YES After renaming modulo { 1->0, 0->1, 4->2, 3->3, 5->4, 2->5 }, it remains to prove termination of the 60-rule system { 0 0 1 -> 2 1 0 0 2 1 1 3 3 2 , 1 4 0 1 -> 1 4 5 5 2 3 1 5 5 5 , 0 1 0 1 -> 0 1 3 5 1 2 2 5 2 5 , 0 1 3 0 -> 0 5 3 3 5 2 2 3 1 0 , 5 0 1 4 -> 5 3 2 2 5 1 5 3 1 4 , 1 0 1 5 0 -> 5 5 1 1 1 2 1 0 5 0 , 0 1 4 1 0 -> 4 1 5 5 3 2 1 5 1 0 , 3 0 1 4 5 -> 5 0 2 1 5 4 4 5 5 3 , 2 2 4 3 1 -> 2 3 0 0 3 5 1 3 3 1 , 1 3 4 4 5 1 -> 5 5 1 0 5 1 1 5 3 2 , 0 1 1 3 4 2 -> 0 1 3 3 2 0 3 3 2 2 , 0 4 3 1 3 0 -> 0 5 5 0 3 1 2 2 3 0 , 0 4 2 0 5 4 -> 0 2 2 1 5 2 5 1 3 4 , 3 1 2 4 0 1 -> 2 0 2 5 3 2 2 5 2 1 , 3 1 4 3 5 4 -> 2 3 0 0 3 3 5 1 1 4 , 3 1 4 3 2 0 -> 2 5 2 3 1 3 0 0 2 0 , 2 0 5 0 0 1 -> 2 4 3 3 1 0 0 2 1 5 , 2 2 2 4 1 4 -> 3 2 3 3 5 2 5 2 0 2 , 4 5 1 2 4 0 -> 4 5 5 5 3 0 1 2 1 3 , 1 4 2 4 3 1 4 -> 1 2 5 2 2 2 3 1 1 4 , 0 1 4 4 3 5 4 -> 3 4 4 3 3 1 5 1 2 4 , 3 1 4 3 4 3 1 -> 0 0 5 2 0 5 1 0 2 1 , 3 0 1 0 4 4 0 -> 5 2 0 0 3 3 3 3 0 0 , 3 5 4 3 1 0 1 -> 5 2 0 5 3 2 3 0 0 5 , 3 3 4 3 2 4 3 -> 1 5 5 2 5 5 0 0 0 5 , 3 2 5 4 1 5 0 -> 3 1 2 3 5 2 2 1 1 0 , 3 2 3 5 0 2 2 -> 3 2 3 2 3 1 3 3 1 5 , 3 4 5 3 4 3 2 -> 3 4 0 1 3 1 1 5 2 5 , 2 2 4 3 5 0 1 -> 2 1 4 2 0 5 5 5 3 1 , 2 4 0 1 1 4 0 -> 4 4 5 5 5 4 4 4 0 2 , 2 4 0 3 0 5 3 -> 4 2 0 0 0 5 3 2 1 5 , 4 0 2 4 5 4 3 -> 4 4 0 2 5 3 1 1 3 2 , 4 0 4 2 5 4 0 -> 4 4 5 3 1 3 2 5 0 1 , 4 2 4 1 4 5 3 -> 4 0 0 2 5 3 1 0 3 1 , 1 0 ->= 5 3 3 5 5 3 3 2 2 5 , 3 1 ->= 0 2 5 5 5 1 3 1 1 5 , 0 1 3 ->= 0 4 5 5 3 0 3 1 5 1 , 5 1 4 ->= 5 2 3 5 3 5 2 3 5 0 , 5 0 4 ->= 5 5 2 1 1 5 2 1 0 4 , 5 3 2 ->= 5 3 2 3 5 2 1 2 2 5 , 3 1 1 ->= 3 3 2 5 2 2 2 5 3 5 , 4 2 5 ->= 4 2 2 5 5 1 5 5 2 3 , 1 1 3 0 ->= 1 3 2 5 5 3 1 1 0 0 , 1 4 2 1 ->= 5 4 4 4 5 3 3 3 5 3 , 0 1 0 5 ->= 0 5 5 5 4 4 5 5 3 2 , 5 1 4 1 ->= 5 2 0 3 2 3 2 0 4 3 , 5 2 5 4 ->= 5 3 2 1 1 5 1 1 3 4 , 3 1 4 3 ->= 0 3 5 1 2 1 3 1 3 2 , 4 5 1 1 ->= 4 2 1 3 1 2 5 5 3 1 , 1 5 0 1 3 ->= 1 5 0 5 3 2 3 5 3 1 , 5 2 0 4 0 ->= 3 3 5 5 2 2 0 3 3 0 , 4 0 0 4 1 ->= 4 4 5 5 1 1 0 2 0 3 , 0 0 0 0 2 4 ->= 0 2 1 3 2 3 5 5 0 3 , 0 2 4 0 2 5 ->= 0 1 2 3 2 3 5 3 2 5 , 5 2 4 5 3 4 ->= 5 2 2 1 1 0 0 0 5 0 , 0 1 3 4 4 3 3 ->= 3 4 5 3 3 3 0 5 3 3 , 5 2 3 0 1 0 1 ->= 5 1 5 3 3 1 0 5 0 1 , 3 1 1 4 5 5 4 ->= 0 0 2 3 4 5 5 5 0 2 , 3 2 1 4 3 2 5 ->= 3 0 2 4 1 3 1 5 3 1 , 2 1 4 2 5 0 5 ->= 0 5 5 5 0 3 0 3 2 5 } Applying context closure of depth 1 in the following form: System R over Sigma maps to { fold(xly) -> fold(xry) | l -> r in R, x,y in Sigma } over Sigma^2, where fold(a_1...a_n) = (a_1,a_2)...