 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 9 10 22 -> 4 9 2 3 12 13 14 15 4 10 22 , 0 1 2 23 ->= 0 1 2 3 4 2 5 6 7 8 23 , 4 9 10 24 -> 4 9 2 3 12 13 14 15 4 10 24 , 12 16 9 17 ->= 12 16 9 17 13 18 19 3 4 20 14 , 0 1 2 25 ->= 0 1 2 3 4 2 5 6 7 8 25 , 22 9 10 26 -> 22 9 2 3 12 13 14 15 4 10 26 , 21 1 2 3 ->= 21 1 2 3 4 2 5 6 7 8 3 , 22 9 10 27 -> 22 9 2 3 12 13 14 15 4 10 27 , 21 1 2 28 ->= 21 1 2 3 4 2 5 6 7 8 28 , 22 9 10 11 -> 22 9 2 3 12 13 14 15 4 10 11 , 24 16 9 2 ->= 24 16 9 17 13 18 19 3 4 20 7 , 21 1 2 8 ->= 21 1 2 3 4 2 5 6 7 8 8 , 22 9 10 21 -> 22 9 2 3 12 13 14 15 4 10 21 , 24 16 9 20 ->= 24 16 9 17 13 18 19 3 4 20 6 , 21 1 2 5 ->= 21 1 2 3 4 2 5 6 7 8 5 , 22 9 10 22 -> 22 9 2 3 12 13 14 15 4 10 22 , 21 1 2 23 ->= 21 1 2 3 4 2 5 6 7 8 23 , 22 9 10 24 -> 22 9 2 3 12 13 14 15 4 10 24 , 24 16 9 17 ->= 24 16 9 17 13 18 19 3 4 20 14 , 21 1 2 25 ->= 21 1 2 3 4 2 5 6 7 8 25 , 23 9 10 26 -> 23 9 2 3 12 13 14 15 4 10 26 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 9 10 27 -> 23 9 2 3 12 13 14 15 4 10 27 , 5 1 2 28 ->= 5 1 2 3 4 2 5 6 7 8 28 , 23 9 10 11 -> 23 9 2 3 12 13 14 15 4 10 11 , 25 16 9 2 ->= 25 16 9 17 13 18 19 3 4 20 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 9 10 21 -> 23 9 2 3 12 13 14 15 4 10 21 , 25 16 9 20 ->= 25 16 9 17 13 18 19 3 4 20 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 9 10 22 -> 23 9 2 3 12 13 14 15 4 10 22 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 9 10 24 -> 23 9 2 3 12 13 14 15 4 10 24 , 25 16 9 17 ->= 25 16 9 17 13 18 19 3 4 20 14 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 1 9 10 26 -> 1 9 2 3 12 13 14 15 4 10 26 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 9 10 27 -> 1 9 2 3 12 13 14 15 4 10 27 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 9 10 11 -> 1 9 2 3 12 13 14 15 4 10 11 , 14 16 9 2 ->= 14 16 9 17 13 18 19 3 4 20 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 9 10 21 -> 1 9 2 3 12 13 14 15 4 10 21 , 14 16 9 20 ->= 14 16 9 17 13 18 19 3 4 20 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 9 10 22 -> 1 9 2 3 12 13 14 15 4 10 22 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 9 10 24 -> 1 9 2 3 12 13 14 15 4 10 24 , 14 16 9 17 ->= 14 16 9 17 13 18 19 3 4 20 14 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 9 9 10 26 -> 9 9 2 3 12 13 14 15 4 10 26 , 20 1 2 3 ->= 20 1 2 3 4 2 5 6 7 8 3 , 9 9 10 27 -> 9 9 2 3 12 13 14 15 4 10 27 , 20 1 2 28 ->= 20 1 2 3 4 2 5 6 7 8 28 , 9 9 10 11 -> 9 9 2 3 12 13 14 15 4 10 11 , 17 16 9 2 ->= 17 16 9 17 13 18 19 3 4 20 7 , 20 1 2 8 ->= 20 1 2 3 4 2 5 6 7 8 8 , 9 9 10 21 -> 9 9 2 3 12 13 14 15 4 10 21 , 17 16 9 20 ->= 17 16 9 17 13 18 19 3 4 20 6 , 20 1 2 5 ->= 20 1 2 3 4 2 5 6 7 8 5 , 9 9 10 22 -> 9 9 2 3 12 13 14 15 4 10 22 , 20 1 2 23 ->= 20 1 2 3 4 2 5 6 7 8 23 , 9 9 10 24 -> 9 9 2 3 12 13 14 15 4 10 24 , 17 16 9 17 ->= 17 16 9 17 13 18 19 3 4 20 14 , 20 1 2 25 ->= 20 1 2 3 4 2 5 6 7 8 25 , 16 9 10 26 -> 16 9 2 3 12 13 14 15 4 10 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 16 9 10 27 -> 16 9 2 3 12 13 14 15 4 10 27 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 16 9 10 11 -> 16 9 2 3 12 13 14 15 4 10 11 , 29 16 9 2 ->= 29 16 9 17 13 18 19 3 4 20 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 16 9 10 21 -> 16 9 2 3 12 13 14 15 4 10 21 , 29 16 9 20 ->= 29 16 9 17 13 18 19 3 4 20 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 16 9 10 22 -> 16 9 2 3 12 13 14 15 4 10 22 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 16 9 10 24 -> 16 9 2 3 12 13 14 15 4 10 24 , 29 16 9 17 ->= 29 16 9 17 13 18 19 3 4 20 14 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 12->9, 16->10, 9->11, 17->12, 13->13, 18->14, 19->15, 20->16, 10->17, 21->18, 14->19, 15->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 11->28, 29->29 }, it remains to prove termination of the 86-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 0 1 2 8 ->= 0 1 2 3 4 2 5 6 7 8 8 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 9 10 11 16 ->= 9 10 11 12 13 14 15 3 4 16 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 11 17 21 -> 4 11 2 3 9 13 19 20 4 17 21 , 0 1 2 22 ->= 0 1 2 3 4 2 5 6 7 8 22 , 4 11 17 23 -> 4 11 2 3 9 13 19 20 4 17 23 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 24 ->= 0 1 2 3 4 2 5 6 7 8 24 , 21 11 17 25 -> 21 11 2 3 9 13 19 20 4 17 25 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 21 11 17 26 -> 21 11 2 3 9 13 19 20 4 17 26 , 18 1 2 27 ->= 18 1 2 3 4 2 5 6 7 8 27 , 21 11 17 28 -> 21 11 2 3 9 13 19 20 4 17 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 21 11 17 18 -> 21 11 2 3 9 13 19 20 4 17 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 21 11 17 21 -> 21 11 2 3 9 13 19 20 4 17 21 , 18 1 2 22 ->= 18 1 2 3 4 2 5 6 7 8 22 , 21 11 17 23 -> 21 11 2 3 9 13 19 20 4 17 23 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 19 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 22 11 17 25 -> 22 11 2 3 9 13 19 20 4 17 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 22 11 17 26 -> 22 11 2 3 9 13 19 20 4 17 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 22 11 17 28 -> 22 11 2 3 9 13 19 20 4 17 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 22 11 17 18 -> 22 11 2 3 9 13 19 20 4 17 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 22 11 17 21 -> 22 11 2 3 9 13 19 20 4 17 21 , 5 1 2 22 ->= 5 1 2 3 4 2 5 6 7 8 22 , 22 11 17 23 -> 22 11 2 3 9 13 19 20 4 17 23 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 19 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 26 -> 1 11 2 3 9 13 19 20 4 17 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 17 28 -> 1 11 2 3 9 13 19 20 4 17 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 21 -> 1 11 2 3 9 13 19 20 4 17 21 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 1 11 17 23 -> 1 11 2 3 9 13 19 20 4 17 23 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 26 -> 11 11 2 3 9 13 19 20 4 17 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 17 28 -> 11 11 2 3 9 13 19 20 4 17 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 21 -> 11 11 2 3 9 13 19 20 4 17 21 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 17 23 -> 11 11 2 3 9 13 19 20 4 17 23 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 26 -> 10 11 2 3 9 13 19 20 4 17 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 17 28 -> 10 11 2 3 9 13 19 20 4 17 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 21 -> 10 11 2 3 9 13 19 20 4 17 21 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 17 23 -> 10 11 2 3 9 13 19 20 4 17 23 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 85-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 9 10 11 16 ->= 9 10 11 12 13 14 15 3 4 16 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 11 17 21 -> 4 11 2 3 9 13 19 20 4 17 21 , 0 1 2 22 ->= 0 1 2 3 4 2 5 6 7 8 22 , 4 11 17 23 -> 4 11 2 3 9 13 19 20 4 17 23 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 24 ->= 0 1 2 3 4 2 5 6 7 8 24 , 21 11 17 25 -> 21 11 2 3 9 13 19 20 4 17 25 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 21 11 17 26 -> 21 11 2 3 9 13 19 20 4 17 26 , 18 1 2 27 ->= 18 1 2 3 4 2 5 6 7 8 27 , 21 11 17 28 -> 21 11 2 3 9 13 19 20 4 17 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 21 11 17 18 -> 21 11 2 3 9 13 19 20 4 17 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 21 11 17 21 -> 21 11 2 3 9 13 19 20 4 17 21 , 18 1 2 22 ->= 18 1 2 3 4 2 5 6 7 8 22 , 21 11 17 23 -> 21 11 2 3 9 13 19 20 4 17 23 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 19 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 22 11 17 25 -> 22 11 2 3 9 13 19 20 4 17 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 22 11 17 26 -> 22 11 2 3 9 13 19 20 4 17 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 22 11 17 28 -> 22 11 2 3 9 13 19 20 4 17 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 22 11 17 18 -> 22 11 2 3 9 13 19 20 4 17 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 22 11 17 21 -> 22 11 2 3 9 13 19 20 4 17 21 , 5 1 2 22 ->= 5 1 2 3 4 2 5 6 7 8 22 , 22 11 17 23 -> 22 11 2 3 9 13 19 20 4 17 23 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 19 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 26 -> 1 11 2 3 9 13 19 20 4 17 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 17 28 -> 1 11 2 3 9 13 19 20 4 17 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 21 -> 1 11 2 3 9 13 19 20 4 17 21 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 1 11 17 23 -> 1 11 2 3 9 13 19 20 4 17 23 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 26 -> 11 11 2 3 9 13 19 20 4 17 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 17 28 -> 11 11 2 3 9 13 19 20 4 17 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 21 -> 11 11 2 3 9 13 19 20 4 17 21 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 17 23 -> 11 11 2 3 9 13 19 20 4 17 23 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 26 -> 10 11 2 3 9 13 19 20 4 17 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 17 28 -> 10 11 2 3 9 13 19 20 4 17 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 21 -> 10 11 2 3 9 13 19 20 4 17 21 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 17 23 -> 10 11 2 3 9 13 19 20 4 17 23 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 21->18, 19->19, 20->20, 22->21, 23->22, 24->23, 25->24, 18->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 84-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 16 ->= 9 10 11 12 13 14 15 3 4 16 6 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 0 1 2 21 ->= 0 1 2 3 4 2 5 6 7 8 21 , 4 11 17 22 -> 4 11 2 3 9 13 19 20 4 17 22 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 23 ->= 0 1 2 3 4 2 5 6 7 8 23 , 18 11 17 24 -> 18 11 2 3 9 13 19 20 4 17 24 , 25 1 2 3 ->= 25 1 2 3 4 2 5 6 7 8 3 , 18 11 17 26 -> 18 11 2 3 9 13 19 20 4 17 26 , 25 1 2 27 ->= 25 1 2 3 4 2 5 6 7 8 27 , 18 11 17 28 -> 18 11 2 3 9 13 19 20 4 17 28 , 22 10 11 2 ->= 22 10 11 12 13 14 15 3 4 16 7 , 25 1 2 8 ->= 25 1 2 3 4 2 5 6 7 8 8 , 18 11 17 25 -> 18 11 2 3 9 13 19 20 4 17 25 , 22 10 11 16 ->= 22 10 11 12 13 14 15 3 4 16 6 , 25 1 2 5 ->= 25 1 2 3 4 2 5 6 