(a_{n-1},a_{n}) After renaming modulo { [0, 0]->0, [0, 1]->1, [1, 0]->2, [0, 2]->3, [2, 1]->4, [1, 1]->5, [1, 3]->6, [3, 3]->7, [3, 2]->8, [2, 0]->9, [1, 4]->10, [4, 0]->11, [4, 5]->12, [5, 5]->13, [5, 2]->14, [2, 3]->15, [3, 1]->16, [1, 5]->17, [5, 0]->18, [3, 5]->19, [5, 1]->20, [1, 2]->21, [2, 2]->22, [2, 5]->23, [3, 0]->24, [0, 5]->25, [5, 3]->26, [4, 1]->27, [0, 4]->28, [0, 3]->29, [5, 4]->30, [4, 4]->31, [2, 4]->32, [4, 3]->33, [3, 4]->34, [4, 2]->35 }, it remains to prove termination of the 2160-rule system { 0 0 1 2 -> 3 4 2 0 3 4 5 6 7 8 9 , 1 10 11 1 2 -> 1 10 12 13 14 15 16 17 13 13 18 , 0 1 2 1 2 -> 0 1 6 19 20 21 22 23 14 23 18 , 0 1 6 24 0 -> 0 25 26 7 19 14 22 15 16 2 0 , 25 18 1 10 11 -> 25 26 8 22 23 20 17 26 16 10 11 , 1 2 1 17 18 0 -> 25 13 20 5 5 21 4 2 25 18 0 , 0 1 10 27 2 0 -> 28 27 17 13 26 8 4 17 20 2 0 , 29 24 1 10 12 18 -> 25 18 3 4 17 30 31 12 13 26 24 , 3 22 32 33 16 2 -> 3 15 24 0 29 19 20 6 7 16 2 , 1 6 34 31 12 20 2 -> 25 13 20 2 25 20 5 17 26 8 9 , 0 1 5 6 34 35 9 -> 0 1 6 7 8 9 29 7 8 22 9 , 0 28 33 16 6 24 0 -> 0 25 13 18 29 16 21 22 15 24 0 , 0 28 35 9 25 30 11 -> 0 3 22 4 17 14 23 20 6 34 11 , 29 16 21 32 11 1 2 -> 3 9 3 23 26 8 22 23 14 4 2 , 29 16 10 33 19 30 11 -> 3 15 24 0 29 7 19 20 5 10 11 , 29 16 10 33 8 9 0 -> 3 23 14 15 16 6 24 0 3 9 0 , 3 9 25 18 0 1 2 -> 3 32 33 7 16 2 0 3 4 17 18 , 3 22 22 32 27 10 11 -> 29 8 15 7 19 14 23 14 9 3 9 , 28 12 20 21 32 11 0 -> 28 12 13 13 26 24 1 21 4 6 24 , 1 10 35 32 33 16 10 11 -> 1 21 23 14 22 22 15 16 5 10 11 , 0 1 10 31 33 19 30 11 -> 29 34 31 33 7 16 17 20 21 32 11 , 29 16 10 33 34 33 16 2 -> 0 0 25 14 9 25 20 2 3 4 2 , 29 24 1 2 28 31 11 0 -> 25 14 9 0 29 7 7 7 24 0 0 , 29 19 30 33 16 2 1 2 -> 25 14 9 25 26 8 15 24 0 25 18 , 29 7 34 33 8 32 33 24 -> 1 17 13 14 23 13 18 0 0 25 18 , 29 8 23 30 27 17 18 0 -> 29 16 21 15 19 14 22 4 5 2 0 , 29 8 15 19 18 3 22 9 -> 29 8 15 8 15 16 6 7 16 17 18 , 29 34 12 26 34 33 8 9 -> 29 34 11 1 6 16 5 17 14 23 18 , 3 22 32 33 19 18 1 2 -> 3 4 10 35 9 25 13 13 26 16 2 , 3 32 11 1 5 10 11 0 -> 28 31 12 13 13 30 31 31 11 3 9 , 3 32 11 29 24 25 26 24 -> 28 35 9 0 0 25 26 8 4 17 18 , 28 11 3 32 12 30 33 24 -> 28 31 11 3 23 26 16 5 6 8 9 , 28 11 28 35 23 30 11 0 -> 28 31 12 26 16 6 8 23 18 1 2 , 28 35 32 27 10 12 26 24 -> 28 11 0 3 23 26 16 2 29 16 2 , 1 2 0 ->= 25 26 7 19 13 26 7 8 22 23 18 , 29 16 2 ->= 0 3 23 13 13 20 6 16 5 17 18 , 0 1 6 24 ->= 0 28 12 13 26 24 29 16 17 20 2 , 25 20 10 11 ->= 25 14 15 19 26 19 14 15 19 18 0 , 25 18 28 11 ->= 25 13 14 4 5 17 14 4 2 28 11 , 25 26 8 9 ->= 25 26 8 15 19 14 4 21 22 23 18 , 29 16 5 2 ->= 29 7 8 23 14 22 22 23 26 19 18 , 28 35 23 18 ->= 28 35 22 23 13 20 17 13 14 15 24 , 1 5 6 24 0 ->= 1 6 8 23 13 26 16 5 2 0 0 , 1 10 35 4 2 ->= 25 30 31 31 12 26 7 7 19 26 24 , 0 1 2 25 18 ->= 0 25 13 13 30 31 12 13 26 8 9 , 25 20 10 27 2 ->= 25 14 9 29 8 15 8 9 28 33 24 , 25 14 23 30 11 ->= 25 26 8 4 5 17 20 5 6 34 11 , 29 16 10 33 24 ->= 0 29 19 20 21 4 6 16 6 8 9 , 28 12 20 5 2 ->= 28 35 4 6 16 21 23 13 26 16 2 , 1 17 18 1 6 24 ->= 1 17 18 25 26 8 15 19 26 16 2 , 25 14 9 28 11 0 ->= 29 7 19 13 14 22 9 29 7 24 0 , 28 11 0 28 27 2 ->= 28 31 12 13 20 5 2 3 9 29 24 , 0 0 0 0 3 32 11 ->= 0 3 4 6 8 15 19 13 18 29 24 , 0 3 32 11 3 23 18 ->= 0 1 21 15 8 15 19 26 8 23 18 , 25 14 32 12 26 34 11 ->= 25 14 22 4 5 2 0 0 25 18 0 , 0 1 6 34 31 33 7 24 ->= 29 34 12 26 7 7 24 25 26 7 24 , 25 14 15 24 1 2 1 2 ->= 25 20 17 26 7 16 2 25 18 1 2 , 29 16 5 10 12 13 30 11 ->= 0 0 3 15 34 12 13 13 18 3 9 , 29 8 4 10 33 8 23 18 ->= 29 24 3 32 27 6 16 17 26 16 2 , 3 4 10 35 23 18 25 18 ->= 0 25 13 13 18 29 24 29 8 23 18 , 0 0 1 5 -> 3 4 2 0 3 4 5 6 7 8 4 , 1 10 11 1 5 -> 1 10 12 13 14 15 16 17 13 13 20 , 0 1 2 1 5 -> 0 1 6 19 20 21 22 23 14 23 20 , 0 1 6 24 1 -> 0 25 26 7 19 14 22 15 16 2 1 , 25 18 1 10 27 -> 25 26 8 22 23 20 17 26 16 10 27 , 1 2 1 17 18 1 -> 25 13 20 5 5 21 4 2 25 18 1 , 0 1 10 27 2 1 -> 28 27 17 13 26 8 4 17 20 2 1 , 29 24 1 10 12 20 -> 25 18 3 4 17 30 31 12 13 26 16 , 3 22 32 33 16 5 -> 3 15 24 0 29 19 20 6 7 16 5 , 1 6 34 31 12 20 5 -> 25 13 20 2 25 20 5 17 26 8 4 , 0 1 5 6 34 35 4 -> 0 1 6 7 8 9 29 7 8 22 4 , 0 28 33 16 6 24 1 -> 0 25 13 18 29 16 21 22 15 24 1 , 0 28 35 9 25 30 27 -> 0 3 22 4 17 14 23 20 6 34 27 , 29 16 21 32 11 1 5 -> 3 9 3 23 26 8 22 23 14 4 5 , 29 16 10 33 19 30 27 -> 3 15 24 0 29 7 19 20 5 10 27 , 29 16 10 33 8 9 1 -> 3 23 14 15 16 