7 8 5 , 18 11 17 18 -> 18 11 2 3 9 13 19 20 4 17 18 , 25 1 2 21 ->= 25 1 2 3 4 2 5 6 7 8 21 , 18 11 17 22 -> 18 11 2 3 9 13 19 20 4 17 22 , 22 10 11 12 ->= 22 10 11 12 13 14 15 3 4 16 19 , 25 1 2 23 ->= 25 1 2 3 4 2 5 6 7 8 23 , 21 11 17 24 -> 21 11 2 3 9 13 19 20 4 17 24 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 21 11 17 26 -> 21 11 2 3 9 13 19 20 4 17 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 21 11 17 28 -> 21 11 2 3 9 13 19 20 4 17 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 17 25 -> 21 11 2 3 9 13 19 20 4 17 25 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 17 18 -> 21 11 2 3 9 13 19 20 4 17 18 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 17 22 -> 21 11 2 3 9 13 19 20 4 17 22 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 19 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 1 11 17 24 -> 1 11 2 3 9 13 19 20 4 17 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 26 -> 1 11 2 3 9 13 19 20 4 17 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 17 28 -> 1 11 2 3 9 13 19 20 4 17 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 17 22 -> 1 11 2 3 9 13 19 20 4 17 22 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 11 11 17 24 -> 11 11 2 3 9 13 19 20 4 17 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 26 -> 11 11 2 3 9 13 19 20 4 17 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 17 28 -> 11 11 2 3 9 13 19 20 4 17 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 17 22 -> 11 11 2 3 9 13 19 20 4 17 22 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 10 11 17 24 -> 10 11 2 3 9 13 19 20 4 17 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 26 -> 10 11 2 3 9 13 19 20 4 17 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 17 28 -> 10 11 2 3 9 13 19 20 4 17 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 17 22 -> 10 11 2 3 9 13 19 20 4 17 22 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 83-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 0 1 2 5 ->= 0 1 2 3 4 2 5 6 7 8 5 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 0 1 2 21 ->= 0 1 2 3 4 2 5 6 7 8 21 , 4 11 17 22 -> 4 11 2 3 9 13 19 20 4 17 22 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 23 ->= 0 1 2 3 4 2 5 6 7 8 23 , 18 11 17 24 -> 18 11 2 3 9 13 19 20 4 17 24 , 25 1 2 3 ->= 25 1 2 3 4 2 5 6 7 8 3 , 18 11 17 26 -> 18 11 2 3 9 13 19 20 4 17 26 , 25 1 2 27 ->= 25 1 2 3 4 2 5 6 7 8 27 , 18 11 17 28 -> 18 11 2 3 9 13 19 20 4 17 28 , 22 10 11 2 ->= 22 10 11 12 13 14 15 3 4 16 7 , 25 1 2 8 ->= 25 1 2 3 4 2 5 6 7 8 8 , 18 11 17 25 -> 18 11 2 3 9 13 19 20 4 17 25 , 22 10 11 16 ->= 22 10 11 12 13 14 15 3 4 16 6 , 25 1 2 5 ->= 25 1 2 3 4 2 5 6 7 8 5 , 18 11 17 18 -> 18 11 2 3 9 13 19 20 4 17 18 , 25 1 2 21 ->= 25 1 2 3 4 2 5 6 7 8 21 , 18 11 17 22 -> 18 11 2 3 9 13 19 20 4 17 22 , 22 10 11 12 ->= 22 10 11 12 13 14 15 3 4 16 19 , 25 1 2 23 ->= 25 1 2 3 4 2 5 6 7 8 23 , 21 11 17 24 -> 21 11 2 3 9 13 19 20 4 17 24 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 21 11 17 26 -> 21 11 2 3 9 13 19 20 4 17 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 21 11 17 28 -> 21 11 2 3 9 13 19 20 4 17 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 17 25 -> 21 11 2 3 9 13 19 20 4 17 25 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 17 18 -> 21 11 2 3 9 13 19 20 4 17 18 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 17 22 -> 21 11 2 3 9 13 19 20 4 17 22 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 19 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 1 11 17 24 -> 1 11 2 3 9 13 19 20 4 17 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 26 -> 1 11 2 3 9 13 19 20 4 17 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 17 28 -> 1 11 2 3 9 13 19 20 4 17 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 17 22 -> 1 11 2 3 9 13 19 20 4 17 22 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 11 11 17 24 -> 11 11 2 3 9 13 19 20 4 17 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 26 -> 11 11 2 3 9 13 19 20 4 17 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 17 28 -> 11 11 2 3 9 13 19 20 4 17 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 17 22 -> 11 11 2 3 9 13 19 20 4 17 22 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 10 11 17 24 -> 10 11 2 3 9 13 19 20 4 17 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 26 -> 10 11 2 3 9 13 19 20 4 17 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 17 28 -> 10 11 2 3 9 13 19 20 4 17 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 17 22 -> 10 11 2 3 9 13 19 20 4 17 22 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 82-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 0 1 2 21 ->= 0 1 2 3 4 2 5 6 7 8 21 , 4 11 17 22 -> 4 11 2 3 9 13 19 20 4 17 22 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 23 ->= 0 1 2 3 4 2 5 6 7 8 23 , 18 11 17 24 -> 18 11 2 3 9 13 19 20 4 17 24 , 25 1 2 3 ->= 25 1 2 3 4 2 5 6 7 8 3 , 18 11 17 26 -> 18 11 2 3 9 13 19 20 4 17 26 , 25 1 2 27 ->= 25 1 2 3 4 2 5 6 7 8 27 , 18 11 17 28 -> 18 11 2 3 9 13 19 20 4 17 28 , 22 10 11 2 ->= 22 10 11 12 13 14 15 3 4 16 7 , 25 1 2 8 ->= 25 1 2 3 4 2 5 6 7 8 8 , 18 11 17 25 -> 18 11 2 3 9 13 19 20 4 17 25 , 22 10 11 16 ->= 22 10 11 12 13 14 15 3 4 16 6 , 25 1 2 5 ->= 25 1 2 3 4 2 5 6 7 8 5 , 18 11 17 18 -> 18 11 2 3 9 13 19 20 4 17 18 , 25 1 2 21 ->= 25 1 2 3 4 2 5 6 7 8 21 , 18 11 17 22 -> 18 11 2 3 9 13 19 20 4 17 22 , 22 10 11 12 ->= 22 10 11 12 13 14 15 3 4 16 19 , 25 1 2 23 ->= 25 1 2 3 4 2 5 6 7 8 23 , 21 11 17 24 -> 21 11 2 3 9 13 19 20 4 17 24 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 21 11 17 26 -> 21 11 2 3 9 13 19 20 4 17 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 21 11 17 28 -> 21 11 2 3 9 13 19 20 4 17 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 17 25 -> 21 11 2 3 9 13 19 20 4 17 25 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 17 18 -> 21 11 2 3 9 13 19 20 4 17 18 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 17 22 -> 21 11 2 3 9 13 19 20 4 17 22 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 19 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 1 11 17 24 -> 1 11 2 3 9 13 19 20 4 17 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 26 -> 1 11 2 3 9 13 19 20 4 17 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 17 28 -> 1 11 2 3 9 13 19 20 4 17 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 17 22 -> 1 11 2 3 9 13 19 20 4 17 22 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 11 11 17 24 -> 11 11 2 3 9 13 19 20 4 17 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 26 -> 11 11 2 3 9 13 19 20 4 17 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 17 28 -> 11 11 2 3 9 13 19 20 4 17 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 17 22 -> 11 11 2 3 9 13 19 20 4 17 22 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 10 11 17 24 -> 10 11 2 3 9 13 19 20 4 17 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 26 -> 10 11 2 3 9 13 19 20 4 17 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 17 28 -> 10 11 2 3 9 13 19 20 4 17 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 17 22 -> 10 11 2 3 9 13 19 20 4 17 22 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 21->17, 17->18, 22->19, 19->20, 20->21, 23->22, 18->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 81-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 0 1 2 17 ->= 0 1 2 3 4 2 5 6 7 8 17 , 4 11 18 19 -> 4 11 2 3 9 13 20 21 4 18 19 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 20 , 0 1 2 22 ->= 0 1 2 3 4 2 5 6 7 8 22 , 23 11 18 24 -> 23 11 2 3 9 13 20 21 4 18 24 , 25 1 2 3 ->= 25 1 2 3 4 2 5 6 7 8 3 , 23 11 18 26 -> 23 11 2 3 9 13 20 21 4 18 26 , 25 1 2 27 ->= 25 1 2 3 4 2 5 6 7 8 27 , 23 11 18 28 -> 23 11 2 3 9 13 20 21 4 18 28 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 25 1 2 8 ->= 25 1 2 3 4 2 5 6 7 8 8 , 23 11 18 25 -> 23 11 2 3 9 13 20 21 4 18 25 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 25 1 2 5 ->= 25 1 2 3 4 2 5 6 7 8 5 , 23 11 18 23 -> 23 11 2 3 9 13 20 21 4 18 23 , 25 1 2 17 ->= 25 1 2 3 4 2 5 6 7 8 17 , 23 11 18 19 -> 23 11 2 3 9 13 20 21 4 18 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 20 , 25 1 2 22 ->= 25 1 2 3 4 2 5 6 7 8 22 , 17 11 18 24 -> 17 11 2 3 9 13 20 21 4 18 24 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 17 11 18 26 -> 17 11 2 3 9 13 20 21 4 18 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 17 11 18 28 -> 17 11 2 3 9 13 20 21 4 18 28 , 22 10 11 2 ->= 22 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 17 11 18 25 -> 17 11 2 3 9 13 20 21 4 18 25 , 22 10 11 16 ->= 22 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 17 11 18 23 -> 17 11 2 3 9 13 20 21 4 18 23 , 5 1 2 17 ->= 5 1 2 3 4 2 5 6 7 8 17 , 17 11 18 19 -> 17 11 2 3 9 13 20 21 4 18 19 , 22 10 11 12 ->= 22 10 11 12 13 14 15 3 4 16 20 , 5 1 2 22 ->= 5 1 2 3 4 2 5 6 7 8 22 , 1 11 18 24 -> 1 11 2 3 9 13 20 21 4 18 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 18 26 -> 1 11 2 3 9 13 20 21 4 18 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 18 28 -> 1 11 2 3 9 13 20 21 4 18 28 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 18 25 -> 1 11 2 3 9 13 20 21 4 18 25 , 20 10 11 16 ->= 20 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 18 23 -> 1 11 2 3 9 13 20 21 4 18 23 , 6 1 2 17 ->= 6 1 2 3 4 2 5 6 7 8 17 , 1 11 18 19 -> 1 11 2 3 9 13 20 21 4 18 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 20 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 11 11 18 24 -> 11 11 2 3 9 13 20 21 4 18 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 18 26 -> 11 11 2 3 9 13 20 21 4 18 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 18 28 -> 11 11 2 3 9 13 20 21 4 18 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 18 25 -> 11 11 2 3 9 13 20 21 4 18 25 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 18 23 -> 11 11 2 3 9 13 20 21 4 18 23 , 16 1 2 17 ->= 16 1 2 3 4 2 5 6 7 8 17 , 11 11 18 19 -> 11 11 2 3 9 13 20 21 4 18 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 20 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 10 11 18 24 -> 10 11 2 3 9 13 20 21 4 18 