6 24 0 3 9 1 , 3 9 25 18 0 1 5 -> 3 32 33 7 16 2 0 3 4 17 20 , 3 22 22 32 27 10 27 -> 29 8 15 7 19 14 23 14 9 3 4 , 28 12 20 21 32 11 1 -> 28 12 13 13 26 24 1 21 4 6 16 , 1 10 35 32 33 16 10 27 -> 1 21 23 14 22 22 15 16 5 10 27 , 0 1 10 31 33 19 30 27 -> 29 34 31 33 7 16 17 20 21 32 27 , 29 16 10 33 34 33 16 5 -> 0 0 25 14 9 25 20 2 3 4 5 , 29 24 1 2 28 31 11 1 -> 25 14 9 0 29 7 7 7 24 0 1 , 29 19 30 33 16 2 1 5 -> 25 14 9 25 26 8 15 24 0 25 20 , 29 7 34 33 8 32 33 16 -> 1 17 13 14 23 13 18 0 0 25 20 , 29 8 23 30 27 17 18 1 -> 29 16 21 15 19 14 22 4 5 2 1 , 29 8 15 19 18 3 22 4 -> 29 8 15 8 15 16 6 7 16 17 20 , 29 34 12 26 34 33 8 4 -> 29 34 11 1 6 16 5 17 14 23 20 , 3 22 32 33 19 18 1 5 -> 3 4 10 35 9 25 13 13 26 16 5 , 3 32 11 1 5 10 11 1 -> 28 31 12 13 13 30 31 31 11 3 4 , 3 32 11 29 24 25 26 16 -> 28 35 9 0 0 25 26 8 4 17 20 , 28 11 3 32 12 30 33 16 -> 28 31 11 3 23 26 16 5 6 8 4 , 28 11 28 35 23 30 11 1 -> 28 31 12 26 16 6 8 23 18 1 5 , 28 35 32 27 10 12 26 16 -> 28 11 0 3 23 26 16 2 29 16 5 , 1 2 1 ->= 25 26 7 19 13 26 7 8 22 23 20 , 29 16 5 ->= 0 3 23 13 13 20 6 16 5 17 20 , 0 1 6 16 ->= 0 28 12 13 26 24 29 16 17 20 5 , 25 20 10 27 ->= 25 14 15 19 26 19 14 15 19 18 1 , 25 18 28 27 ->= 25 13 14 4 5 17 14 4 2 28 27 , 25 26 8 4 ->= 25 26 8 15 19 14 4 21 22 23 20 , 29 16 5 5 ->= 29 7 8 23 14 22 22 23 26 19 20 , 28 35 23 20 ->= 28 35 22 23 13 20 17 13 14 15 16 , 1 5 6 24 1 ->= 1 6 8 23 13 26 16 5 2 0 1 , 1 10 35 4 5 ->= 25 30 31 31 12 26 7 7 19 26 16 , 0 1 2 25 20 ->= 0 25 13 13 30 31 12 13 26 8 4 , 25 20 10 27 5 ->= 25 14 9 29 8 15 8 9 28 33 16 , 25 14 23 30 27 ->= 25 26 8 4 5 17 20 5 6 34 27 , 29 16 10 33 16 ->= 0 29 19 20 21 4 6 16 6 8 4 , 28 12 20 5 5 ->= 28 35 4 6 16 21 23 13 26 16 5 , 1 17 18 1 6 16 ->= 1 17 18 25 26 8 15 19 26 16 5 , 25 14 9 28 11 1 ->= 29 7 19 13 14 22 9 29 7 24 1 , 28 11 0 28 27 5 ->= 28 31 12 13 20 5 2 3 9 29 16 , 0 0 0 0 3 32 27 ->= 0 3 4 6 8 15 19 13 18 29 16 , 0 3 32 11 3 23 20 ->= 0 1 21 15 8 15 19 26 8 23 20 , 25 14 32 12 26 34 27 ->= 25 14 22 4 5 2 0 0 25 18 1 , 0 1 6 34 31 33 7 16 ->= 29 34 12 26 7 7 24 25 26 7 16 , 25 14 15 24 1 2 1 5 ->= 25 20 17 26 7 16 2 25 18 1 5 , 29 16 5 10 12 13 30 27 ->= 0 0 3 15 34 12 13 13 18 3 4 , 29 8 4 10 33 8 23 20 ->= 29 24 3 32 27 6 16 17 26 16 5 , 3 4 10 35 23 18 25 20 ->= 0 