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 18 26 -> 10 11 2 3 9 13 20 21 4 18 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 18 28 -> 10 11 2 3 9 13 20 21 4 18 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 18 25 -> 10 11 2 3 9 13 20 21 4 18 25 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 18 23 -> 10 11 2 3 9 13 20 21 4 18 23 , 13 1 2 17 ->= 13 1 2 3 4 2 5 6 7 8 17 , 10 11 18 19 -> 10 11 2 3 9 13 20 21 4 18 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 20 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 17->28, 29->29 }, it remains to prove termination of the 80-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 4 11 17 18 -> 4 11 2 3 9 13 19 20 4 17 18 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 19 , 0 1 2 21 ->= 0 1 2 3 4 2 5 6 7 8 21 , 22 11 17 23 -> 22 11 2 3 9 13 19 20 4 17 23 , 24 1 2 3 ->= 24 1 2 3 4 2 5 6 7 8 3 , 22 11 17 25 -> 22 11 2 3 9 13 19 20 4 17 25 , 24 1 2 26 ->= 24 1 2 3 4 2 5 6 7 8 26 , 22 11 17 27 -> 22 11 2 3 9 13 19 20 4 17 27 , 18 10 11 2 ->= 18 10 11 12 13 14 15 3 4 16 7 , 24 1 2 8 ->= 24 1 2 3 4 2 5 6 7 8 8 , 22 11 17 24 -> 22 11 2 3 9 13 19 20 4 17 24 , 18 10 11 16 ->= 18 10 11 12 13 14 15 3 4 16 6 , 24 1 2 5 ->= 24 1 2 3 4 2 5 6 7 8 5 , 22 11 17 22 -> 22 11 2 3 9 13 19 20 4 17 22 , 24 1 2 28 ->= 24 1 2 3 4 2 5 6 7 8 28 , 22 11 17 18 -> 22 11 2 3 9 13 19 20 4 17 18 , 18 10 11 12 ->= 18 10 11 12 13 14 15 3 4 16 19 , 24 1 2 21 ->= 24 1 2 3 4 2 5 6 7 8 21 , 28 11 17 23 -> 28 11 2 3 9 13 19 20 4 17 23 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 28 11 17 25 -> 28 11 2 3 9 13 19 20 4 17 25 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 28 11 17 27 -> 28 11 2 3 9 13 19 20 4 17 27 , 21 10 11 2 ->= 21 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 28 11 17 24 -> 28 11 2 3 9 13 19 20 4 17 24 , 21 10 11 16 ->= 21 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 28 11 17 22 -> 28 11 2 3 9 13 19 20 4 17 22 , 5 1 2 28 ->= 5 1 2 3 4 2 5 6 7 8 28 , 28 11 17 18 -> 28 11 2 3 9 13 19 20 4 17 18 , 21 10 11 12 ->= 21 10 11 12 13 14 15 3 4 16 19 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 1 11 17 23 -> 1 11 2 3 9 13 19 20 4 17 23 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 17 25 -> 1 11 2 3 9 13 19 20 4 17 25 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 17 27 -> 1 11 2 3 9 13 19 20 4 17 27 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 17 24 -> 1 11 2 3 9 13 19 20 4 17 24 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 17 22 -> 1 11 2 3 9 13 19 20 4 17 22 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 17 18 -> 1 11 2 3 9 13 19 20 4 17 18 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 19 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 11 11 17 23 -> 11 11 2 3 9 13 19 20 4 17 23 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 17 25 -> 11 11 2 3 9 13 19 20 4 17 25 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 17 27 -> 11 11 2 3 9 13 19 20 4 17 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 17 24 -> 11 11 2 3 9 13 19 20 4 17 24 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 17 22 -> 11 11 2 3 9 13 19 20 4 17 22 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 17 18 -> 11 11 2 3 9 13 19 20 4 17 18 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 19 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 10 11 17 23 -> 10 11 2 3 9 13 19 20 4 17 23 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 17 25 -> 10 11 2 3 9 13 19 20 4 17 25 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 17 27 -> 10 11 2 3 9 13 19 20 4 17 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 17 24 -> 10 11 2 3 9 13 19 20 4 17 24 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 17 22 -> 10 11 2 3 9 13 19 20 4 17 22 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 17 18 -> 10 11 2 3 9 13 19 20 4 17 18 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 19 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 19->17, 21->18, 22->19, 17->20, 23->21, 20->22, 24->23, 25->24, 26->25, 27->26, 18->27, 28->28, 29->29 }, it remains to prove termination of the 79-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 0 1 2 18 ->= 0 1 2 3 4 2 5 6 7 8 18 , 19 11 20 21 -> 19 11 2 3 9 13 17 22 4 20 21 , 23 1 2 3 ->= 23 1 2 3 4 2 5 6 7 8 3 , 19 11 20 24 -> 19 11 2 3 9 13 17 22 4 20 24 , 23 1 2 25 ->= 23 1 2 3 4 2 5 6 7 8 25 , 19 11 20 26 -> 19 11 2 3 9 13 17 22 4 20 26 , 27 10 11 2 ->= 27 10 11 12 13 14 15 3 4 16 7 , 23 1 2 8 ->= 23 1 2 3 4 2 5 6 7 8 8 , 19 11 20 23 -> 19 11 2 3 9 13 17 22 4 20 23 , 27 10 11 16 ->= 27 10 11 12 13 14 15 3 4 16 6 , 23 1 2 5 ->= 23 1 2 3 4 2 5 6 7 8 5 , 19 11 20 19 -> 19 11 2 3 9 13 17 22 4 20 19 , 23 1 2 28 ->= 23 1 2 3 4 2 5 6 7 8 28 , 19 11 20 27 -> 19 11 2 3 9 13 17 22 4 20 27 , 27 10 11 12 ->= 27 10 11 12 13 14 15 3 4 16 17 , 23 1 2 18 ->= 23 1 2 3 4 2 5 6 7 8 18 , 28 11 20 21 -> 28 11 2 3 9 13 17 22 4 20 21 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 28 11 20 24 -> 28 11 2 3 9 13 17 22 4 20 24 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 28 11 20 26 -> 28 11 2 3 9 13 17 22 4 20 26 , 18 10 11 2 ->= 18 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 28 11 20 23 -> 28 11 2 3 9 13 17 22 4 20 23 , 18 10 11 16 ->= 18 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 28 11 20 19 -> 28 11 2 3 9 13 17 22 4 20 19 , 5 1 2 28 ->= 5 1 2 3 4 2 5 6 7 8 28 , 28 11 20 27 -> 28 11 2 3 9 13 17 22 4 20 27 , 18 10 11 12 ->= 18 10 11 12 13 14 15 3 4 16 17 , 5 1 2 18 ->= 5 1 2 3 4 2 5 6 7 8 18 , 1 11 20 21 -> 1 11 2 3 9 13 17 22 4 20 21 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 20 24 -> 1 11 2 3 9 13 17 22 4 20 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 20 26 -> 1 11 2 3 9 13 17 22 4 20 26 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 20 23 -> 1 11 2 3 9 13 17 22 4 20 23 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 20 19 -> 1 11 2 3 9 13 17 22 4 20 19 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 20 27 -> 1 11 2 3 9 13 17 22 4 20 27 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 18 ->= 6 1 2 3 4 2 5 6 7 8 18 , 11 11 20 21 -> 11 11 2 3 9 13 17 22 4 20 21 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 20 24 -> 11 11 2 3 9 13 17 22 4 20 24 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 20 26 -> 11 11 2 3 9 13 17 22 4 20 26 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 20 23 -> 11 11 2 3 9 13 17 22 4 20 23 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 20 19 -> 11 11 2 3 9 13 17 22 4 20 19 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 20 27 -> 11 11 2 3 9 13 17 22 4 20 27 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 18 ->= 16 1 2 3 4 2 5 6 7 8 18 , 10 11 20 21 -> 10 11 2 3 9 13 17 22 4 20 21 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 20 24 -> 10 11 2 3 9 13 17 22 4 20 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 20 26 -> 10 11 2 3 9 13 17 22 4 20 26 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 20 23 -> 10 11 2 3 9 13 17 22 4 20 23 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 20 19 -> 10 11 2 3 9 13 17 22 4 20 19 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 20 27 -> 10 11 2 3 9 13 17 22 4 20 27 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 18 ->= 13 1 2 3 4 2 5 6 7 8 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 18->28, 29->29 }, it remains to prove termination of the 78-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 11 19 20 -> 18 11 2 3 9 13 17 21 4 19 20 , 22 1 2 3 ->= 22 1 2 3 4 2 5 6 7 8 3 , 18 11 19 23 -> 18 11 2 3 9 13 17 21 4 19 23 , 22 1 2 24 ->= 22 1 2 3 4 2 5 6 7 8 24 , 18 11 19 25 -> 18 11 2 3 9 13 17 21 4 19 25 , 26 10 11 2 ->= 26 10 11 12 13 14 15 3 4 16 7 , 22 1 2 8 ->= 22 1 2 3 4 2 5 6 7 8 8 , 18 11 19 22 -> 18 11 2 3 9 13 17 21 4 19 22 , 26 10 11 16 ->= 26 10 11 12 13 14 15 3 4 16 6 , 22 1 2 5 ->= 22 1 2 3 4 2 5 6 7 8 5 , 18 11 19 18 -> 18 11 2 3 9 13 17 21 4 19 18 , 22 1 2 27 ->= 22 1 2 3 4 2 5 6 7 8 27 , 18 11 19 26 -> 18 11 2 3 9 13 17 21 4 19 26 , 26 10 11 12 ->= 26 10 11 12 13 14 15 3 4 16 17 , 22 1 2 28 ->= 22 1 2 3 4 2 5 6 7 8 28 , 27 11 19 20 -> 27 11 2 3 9 13 17 21 4 19 20 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 27 11 19 23 -> 27 11 2 3 9 13 17 21 4 19 23 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 27 11 19 25 -> 27 11 2 3 9 13 17 21 4 19 25 , 28 10 11 2 ->= 28 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 27 11 19 22 -> 27 11 2 3 9 13 17 21 4 19 22 , 28 10 11 16 ->= 28 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 27 11 19 18 -> 27 11 2 3 9 13 17 21 4 19 18 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 27 11 19 26 -> 27 11 2 3 9 13 17 21 4 19 26 , 28 10 11 12 ->= 28 10 11 12 13 14 15 3 4 16 17 , 5 1 2 28 ->= 5 1 2 3 4 2 5 6 7 8 28 , 1 11 19 20 -> 1 11 2 3 9 13 17 21 4 19 20 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 19 23 -> 1 11 2 3 9 13 17 21 4 19 23 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 11 19 25 -> 1 11 2 3 9 13 17 21 4 19 25 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 19 22 -> 1 11 2 3 9 13 17 21 4 19 22 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 19 18 -> 1 11 2 3 9 13 17 21 4 19 18 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 19 26 -> 1 11 2 3 9 13 17 21 4 19 26 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 11 11 19 20 -> 11 11 2 3 9 13 17 21 4 19 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 19 23 -> 11 11 2 3 9 13 17 21 4 19 23 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 11 11 19 25 -> 11 11 2 3 9 13 17 21 4 19 25 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 19 22 -> 11 11 2 3 9 13 17 21 4 19 22 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 19 18 -> 11 11 2 3 9 13 17 21 4 19 18 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 19 26 -> 11 11 2 3 9 13 17 21 4 19 26 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 10 11 19 20 -> 10 11 2 3 9 13 17 21 4 19 20 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 19 23 -> 10 11 2 3 9 13 17 21 4 19 23 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 , 10 11 19 25 -> 10 11 2 3 9 13 17 21 4 19 25 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 19 22 -> 10 11 2 3 9 13 17 21 4 19 22 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 19 18 -> 10 11 2 3 9 13 17 21 4 19 18 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 19 26 -> 10 11 2 3 9 13 17 21 4 19 26 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 22->18, 18->19, 19->20, 23->21, 21->22, 24->23, 25->24, 26->25, 27->26, 28->27, 20->28, 29->29 }, it remains to prove termination of the 77-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 11 20 21 -> 19 11 2 3 9 13 17 22 4 20 21 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 19 11 20 24 -> 19 11 2 3 9 13 17 22 4 20 24 , 25 10 11 2 ->= 25 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 19 11 20 18 -> 19 11 2 3 9 13 17 22 4 20 18 , 25 10 11 16 ->= 25 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 19 11 20 19 -> 19 11 2 3 9 13 17 22 4 20 19 , 18 1 2 26 ->= 18 1 2 3 4 2 5 6 7 8 26 , 19 11 20 25 -> 19 11 2 3 9 13 17 22 4 20 25 , 25 10 11 12 ->= 25 10 11 12 13 14 15 3 4 16 17 , 18 1 2 27 ->= 18 1 2 3 4 2 5 6 7 8 27 , 26 11 20 28 -> 26 11 2 3 9 13 17 22 4 20 28 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 26 11 20 21 -> 26 11 2 3 9 13 17 22 4 20 21 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 26 11 20 24 -> 26 11 2 3 9 13 17 22 4 20 24 , 27 10 11 2 ->= 27 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 26 11 20 18 -> 26 11 2 3 9 13 17 22 4 20 18 , 27 10 11 16 ->= 27 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 26 11 20 19 -> 26 11 2 3 9 13 17 22 4 20 19 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 26 11 20 25 -> 26 11 2 3 9 13 17 22 4 20 25 , 27 10 11 12 ->= 27 10 11 12 13 14 15 3 4 16 17 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 1 11 20 28 -> 1 11 2 3 9 13 17 22 4 20 28 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 20 21 -> 1 11 2 3 9 13 17 22 4 20 21 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 20 24 -> 1 11 2 3 9 13 17 22 4 20 24 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 20 18 -> 1 11 2 3 9 13 17 22 4 20 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 20 19 -> 1 11 2 3 9 13 17 22 4 20 19 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 20 25 -> 1 11 2 3 9 13 17 22 4 20 25 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 11 11 20 28 -> 11 11 2 3 9 13 17 22 4 20 28 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 20 21 -> 11 11 2 3 9 13 17 22 4 20 21 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 20 24 -> 11 11 2 3 9 13 17 22 4 20 24 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 20 18 -> 11 11 2 3 9 13 17 22 4 20 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 20 19 -> 11 11 2 3 9 13 17 22 4 20 19 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 20 25 -> 11 11 2 3 9 13 17 22 4 20 25 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 10 11 20 28 -> 10 11 2 3 9 13 17 22 4 20 28 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 20 21 -> 10 11 2 3 9 13 17 22 4 20 21 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 20 24 -> 10 11 2 3 9 13 17 22 4 20 24 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 20 18 -> 10 11 2 3 9 13 17 22 4 20 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 20 19 -> 10 11 2 3 9 13 17 22 4 20 19 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 20 25 -> 10 11 2 3 9 13 17 22 4 20 25 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 23->19, 19->20, 20->21, 24->22, 22->23, 25->24, 26->25, 27->26, 28->27, 21->28, 29->29 }, it remains to prove termination of the 76-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 18 1 2 19 ->= 18 1 2 3 4 2 5 6 7 8 19 , 20 11 21 22 -> 20 11 2 3 9 13 17 23 4 21 22 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 20 11 21 18 -> 20 11 2 3 9 13 17 23 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 20 11 21 20 -> 20 11 2 3 9 13 17 23 4 21 20 , 18 1 2 25 ->= 18 1 2 3 4 2 5 6 7 8 25 , 20 11 21 24 -> 20 11 2 3 9 13 17 23 4 21 24 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 18 1 2 26 ->= 18 1 2 3 4 2 5 6 7 8 26 , 25 11 21 27 -> 25 11 2 3 9 13 17 23 4 21 27 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 25 11 21 28 -> 25 11 2 3 9 13 17 23 4 21 28 , 5 1 2 19 ->= 5 1 2 3 4 2 5 6 7 8 19 , 25 11 21 22 -> 25 11 2 3 9 13 17 23 4 21 22 , 26 10 11 2 ->= 26 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 25 11 21 18 -> 25 11 2 3 9 13 17 23 4 21 18 , 26 10 11 16 ->= 26 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 25 11 21 20 -> 25 11 2 3 9 13 17 23 4 21 20 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 25 11 21 24 -> 25 11 2 3 9 13 17 23 4 21 24 , 26 10 11 12 ->= 26 10 11 12 13 14 15 3 4 16 17 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 1 11 21 27 -> 1 11 2 3 9 13 17 23 4 21 27 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 28 -> 1 11 2 3 9 13 17 23 4 21 28 , 6 1 2 19 ->= 6 1 2 3 4 2 5 6 7 8 19 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 23 4 21 20 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 21 24 -> 1 11 2 3 9 13 17 23 4 21 24 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 11 11 21 27 -> 11 11 2 3 9 13 17 23 4 21 27 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 28 -> 11 11 2 3 9 13 17 23 4 21 28 , 16 1 2 19 ->= 16 1 2 3 4 2 5 6 7 8 19 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 23 4 21 20 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 21 24 -> 11 11 2 3 9 13 17 23 4 21 24 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 10 11 21 27 -> 10 11 2 3 9 13 17 23 4 21 27 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 28 -> 10 11 2 3 9 13 17 23 4 21 28 , 13 1 2 19 ->= 13 1 2 3 4 2 5 6 7 8 19 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 23 4 21 20 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 21 24 -> 10 11 2 3 9 13 17 23 4 21 24 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 19->28, 29->29 }, it remains to prove termination of the 75-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 11 20 21 -> 19 11 2 3 9 13 17 22 4 20 21 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 19 11 20 18 -> 19 11 2 3 9 13 17 22 4 20 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 19 11 20 19 -> 19 11 2 3 9 13 17 22 4 20 19 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 19 11 20 23 -> 19 11 2 3 9 13 17 22 4 20 23 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 18 1 2 25 ->= 18 1 2 3 4 2 5 6 7 8 25 , 24 11 20 26 -> 24 11 2 3 9 13 17 22 4 20 26 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 24 11 20 27 -> 24 11 2 3 9 13 17 22 4 20 27 , 5 1 2 28 ->= 5 1 2 3 4 2 5 6 7 8 28 , 24 11 20 21 -> 24 11 2 3 9 13 17 22 4 20 21 , 25 10 11 2 ->= 25 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 24 11 20 18 -> 24 11 2 3 9 13 17 22 4 20 18 , 25 10 11 16 ->= 25 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 24 11 20 19 -> 24 11 2 3 9 13 17 22 4 20 19 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 24 11 20 23 -> 24 11 2 3 9 13 17 22 4 20 23 , 25 10 11 12 ->= 25 10 11 12 13 14 15 3 4 16 17 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 1 11 20 26 -> 1 11 2 3 9 13 17 22 4 20 26 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 20 27 -> 1 11 2 3 9 13 17 22 4 20 27 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 20 21 -> 1 11 2 3 9 13 17 22 4 20 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 20 18 -> 1 11 2 3 9 13 17 22 4 20 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 20 19 -> 1 11 2 3 9 13 17 22 4 20 19 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 11 20 23 -> 1 11 2 3 9 13 17 22 4 20 23 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 11 11 20 26 -> 11 11 2 3 9 13 17 22 4 20 26 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 20 27 -> 11 11 2 3 9 13 17 22 4 20 27 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 20 21 -> 11 11 2 3 9 13 17 22 4 20 21 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 20 18 -> 11 11 2 3 9 13 17 22 4 20 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 20 19 -> 11 11 2 3 9 13 17 22 4 20 19 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 11 11 20 23 -> 11 11 2 3 9 13 17 22 4 20 23 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 10 11 20 26 -> 10 11 2 3 9 13 17 22 4 20 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 20 27 -> 10 11 2 3 9 13 17 22 4 20 27 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 20 21 -> 10 11 2 3 9 13 17 22 4 20 21 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 20 18 -> 10 11 2 3 9 13 17 22 4 20 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 20 19 -> 10 11 2 3 9 13 17 22 4 20 19 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 , 10 11 20 23 -> 10 11 2 3 9 13 17 22 4 20 23 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 23->19, 19->20, 20->21, 22->22, 24->23, 25->24, 26->25, 27->26, 28->27, 21->28, 29->29 }, it remains to prove termination of the 74-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 18 1 2 8 ->= 18 1 2 3 4 2 5 6 7 8 8 , 20 11 21 18 -> 20 11 2 3 9 13 17 22 4 21 18 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 20 11 21 20 -> 20 11 2 3 9 13 17 22 4 21 20 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 23 11 21 25 -> 23 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 11 21 26 -> 23 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 23 11 21 28 -> 23 11 2 3 9 13 17 22 4 21 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 11 21 18 -> 23 11 2 3 9 13 17 22 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 11 21 20 -> 23 11 2 3 9 13 17 22 4 21 20 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 11 21 19 -> 23 11 2 3 9 13 17 22 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 73-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 20 11 21 18 -> 20 11 2 3 9 13 17 22 4 21 18 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 20 11 21 20 -> 20 11 2 3 9 13 17 22 4 21 20 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 23 11 21 25 -> 23 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 11 21 26 -> 23 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 23 11 21 28 -> 23 11 2 3 9 13 17 22 4 21 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 