25 13 13 18 29 24 29 8 23 20 , 0 0 1 21 -> 3 4 2 0 3 4 5 6 7 8 22 , 1 10 11 1 21 -> 1 10 12 13 14 15 16 17 13 13 14 , 0 1 2 1 21 -> 0 1 6 19 20 21 22 23 14 23 14 , 0 1 6 24 3 -> 0 25 26 7 19 14 22 15 16 2 3 , 25 18 1 10 35 -> 25 26 8 22 23 20 17 26 16 10 35 , 1 2 1 17 18 3 -> 25 13 20 5 5 21 4 2 25 18 3 , 0 1 10 27 2 3 -> 28 27 17 13 26 8 4 17 20 2 3 , 29 24 1 10 12 14 -> 25 18 3 4 17 30 31 12 13 26 8 , 3 22 32 33 16 21 -> 3 15 24 0 29 19 20 6 7 16 21 , 1 6 34 31 12 20 21 -> 25 13 20 2 25 20 5 17 26 8 22 , 0 1 5 6 34 35 22 -> 0 1 6 7 8 9 29 7 8 22 22 , 0 28 33 16 6 24 3 -> 0 25 13 18 29 16 21 22 15 24 3 , 0 28 35 9 25 30 35 -> 0 3 22 4 17 14 23 20 6 34 35 , 29 16 21 32 11 1 21 -> 3 9 3 23 26 8 22 23 14 4 21 , 29 16 10 33 19 30 35 -> 3 15 24 0 29 7 19 20 5 10 35 , 29 16 10 33 8 9 3 -> 3 23 14 15 16 6 24 0 3 9 3 , 3 9 25 18 0 1 21 -> 3 32 33 7 16 2 0 3 4 17 14 , 3 22 22 32 27 10 35 -> 29 8 15 7 19 14 23 14 9 3 22 , 28 12 20 21 32 11 3 -> 28 12 13 13 26 24 1 21 4 6 8 , 1 10 35 32 33 16 10 35 -> 1 21 23 14 22 22 15 16 5 10 35 , 0 1 10 31 33 19 30 35 -> 29 34 31 33 7 16 17 20 21 32 35 , 29 16 10 33 34 33 16 21 -> 0 0 25 14 9 25 20 2 3 4 21 , 29 24 1 2 28 31 11 3 -> 25 14 9 0 29 7 7 7 24 0 3 , 29 19 30 33 16 2 1 21 -> 25 14 9 25 26 8 15 24 0 25 14 , 29 7 34 33 8 32 33 8 -> 1 17 13 14 23 13 18 0 0 25 14 , 29 8 23 30 27 17 18 3 -> 29 16 21 15 19 14 22 4 5 2 3 , 29 8 15 19 18 3 22 22 -> 29 8 15 8 15 16 6 7 16 17 14 , 29 34 12 26 34 33 8 22 -> 29 34 11 1 6 16 5 17 14 23 14 , 3 22 32 33 19 18 1 21 -> 3 4 10 35 9 25 13 13 26 16 21 , 3 32 11 1 5 10 11 3 -> 28 31 12 13 13 30 31 31 11 3 22 , 3 32 11 29 24 25 26 8 -> 28 35 9 0 0 25 26 8 4 17 14 , 28 11 3 32 12 30 33 8 -> 28 31 11 3 23 26 16 5 6 8 22 , 28 11 28 35 23 30 11 3 -> 28 31 12 26 16 6 8 23 18 1 21 , 28 35 32 27 10 12 26 8 -> 28 11 0 3 23 26 16 2 29 16 21 , 1 2 3 ->= 25 26 7 19 13 26 7 8 22 23 14 , 29 16 21 ->= 0 3 23 13 13 20 6 16 5 17 14 , 0 1 6 8 ->= 0 28 12 13 26 24 29 16 17 20 21 , 25 20 10 35 ->= 25 14 15 19 26 19 14 15 19 18 3 , 25 18 28 35 ->= 25 13 14 4 5 17 14 4 2 28 35 , 25 26 8 22 ->= 25 26 8 15 19 14 4 21 22 23 14 , 29 16 5 21 ->= 29 7 8 23 14 22 22 23 26 19 14 , 28 35 23 14 ->= 28 35 22 23 13 20 17 13 14 15 8 , 1 5 6 24 3 ->= 1 6 8 23 13 26 16 5 2 0 3 , 1 10 35 4 21 ->= 25 30 31 31 12 26 7 