11 21 18 -> 23 11 2 3 9 13 17 22 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 11 21 20 -> 23 11 2 3 9 13 17 22 4 21 20 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 11 21 19 -> 23 11 2 3 9 13 17 22 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 72-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 16 ->= 19 10 11 12 13 14 15 3 4 16 6 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 20 11 21 20 -> 20 11 2 3 9 13 17 22 4 21 20 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 23 11 21 25 -> 23 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 11 21 26 -> 23 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 23 11 21 28 -> 23 11 2 3 9 13 17 22 4 21 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 11 21 18 -> 23 11 2 3 9 13 17 22 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 11 21 20 -> 23 11 2 3 9 13 17 22 4 21 20 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 11 21 19 -> 23 11 2 3 9 13 17 22 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 71-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 18 1 2 5 ->= 18 1 2 3 4 2 5 6 7 8 5 , 20 11 21 20 -> 20 11 2 3 9 13 17 22 4 21 20 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 23 11 21 25 -> 23 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 11 21 26 -> 23 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 23 11 21 28 -> 23 11 2 3 9 13 17 22 4 21 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 11 21 18 -> 23 11 2 3 9 13 17 22 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 11 21 20 -> 23 11 2 3 9 13 17 22 4 21 20 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 11 21 19 -> 23 11 2 3 9 13 17 22 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 70-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 20 11 21 20 -> 20 11 2 3 9 13 17 22 4 21 20 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 23 11 21 25 -> 23 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 23 11 21 26 -> 23 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 23 11 21 28 -> 23 11 2 3 9 13 17 22 4 21 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 23 11 21 18 -> 23 11 2 3 9 13 17 22 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 23 11 21 20 -> 23 11 2 3 9 13 17 22 4 21 20 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 23 11 21 19 -> 23 11 2 3 9 13 17 22 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 23->20, 20->21, 21->22, 22->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 69-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 18 1 2 20 ->= 18 1 2 3 4 2 5 6 7 8 20 , 21 11 22 19 -> 21 11 2 3 9 13 17 23 4 22 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 24 ->= 18 1 2 3 4 2 5 6 7 8 24 , 20 11 22 25 -> 20 11 2 3 9 13 17 23 4 22 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 11 22 26 -> 20 11 2 3 9 13 17 23 4 22 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 20 11 22 28 -> 20 11 2 3 9 13 17 23 4 22 28 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 20 11 22 18 -> 20 11 2 3 9 13 17 23 4 22 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 20 11 22 21 -> 20 11 2 3 9 13 17 23 4 22 21 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 20 11 22 19 -> 20 11 2 3 9 13 17 23 4 22 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 22 25 -> 1 11 2 3 9 13 17 23 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 23 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 23 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 21 -> 1 11 2 3 9 13 17 23 4 22 21 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 22 25 -> 11 11 2 3 9 13 17 23 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 23 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 21 -> 11 11 2 3 9 13 17 23 4 22 21 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 22 25 -> 10 11 2 3 9 13 17 23 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 23 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 21 -> 10 11 2 3 9 13 17 23 4 22 21 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 21->20, 22->21, 23->22, 24->23, 20->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 68-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 20 11 21 19 -> 20 11 2 3 9 13 17 22 4 21 19 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 23 ->= 18 1 2 3 4 2 5 6 7 8 23 , 24 11 21 25 -> 24 11 2 3 9 13 17 22 4 21 25 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 24 11 21 26 -> 24 11 2 3 9 13 17 22 4 21 26 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 24 11 21 28 -> 24 11 2 3 9 13 17 22 4 21 28 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 24 11 21 18 -> 24 11 2 3 9 13 17 22 4 21 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 24 11 21 20 -> 24 11 2 3 9 13 17 22 4 21 20 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 24 11 21 19 -> 24 11 2 3 9 13 17 22 4 21 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 5 1 2 23 ->= 5 1 2 3 4 2 5 6 7 8 23 , 1 11 21 25 -> 1 11 2 3 9 13 17 22 4 21 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 26 -> 1 11 2 3 9 13 17 22 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 28 -> 1 11 2 3 9 13 17 22 4 21 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 22 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 20 -> 1 11 2 3 9 13 17 22 4 21 20 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 11 21 19 -> 1 11 2 3 9 13 17 22 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 23 ->= 6 1 2 3 4 2 5 6 7 8 23 , 11 11 21 25 -> 11 11 2 3 9 13 17 22 4 21 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 26 -> 11 11 2 3 9 13 17 22 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 28 -> 11 11 2 3 9 13 17 22 4 21 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 22 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 20 -> 11 11 2 3 9 13 17 22 4 21 20 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 11 11 21 19 -> 11 11 2 3 9 13 17 22 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 23 ->= 16 1 2 3 4 2 5 6 7 8 23 , 10 11 21 25 -> 10 11 2 3 9 13 17 22 4 21 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 26 -> 10 11 2 3 9 13 17 22 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 28 -> 10 11 2 3 9 13 17 22 4 21 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 22 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 20 -> 10 11 2 3 9 13 17 22 4 21 20 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 , 10 11 21 19 -> 10 11 2 3 9 13 17 22 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 23 ->= 13 1 2 3 4 2 5 6 7 8 23 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 23->20, 24->21, 21->22, 25->23, 22->24, 26->25, 27->26, 28->27, 20->28, 29->29 }, it remains to prove termination of the 67-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 18 1 2 20 ->= 18 1 2 3 4 2 5 6 7 8 20 , 21 11 22 23 -> 21 11 2 3 9 13 17 24 4 22 23 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 21 11 22 25 -> 21 11 2 3 9 13 17 24 4 22 25 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 21 11 22 27 -> 21 11 2 3 9 13 17 24 4 22 27 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 22 18 -> 21 11 2 3 9 13 17 24 4 22 18 , 20 10 11 16 ->= 20 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 28 -> 21 11 2 3 9 13 17 24 4 22 28 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 24 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 25 -> 1 11 2 3 9 13 17 24 4 22 25 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 22 27 -> 1 11 2 3 9 13 17 24 4 22 27 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 28 -> 1 11 2 3 9 13 17 24 4 22 28 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 25 -> 11 11 2 3 9 13 17 24 4 22 25 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 22 27 -> 11 11 2 3 9 13 17 24 4 22 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 25 -> 10 11 2 3 9 13 17 24 4 22 25 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 22 27 -> 10 11 2 3 9 13 17 24 4 22 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 20->27, 28->28, 29->29 }, it remains to prove termination of the 66-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 20 11 21 22 -> 20 11 2 3 9 13 17 23 4 21 22 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 11 21 24 -> 20 11 2 3 9 13 17 23 4 21 24 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 20 11 21 26 -> 20 11 2 3 9 13 17 23 4 21 26 , 27 10 11 2 ->= 27 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 20 11 21 18 -> 20 11 2 3 9 13 17 23 4 21 18 , 27 10 11 16 ->= 27 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 20 11 21 28 -> 20 11 2 3 9 13 17 23 4 21 28 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 20 11 21 19 -> 20 11 2 3 9 13 17 23 4 21 19 , 27 10 11 12 ->= 27 10 11 12 13 14 15 3 4 16 17 , 5 1 2 27 ->= 5 1 2 3 4 2 5 6 7 8 27 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 24 -> 1 11 2 3 9 13 17 23 4 21 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 21 26 -> 1 11 2 3 9 13 17 23 4 21 26 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 28 -> 1 11 2 3 9 13 17 23 4 21 28 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 24 -> 11 11 2 3 9 13 17 23 4 21 24 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 21 26 -> 11 11 2 3 9 13 17 23 4 21 26 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 28 -> 11 11 2 3 9 13 17 23 4 21 28 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 24 -> 10 11 2 3 9 13 17 23 4 21 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 21 26 -> 10 11 2 3 9 13 17 23 4 21 26 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 28 -> 10 11 2 3 9 13 17 23 4 21 28 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 24->22, 23->23, 25->24, 26->25, 27->26, 28->27, 22->28, 29->29 }, it remains to prove termination of the 65-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 11 21 22 -> 20 11 2 3 9 13 17 23 4 21 22 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 20 11 21 25 -> 20 11 2 3 9 13 17 23 4 21 25 , 26 10 11 2 ->= 26 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 20 11 21 18 -> 20 11 2 3 9 13 17 23 4 21 18 , 26 10 11 16 ->= 26 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 20 11 21 27 -> 20 11 2 3 9 13 17 23 4 21 27 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 20 11 21 19 -> 20 11 2 3 9 13 17 23 4 21 19 , 26 10 11 12 ->= 26 10 11 12 13 14 15 3 4 16 17 , 5 1 2 26 ->= 5 1 2 3 4 2 5 6 7 8 26 , 1 11 21 28 -> 1 11 2 3 9 13 17 23 4 21 28 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 23 4 21 25 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 27 -> 1 11 2 3 9 13 17 23 4 21 27 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 11 11 21 28 -> 11 11 2 3 9 13 17 23 4 21 28 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 23 4 21 25 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 27 -> 11 11 2 3 9 13 17 23 4 21 27 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 10 11 21 28 -> 10 11 2 3 9 13 17 23 4 21 28 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 23 4 21 25 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 27 -> 10 11 2 3 9 13 17 23 4 21 27 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 24->20, 20->21, 21->22, 25->23, 23->24, 26->25, 27->26, 28->27, 22->28, 29->29 }, it remains to prove termination of the 64-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 21 11 22 23 -> 21 11 2 3 9 13 17 24 4 22 23 , 25 10 11 2 ->= 25 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 22 18 -> 21 11 2 3 9 13 17 24 4 22 18 , 25 10 11 16 ->= 25 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 26 -> 21 11 2 3 9 13 17 24 4 22 26 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 24 4 22 19 , 25 10 11 12 ->= 25 10 11 12 13 14 15 3 4 16 17 , 5 1 2 25 ->= 5 1 2 3 4 2 5 6 7 8 25 , 1 11 22 27 -> 1 11 2 3 9 13 17 24 4 22 27 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 28 -> 1 11 2 3 9 13 17 24 4 22 28 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 26 -> 1 11 2 3 9 13 17 24 4 22 26 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 11 11 22 27 -> 11 11 2 3 9 13 17 24 4 22 27 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 26 -> 11 11 2 3 9 13 17 24 4 22 26 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 10 11 22 27 -> 10 11 2 3 9 13 17 24 4 22 27 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 26 -> 10 11 2 3 9 13 17 24 4 22 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 28->27, 20->28, 29->29 }, it remains to prove termination of the 63-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 11 21 22 -> 20 11 2 3 9 13 17 23 4 21 22 , 24 10 11 2 ->= 24 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 20 11 21 18 -> 20 11 2 3 9 13 17 23 4 21 18 , 24 10 11 16 ->= 24 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 20 11 21 25 -> 20 11 2 3 9 13 17 23 4 21 25 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 20 11 21 19 -> 20 11 2 3 9 13 17 23 4 21 19 , 24 10 11 12 ->= 24 10 11 12 13 14 15 3 4 16 17 , 5 1 2 24 ->= 5 1 2 3 4 2 5 6 7 8 24 , 1 11 21 26 -> 1 11 2 3 9 13 17 23 4 21 26 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 27 -> 1 11 2 3 9 13 17 23 4 21 27 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 25 -> 1 11 2 3 9 13 17 23 4 21 25 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 11 11 21 26 -> 11 11 2 3 9 13 17 23 4 21 26 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 27 -> 11 11 2 3 9 13 17 23 4 21 27 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 25 -> 11 11 2 3 9 13 17 23 4 21 25 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 10 11 21 26 -> 10 11 2 3 9 13 17 23 4 21 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 27 -> 10 11 2 3 9 13 17 23 4 21 27 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 25 -> 10 11 2 3 9 13 17 23 4 21 25 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 24->20, 20->21, 21->22, 23->23, 25->24, 26->25, 27->26, 28->27, 22->28, 29->29 }, it remains to prove termination of the 62-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 5 1 2 8 ->= 5 1 2 3 4 2 5 6 7 8 8 , 21 11 22 18 -> 21 11 2 3 9 13 17 23 4 22 18 , 20 10 11 16 ->= 20 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 24 -> 21 11 2 3 9 13 17 23 4 22 24 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 23 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 25 -> 1 11 2 3 9 13 17 23 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 23 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 23 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 24 -> 1 11 2 3 9 13 17 23 4 22 24 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 25 -> 11 11 2 3 9 13 17 23 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 23 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 24 -> 11 11 2 3 9 13 17 23 4 22 24 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 25 -> 10 11 2 3 9 13 17 23 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 23 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 24 -> 10 11 2 3 9 13 17 23 4 22 24 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 61-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 21 11 22 18 -> 21 11 2 3 9 13 17 23 4 22 18 , 20 10 11 16 ->= 20 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 24 -> 21 11 2 3 9 13 17 23 4 22 24 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 23 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 25 -> 1 11 2 3 9 13 17 23 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 23 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 23 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 24 -> 1 11 2 3 9 13 17 23 4 22 24 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 25 -> 11 11 2 3 9 13 17 23 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 23 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 24 -> 11 11 2 3 9 13 17 23 4 22 24 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 25 -> 10 11 2 3 9 13 17 23 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 23 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 24 -> 10 11 2 3 9 13 17 23 4 22 24 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 24->23, 23->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 60-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 16 ->= 20 10 11 12 13 14 15 3 4 16 6 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 23 -> 21 11 2 3 9 13 17 24 4 22 23 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 24 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 25 -> 1 11 2 3 9 13 17 24 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 24 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 24 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 25 -> 11 11 2 3 9 13 17 24 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 24 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 25 -> 10 11 2 3 9 13 17 24 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 24 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 59-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 5 1 2 5 ->= 5 1 2 3 4 2 5 6 7 8 5 , 21 11 22 23 -> 21 11 2 3 9 13 17 24 4 22 23 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 24 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 25 -> 1 11 2 3 9 13 17 24 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 24 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 24 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 25 -> 11 11 2 3 9 13 17 24 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 24 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 25 -> 10 11 2 3 9 13 17 24 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 24 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 58-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 21 11 22 23 -> 21 11 2 3 9 13 17 24 4 22 23 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 24 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 25 -> 1 11 2 3 9 13 17 24 4 22 25 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 26 -> 1 11 2 3 9 13 17 24 4 22 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 22 28 -> 1 11 2 3 9 13 17 24 4 22 28 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 25 -> 11 11 2 3 9 13 17 24 4 22 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 26 -> 11 11 2 3 9 13 17 24 4 22 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 25 -> 10 11 2 3 9 13 17 24 4 22 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 26 -> 10 11 2 3 9 13 17 24 4 22 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 24->23, 25->24, 26->25, 27->26, 28->27, 23->28, 29->29 }, it remains to prove termination of the 57-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 5 1 2 21 ->= 5 1 2 3 4 2 5 6 7 8 21 , 21 11 22 19 -> 21 11 2 3 9 13 17 23 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 24 -> 1 11 2 3 9 13 17 23 4 22 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 25 -> 1 11 2 3 9 13 17 23 4 22 25 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 22 27 -> 1 11 2 3 9 13 17 23 4 22 27 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 28 -> 1 11 2 3 9 13 17 23 4 22 28 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 24 -> 11 11 2 3 9 13 17 23 4 22 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 25 -> 11 11 2 3 9 13 17 23 4 22 25 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 22 27 -> 11 11 2 3 9 13 17 23 4 22 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 24 -> 10 11 2 3 9 13 17 23 4 22 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 25 -> 10 11 2 3 9 13 17 23 4 22 25 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 22 27 -> 10 11 2 3 9 13 17 23 4 22 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 56-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 21 11 22 19 -> 21 11 2 3 9 13 17 23 4 22 19 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 22 24 -> 1 11 2 3 9 13 17 23 4 22 24 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 22 25 -> 1 11 2 3 9 13 17 23 4 22 25 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 22 27 -> 1 11 2 3 9 13 17 23 4 22 27 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 28 -> 1 11 2 3 9 13 17 23 4 22 28 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 24 -> 11 11 2 3 9 13 17 23 4 22 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 25 -> 11 11 2 3 9 13 17 23 4 22 25 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 