7 19 26 8 , 0 1 2 25 14 ->= 0 25 13 13 30 31 12 13 26 8 22 , 25 20 10 27 21 ->= 25 14 9 29 8 15 8 9 28 33 8 , 25 14 23 30 35 ->= 25 26 8 4 5 17 20 5 6 34 35 , 29 16 10 33 8 ->= 0 29 19 20 21 4 6 16 6 8 22 , 28 12 20 5 21 ->= 28 35 4 6 16 21 23 13 26 16 21 , 1 17 18 1 6 8 ->= 1 17 18 25 26 8 15 19 26 16 21 , 25 14 9 28 11 3 ->= 29 7 19 13 14 22 9 29 7 24 3 , 28 11 0 28 27 21 ->= 28 31 12 13 20 5 2 3 9 29 8 , 0 0 0 0 3 32 35 ->= 0 3 4 6 8 15 19 13 18 29 8 , 0 3 32 11 3 23 14 ->= 0 1 21 15 8 15 19 26 8 23 14 , 25 14 32 12 26 34 35 ->= 25 14 22 4 5 2 0 0 25 18 3 , 0 1 6 34 31 33 7 8 ->= 29 34 12 26 7 7 24 25 26 7 8 , 25 14 15 24 1 2 1 21 ->= 25 20 17 26 7 16 2 25 18 1 21 , 29 16 5 10 12 13 30 35 ->= 0 0 3 15 34 12 13 13 18 3 22 , 29 8 4 10 33 8 23 14 ->= 29 24 3 32 27 6 16 17 26 16 21 , 3 4 10 35 23 18 25 14 ->= 0 25 13 13 18 29 24 29 8 23 14 , 0 0 1 6 -> 3 4 2 0 3 4 5 6 7 8 15 , 1 10 11 1 6 -> 1 10 12 13 14 15 16 17 13 13 26 , 0 1 2 1 6 -> 0 1 6 19 20 21 22 23 14 23 26 , 0 1 6 24 29 -> 0 25 26 7 19 14 22 15 16 2 29 , 25 18 1 10 33 -> 25 26 8 22 23 20 17 26 16 10 33 , 1 2 1 17 18 29 -> 25 13 20 5 5 21 4 2 25 18 29 , 0 1 10 27 2 29 -> 28 27 17 13 26 8 4 17 20 2 29 , 29 24 1 10 12 26 -> 25 18 3 4 17 30 31 12 13 26 7 , 3 22 32 33 16 6 -> 3 15 24 0 29 19 20 6 7 16 6 , 1 6 34 31 12 20 6 -> 25 13 20 2 25 20 5 17 26 8 15 , 0 1 5 6 34 35 15 -> 0 1 6 7 8 9 29 7 8 22 15 , 0 28 33 16 6 24 29 -> 0 25 13 18 29 16 21 22 15 24 29 , 0 28 35 9 25 30 33 -> 0 3 22 4 17 14 23 20 6 34 33 , 29 16 21 32 11 1 6 -> 3 9 3 23 26 8 22 23 14 4 6 , 29 16 10 33 19 30 33 -> 3 15 24 0 29 7 19 20 5 10 33 , 29 16 10 33 8 9 29 -> 3 23 14 15 16 6 24 0 3 9 29 , 3 9 25 18 0 1 6 -> 3 32 33 7 16 2 0 3 4 17 26 , 3 22 22 32 27 10 33 -> 29 8 15 7 19 14 23 14 9 3 15 , 28 12 20 21 32 11 29 -> 28 12 13 13 26 24 1 21 4 6 7 , 1 10 35 32 33 16 10 33 -> 1 21 23 14 22 22 15 16 5 10 33 , 0 1 10 31 33 19 30 33 -> 29 34 31 33 7 16 17 20 21 32 33 , 29 16 10 33 34 33 16 6 -> 0 0 25 14 9 25 20 2 3 4 6 , 29 24 1 2 28 31 11 29 -> 25 14 9 0 29 7 7 7 24 0 29 , 29 19 30 33 16 2 1 6 -> 25 14 9 25 26 8 15 24 0 25 26 , 29 7 34 33 8 32 33 7 -> 1 17 13 14 23 13 18 0 0 25 26 , 29 8 23 30 27 17 18 29 -> 29 16 21 15 19 14 22 4 5 2 29 , 29 8 15 19 18 3 22 15 -> 29 8 15 8 15 16 6 7 16 17 26 , 29 34 12 26 34 33 8 15 -> 29 34 11 1 6 16 5 17 14 23 26 , 3 22 32 33 19 18 1 6 -> 3 4 10 35 9 25 13 13 26 16 6 , 3 32 11 1 5 10 11 29 -> 28 31 12 13 13 30 31 31 11 3 15 , 3 32 11 29 24 25 26 7 -> 28 35 9 0 0 25 26 8 4 17 26 , 28 11 3 32 12 30 33 7 -> 28 31 11 3 23 26 16 5 6 8 15 , 28 11 28 35 23 30 11 29 -> 28 31 12 26 16 6 8 23 18 1 6 , 28 35 32 27 10 12 26 7 -> 28 11 0 3 23 26 16 2 29 16 6 , 1 2 29 ->= 25 26 7 19 13 26 7 8 22 23 26 , 29 16 6 ->= 0 3 23 13 13 20 6 16 5 17 26 , 0 1 6 7 ->= 0 28 12 13 26 24 29 16 17 20 6 , 25 20 10 33 ->= 25 14 15 19 26 19 14 15 19 18 29 , 25 18 28 33 ->= 25 13 14 4 5 17 14 4 2 28 33 , 25 26 8 15 ->= 25 26 8 15 19 14 4 21 22 23 26 , 29 16 5 6 ->= 29 7 8 23 14 22 22 23 26 19 26 , 28 35 23 26 ->= 28 35 22 23 13 20 17 13 14 15 7 , 1 5 6 24 29 ->= 1 6 8 23 13 26 16 5 2 0 29 , 1 10 35 4 6 ->= 25 30 31 31 12 26 7 7 19 26 7 , 0 1 2 25 26 ->= 0 25 13 13 30 31 12 13 26 8 15 , 25 20 10 27 6 ->= 25 14 9 29 8 15 8 9 28 33 7 , 25 14 23 30 33 ->= 25 26 8 4 5 17 20 5 6 34 33 , 29 16 10 33 7 ->= 0 29 19 20 21 4 6 16 6 8 15 , 28 12 20 5 6 ->= 28 35 4 6 16 21 23 13 26 16 6 , 1 17 18 1 6 7 ->= 1 17 18 25 26 8 15 19 26 16 6 , 25 14 9 28 11 29 ->= 29 7 19 13 14 22 9 29 7 24 29 , 28 11 0 28 27 6 ->= 28 31 12 13 20 5 2 3 9 29 7 , 0 0 0 0 3 32 33 ->= 0 3 4 6 8 15 19 13 18 29 7 , 0 3 32 11 3 23 26 ->= 0 1 21 15 8 15 19 26 8 23 26 , 25 14 32 12 26 34 33 ->= 25 14 22 4 5 2 0 0 25 18 29 , 0 1 6 34 31 33 7 7 ->= 29 34 12 26 7 7 24 25 26 7 7 , 25 14 15 24 1 2 1 6 ->= 25 20 17 26 7 16 2 25 18 1 6 , 29 16 5 10 12 13 30 33 ->= 0 0 3 15 34 12 13 13 18 3 15 , 29 8 4 10 33 8 23 26 ->= 29 24 3 32 27 6 16 17 26 16 6 , 3 4 10 35 23 18 25 26 ->= 0 25 13 13 18 29 24 29 8 23 26 , 0 0 1 10 -> 3 4 2 0 3 4 5 6 7 8 32 , 1 10 11 1 10 -> 1 10 12 13 14 15 16 17 13 13 30 , 0 1 2 1 10 -> 0 1 6 19 20 21 22 23 14 23 30 , 0 1 6 24 28 -> 0 25 26 7 19 14 22 15 16 2 28 , 25 18 1 10 31 -> 25 26 8 22 23 20 17 26 16 10 31 , 1 2 1 17 18 28 -> 25 13 20 5 5 21 4 2 25 18 28 , 0 1 10 27 2 28 -> 28 27 17 13 26 8 4 17 20 2 28 , 29 24 1 10 12 30 -> 25 18 3 4 17 30 31 12 13 26 34 , 3 22 32 33 16 10 -> 3 15 24 0 29 19 20 6 7 16 10 , 1 6 34 31 12 20 10 -> 25 13 20 2 25 20 5 17 26 8 32 , 0 1 5 6 34 35 32 -> 0 1 6 7 8 9 29 7 8 22 32 , 0 28 33 16 6 24 28 -> 0 25 13 18 29 16 21 22 15 24 28 , 0 28 35 9 25 30 31 -> 