22 27 -> 11 11 2 3 9 13 17 23 4 22 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 24 -> 10 11 2 3 9 13 17 23 4 22 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 25 -> 10 11 2 3 9 13 17 23 4 22 25 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 22 27 -> 10 11 2 3 9 13 17 23 4 22 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 22->21, 24->22, 23->23, 25->24, 26->25, 27->26, 28->27, 21->28, 29->29 }, it remains to prove termination of the 55-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 5 1 2 20 ->= 5 1 2 3 4 2 5 6 7 8 20 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 24 -> 1 11 2 3 9 13 17 23 4 21 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 21 26 -> 1 11 2 3 9 13 17 23 4 21 26 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 27 -> 1 11 2 3 9 13 17 23 4 21 27 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 24 -> 11 11 2 3 9 13 17 23 4 21 24 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 21 26 -> 11 11 2 3 9 13 17 23 4 21 26 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 27 -> 11 11 2 3 9 13 17 23 4 21 27 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 24 -> 10 11 2 3 9 13 17 23 4 21 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 21 26 -> 10 11 2 3 9 13 17 23 4 21 26 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 27 -> 10 11 2 3 9 13 17 23 4 21 27 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 54-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 24 -> 1 11 2 3 9 13 17 23 4 21 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 21 26 -> 1 11 2 3 9 13 17 23 4 21 26 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 27 -> 1 11 2 3 9 13 17 23 4 21 27 , 6 1 2 28 ->= 6 1 2 3 4 2 5 6 7 8 28 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 24 -> 11 11 2 3 9 13 17 23 4 21 24 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 21 26 -> 11 11 2 3 9 13 17 23 4 21 26 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 27 -> 11 11 2 3 9 13 17 23 4 21 27 , 16 1 2 28 ->= 16 1 2 3 4 2 5 6 7 8 28 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 24 -> 10 11 2 3 9 13 17 23 4 21 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 21 26 -> 10 11 2 3 9 13 17 23 4 21 26 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 27 -> 10 11 2 3 9 13 17 23 4 21 27 , 13 1 2 28 ->= 13 1 2 3 4 2 5 6 7 8 28 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 24->22, 23->23, 25->24, 26->25, 27->26, 28->27, 22->28, 29->29 }, it remains to prove termination of the 53-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 1 11 21 22 -> 1 11 2 3 9 13 17 23 4 21 22 , 6 1 2 24 ->= 6 1 2 3 4 2 5 6 7 8 24 , 1 11 21 25 -> 1 11 2 3 9 13 17 23 4 21 25 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 21 18 -> 1 11 2 3 9 13 17 23 4 21 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 21 26 -> 1 11 2 3 9 13 17 23 4 21 26 , 6 1 2 27 ->= 6 1 2 3 4 2 5 6 7 8 27 , 1 11 21 19 -> 1 11 2 3 9 13 17 23 4 21 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 21 28 -> 11 11 2 3 9 13 17 23 4 21 28 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 21 22 -> 11 11 2 3 9 13 17 23 4 21 22 , 16 1 2 24 ->= 16 1 2 3 4 2 5 6 7 8 24 , 11 11 21 25 -> 11 11 2 3 9 13 17 23 4 21 25 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 21 18 -> 11 11 2 3 9 13 17 23 4 21 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 21 26 -> 11 11 2 3 9 13 17 23 4 21 26 , 16 1 2 27 ->= 16 1 2 3 4 2 5 6 7 8 27 , 11 11 21 19 -> 11 11 2 3 9 13 17 23 4 21 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 21 28 -> 10 11 2 3 9 13 17 23 4 21 28 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 21 22 -> 10 11 2 3 9 13 17 23 4 21 22 , 13 1 2 24 ->= 13 1 2 3 4 2 5 6 7 8 24 , 10 11 21 25 -> 10 11 2 3 9 13 17 23 4 21 25 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 21 18 -> 10 11 2 3 9 13 17 23 4 21 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 21 26 -> 10 11 2 3 9 13 17 23 4 21 26 , 13 1 2 27 ->= 13 1 2 3 4 2 5 6 7 8 27 , 10 11 21 19 -> 10 11 2 3 9 13 17 23 4 21 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 24->21, 21->22, 25->23, 23->24, 26->25, 27->26, 28->27, 22->28, 29->29 }, it remains to prove termination of the 52-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 24 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 25 -> 1 11 2 3 9 13 17 24 4 22 25 , 6 1 2 26 ->= 6 1 2 3 4 2 5 6 7 8 26 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 27 -> 11 11 2 3 9 13 17 24 4 22 27 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 25 -> 11 11 2 3 9 13 17 24 4 22 25 , 16 1 2 26 ->= 16 1 2 3 4 2 5 6 7 8 26 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 27 -> 10 11 2 3 9 13 17 24 4 22 27 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 25 -> 10 11 2 3 9 13 17 24 4 22 25 , 13 1 2 26 ->= 13 1 2 3 4 2 5 6 7 8 26 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 24->23, 25->24, 26->25, 27->26, 28->27, 23->28, 29->29 }, it remains to prove termination of the 51-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 1 11 22 18 -> 1 11 2 3 9 13 17 23 4 22 18 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 24 -> 1 11 2 3 9 13 17 23 4 22 24 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 22 19 -> 1 11 2 3 9 13 17 23 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 26 -> 11 11 2 3 9 13 17 23 4 22 26 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 27 -> 11 11 2 3 9 13 17 23 4 22 27 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 28 -> 11 11 2 3 9 13 17 23 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 23 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 24 -> 11 11 2 3 9 13 17 23 4 22 24 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 22 19 -> 11 11 2 3 9 13 17 23 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 26 -> 10 11 2 3 9 13 17 23 4 22 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 27 -> 10 11 2 3 9 13 17 23 4 22 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 28 -> 10 11 2 3 9 13 17 23 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 23 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 24 -> 10 11 2 3 9 13 17 23 4 22 24 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 22 19 -> 10 11 2 3 9 13 17 23 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 24->23, 23->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 50-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 1 11 22 23 -> 1 11 2 3 9 13 17 24 4 22 23 , 6 1 2 25 ->= 6 1 2 3 4 2 5 6 7 8 25 , 1 11 22 19 -> 1 11 2 3 9 13 17 24 4 22 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 22 26 -> 11 11 2 3 9 13 17 24 4 22 26 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 22 27 -> 11 11 2 3 9 13 17 24 4 22 27 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 22 28 -> 11 11 2 3 9 13 17 24 4 22 28 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 22 18 -> 11 11 2 3 9 13 17 24 4 22 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 22 23 -> 11 11 2 3 9 13 17 24 4 22 23 , 16 1 2 25 ->= 16 1 2 3 4 2 5 6 7 8 25 , 11 11 22 19 -> 11 11 2 3 9 13 17 24 4 22 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 22 26 -> 10 11 2 3 9 13 17 24 4 22 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 22 27 -> 10 11 2 3 9 13 17 24 4 22 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 22 28 -> 10 11 2 3 9 13 17 24 4 22 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 22 18 -> 10 11 2 3 9 13 17 24 4 22 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 22 23 -> 10 11 2 3 9 13 17 24 4 22 23 , 13 1 2 25 ->= 13 1 2 3 4 2 5 6 7 8 25 , 10 11 22 19 -> 10 11 2 3 9 13 17 24 4 22 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 25->22, 22->23, 24->24, 26->25, 27->26, 28->27, 23->28, 29->29 }, it remains to prove termination of the 49-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 1 11 23 19 -> 1 11 2 3 9 13 17 24 4 23 19 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 23 25 -> 11 11 2 3 9 13 17 24 4 23 25 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 23 26 -> 11 11 2 3 9 13 17 24 4 23 26 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 23 27 -> 11 11 2 3 9 13 17 24 4 23 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 24 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 28 -> 11 11 2 3 9 13 17 24 4 23 28 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 24 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 25 -> 10 11 2 3 9 13 17 24 4 23 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 24 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 24 4 23 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 24 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 28 -> 10 11 2 3 9 13 17 24 4 23 28 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 24 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 25->24, 24->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 48-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 23 26 -> 11 11 2 3 9 13 17 25 4 23 26 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 23 27 -> 11 11 2 3 9 13 17 25 4 23 27 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 25 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 28 -> 11 11 2 3 9 13 17 25 4 23 28 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 26->24, 25->25, 27->26, 28->27, 24->28, 29->29 }, it remains to prove termination of the 47-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 23 26 -> 11 11 2 3 9 13 17 25 4 23 26 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 25 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 27 -> 11 11 2 3 9 13 17 25 4 23 27 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 26->24, 25->25, 27->26, 28->27, 24->28, 29->29 }, it remains to prove termination of the 46-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 16 1 2 21 ->= 16 1 2 3 4 2 5 6 7 8 21 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 25 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 26 -> 11 11 2 3 9 13 17 25 4 23 26 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 45-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 25 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 26 -> 11 11 2 3 9 13 17 25 4 23 26 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 25->24, 26->25, 27->26, 28->27, 24->28, 29->29 }, it remains to prove termination of the 44-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 8 ->= 16 1 2 3 4 2 5 6 7 8 8 , 11 11 23 18 -> 11 11 2 3 9 13 17 24 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 25 -> 11 11 2 3 9 13 17 24 4 23 25 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 24 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 26 -> 10 11 2 3 9 13 17 24 4 23 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 27 -> 10 11 2 3 9 13 17 24 4 23 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 28 -> 10 11 2 3 9 13 17 24 4 23 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 24 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 25 -> 10 11 2 3 9 13 17 24 4 23 25 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 24 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 43-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 11 11 23 18 -> 11 11 2 3 9 13 17 24 4 23 18 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 25 -> 11 11 2 3 9 13 17 24 4 23 25 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 24 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 26 -> 10 11 2 3 9 13 17 24 4 23 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 27 -> 10 11 2 3 9 13 17 24 4 23 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 28 -> 10 11 2 3 9 13 17 24 4 23 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 24 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 25 -> 10 11 2 3 9 13 17 24 4 23 25 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 24 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 25->24, 24->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 42-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 16 ->= 12 10 11 12 13 14 15 3 4 16 6 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 41-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 5 ->= 16 1 2 3 4 2 5 6 7 8 5 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 40-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 11 11 23 24 -> 11 11 2 3 9 13 17 25 4 23 24 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 25 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 29 10 11 2 ->= 29 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 29 10 11 16 ->= 29 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 29 10 11 12 ->= 29 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 25->24, 26->25, 27->26, 28->27, 29->28, 24->29 }, it remains to prove termination of the 39-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 16 1 2 22 ->= 16 1 2 3 4 2 5 6 7 8 22 , 11 11 23 19 -> 11 11 2 3 9 13 17 24 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 25 -> 10 11 2 3 9 13 17 24 4 23 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 24 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 24 4 23 27 , 28 10 11 2 ->= 28 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 24 4 23 18 , 28 10 11 16 ->= 28 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 29 -> 10 11 2 3 9 13 17 24 4 23 29 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 24 4 23 19 , 28 10 11 12 ->= 28 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 38-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 11 11 23 19 -> 11 11 2 3 9 13 17 24 4 23 19 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 25 -> 10 11 2 3 9 13 17 24 4 23 25 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 24 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 24 4 23 27 , 28 10 11 2 ->= 28 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 24 4 23 18 , 28 10 11 16 ->= 28 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 29 -> 10 11 2 3 9 13 17 24 4 23 29 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 24 4 23 19 , 28 10 11 12 ->= 28 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 25->24, 24->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 37-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 16 1 2 20 ->= 16 1 2 3 4 2 5 6 7 8 20 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 28 10 11 2 ->= 28 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 28 10 11 16 ->= 28 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 29 -> 10 11 2 3 9 13 17 25 4 23 29 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 28 10 11 12 ->= 28 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29 }, it remains to prove termination of the 36-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 28 10 11 2 ->= 28 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 28 10 11 16 ->= 28 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 29 -> 10 11 2 3 9 13 17 25 4 23 29 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 28 10 11 12 ->= 28 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 26->24, 25->25, 27->26, 28->27, 29->28 }, it remains to prove termination of the 35-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 26 -> 10 11 2 3 9 13 17 25 4 23 26 , 27 10 11 2 ->= 27 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 27 10 11 16 ->= 27 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 28 -> 10 11 2 3 9 13 17 25 4 23 28 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 27 10 11 12 ->= 27 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 26->24, 25->25, 27->26, 28->27 }, it remains to prove termination of the 34-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 13 1 2 21 ->= 13 1 2 3 4 2 5 6 7 8 21 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 26 10 11 2 ->= 26 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 26 10 11 16 ->= 26 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 26 10 11 12 ->= 26 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27 }, it remains to prove termination of the 33-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 10 11 23 24 -> 10 11 2 3 9 13 17 25 4 23 24 , 26 10 11 2 ->= 26 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 23 18 -> 10 11 2 3 9 13 17 25 4 23 18 , 26 10 11 16 ->= 26 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 23 27 -> 10 11 2 3 9 13 17 25 4 23 27 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 23 19 -> 10 11 2 3 9 13 17 25 4 23 19 , 26 10 11 12 ->= 26 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 26->23, 23->24, 25->25, 27->26 }, it remains to prove termination of the 32-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 13 1 2 8 ->= 13 1 2 3 4 2 5 6 7 8 8 , 10 11 24 18 -> 10 11 2 3 9 13 17 25 4 24 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 24 26 -> 10 11 2 3 9 13 17 25 4 24 26 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 25 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26 }, it remains to prove termination of the 31-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 10 11 24 18 -> 10 11 2 3 9 13 17 25 4 24 18 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 24 26 -> 10 11 2 3 9 13 17 25 4 24 26 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 25 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 26->25, 25->26 }, it remains to prove termination of the 30-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 23 10 11 16 ->= 23 10 11 12 13 14 15 3 4 16 6 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 24 25 -> 10 11 2 3 9 13 17 26 4 24 25 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 26 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26 }, it remains to prove termination of the 29-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 13 1 2 5 ->= 13 1 2 3 4 2 5 6 7 8 5 , 10 11 24 25 -> 10 11 2 3 9 13 17 26 4 24 25 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 26 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25, 26->26 }, it remains to prove termination of the 28-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 10 11 24 25 -> 10 11 2 3 9 13 17 26 4 24 25 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 26 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 26->25 }, it remains to prove termination of the 27-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 13 1 2 22 ->= 13 1 2 3 4 2 5 6 7 8 22 , 10 11 24 19 -> 10 11 2 3 9 13 17 25 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 25->25 }, it remains to prove termination of the 26-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 10 11 24 19 -> 10 11 2 3 9 13 17 25 4 24 19 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 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 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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 1 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 1 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 1 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 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 | | 0 1 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, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23 }, it remains to prove termination of the 25-rule system { 0 1 2 3 ->= 0 1 2 3 4 2 5 6 7 8 3 , 9 10 11 2 ->= 9 10 11 12 13 14 15 3 4 16 7 , 9 10 11 12 ->= 9 10 11 12 13 14 15 3 4 16 17 , 18 1 2 3 ->= 18 1 2 3 4 2 5 6 7 8 3 , 19 10 11 2 ->= 19 10 11 12 13 14 15 3 4 16 7 , 19 10 11 12 ->= 19 10 11 12 13 14 15 3 4 16 17 , 5 1 2 3 ->= 5 1 2 3 4 2 5 6 7 8 3 , 20 10 11 2 ->= 20 10 11 12 13 14 15 3 4 16 7 , 20 10 11 12 ->= 20 10 11 12 13 14 15 3 4 16 17 , 6 1 2 3 ->= 6 1 2 3 4 2 5 6 7 8 3 , 6 1 2 21 ->= 6 1 2 3 4 2 5 6 7 8 21 , 17 10 11 2 ->= 17 10 11 12 13 14 15 3 4 16 7 , 6 1 2 8 ->= 6 1 2 3 4 2 5 6 7 8 8 , 17 10 11 16 ->= 17 10 11 12 13 14 15 3 4 16 6 , 6 1 2 5 ->= 6 1 2 3 4 2 5 6 7 8 5 , 6 1 2 22 ->= 6 1 2 3 4 2 5 6 7 8 22 , 17 10 11 12 ->= 17 10 11 12 13 14 15 3 4 16 17 , 6 1 2 20 ->= 6 1 2 3 4 2 5 6 7 8 20 , 16 1 2 3 ->= 16 1 2 3 4 2 5 6 7 8 3 , 12 10 11 2 ->= 12 10 11 12 13 14 15 3 4 16 7 , 12 10 11 12 ->= 12 10 11 12 13 14 15 3 4 16 17 , 13 1 2 3 ->= 13 1 2 3 4 2 5 6 7 8 3 , 23 10 11 2 ->= 23 10 11 12 13 14 15 3 4 16 7 , 23 10 11 12 ->= 23 10 11 12 13 14 15 3 4 16 17 , 13 1 2 20 ->= 13 1 2 3 4 2 5 6 7 8 20 } The system is trivially terminating.