0 3 22 4 17 14 23 20 6 34 31 , 29 16 21 32 11 1 10 -> 3 9 3 23 26 8 22 23 14 4 10 , 29 16 10 33 19 30 31 -> 3 15 24 0 29 7 19 20 5 10 31 , 29 16 10 33 8 9 28 -> 3 23 14 15 16 6 24 0 3 9 28 , 3 9 25 18 0 1 10 -> 3 32 33 7 16 2 0 3 4 17 30 , 3 22 22 32 27 10 31 -> 29 8 15 7 19 14 23 14 9 3 32 , 28 12 20 21 32 11 28 -> 28 12 13 13 26 24 1 21 4 6 34 , 1 10 35 32 33 16 10 31 -> 1 21 23 14 22 22 15 16 5 10 31 , 0 1 10 31 33 19 30 31 -> 29 34 31 33 7 16 17 20 21 32 31 , 29 16 10 33 34 33 16 10 -> 0 0 25 14 9 25 20 2 3 4 10 , 29 24 1 2 28 31 11 28 -> 25 14 9 0 29 7 7 7 24 0 28 , 29 19 30 33 16 2 1 10 -> 25 14 9 25 26 8 15 24 0 25 30 , 29 7 34 33 8 32 33 34 -> 1 17 13 14 23 13 18 0 0 25 30 , 29 8 23 30 27 17 18 28 -> 29 16 21 15 19 14 22 4 5 2 28 , 29 8 15 19 18 3 22 32 -> 29 8 15 8 15 16 6 7 16 17 30 , 29 34 12 26 34 33 8 32 -> 29 34 11 1 6 16 5 17 14 23 30 , 3 22 32 33 19 18 1 10 -> 3 4 10 35 9 25 13 13 26 16 10 , 3 32 11 1 5 10 11 28 -> 28 31 12 13 13 30 31 31 11 3 32 , 3 32 11 29 24 25 26 34 -> 28 35 9 0 0 25 26 8 4 17 30 , 28 11 3 32 12 30 33 34 -> 28 31 11 3 23 26 16 5 6 8 32 , 28 11 28 35 23 30 11 28 -> 28 31 12 26 16 6 8 23 18 1 10 , 28 35 32 27 10 12 26 34 -> 28 11 0 3 23 26 16 2 29 16 10 , 1 2 28 ->= 25 26 7 19 13 26 7 8 22 23 30 , 29 16 10 ->= 0 3 23 13 13 20 6 16 5 17 30 , 0 1 6 34 ->= 0 28 12 13 26 24 29 16 17 20 10 , 25 20 10 31 ->= 25 14 15 19 26 19 14 15 19 18 28 , 25 18 28 31 ->= 25 13 14 4 5 17 14 4 2 28 31 , 25 26 8 32 ->= 25 26 8 15 19 14 4 21 22 23 30 , 29 16 5 10 ->= 29 7 8 23 14 22 22 23 26 19 30 , 28 35 23 30 ->= 28 35 22 23 13 20 17 13 14 15 34 , 1 5 6 24 28 ->= 1 6 8 23 13 26 16 5 2 0 28 , 1 10 35 4 10 ->= 25 30 31 31 12 26 7 7 19 26 34 , 0 1 2 25 30 ->= 0 25 13 13 30 31 12 13 26 8 32 , 25 20 10 27 10 ->= 25 14 9 29 8 15 8 9 28 33 34 , 25 14 23 30 31 ->= 25 26 8 4 5 17 20 5 6 34 31 , 29 16 10 33 34 ->= 0 29 19 20 21 4 6 16 6 8 32 , 28 12 20 5 10 ->= 28 35 4 6 16 21 23 13 26 16 10 , 1 17 18 1 6 34 ->= 1 17 18 25 26 8 15 19 26 16 10 , 25 14 9 28 11 28 ->= 29 7 19 13 14 22 9 29 7 24 28 , 28 11 0 28 27 10 ->= 28 31 12 13 20 5 2 3 9 29 34 , 0 0 0 0 3 32 31 ->= 0 3 4 6 8 15 19 13 18 29 34 , 0 3 32 11 3 23 30 ->= 0 1 21 15 8 15 19 26 8 23 30 , 25 14 32 12 26 34 31 ->= 25 14 22 4 5 2 0 0 25 18 28 , 0 1 6 34 31 33 7 34 ->= 29 34 12 26 7 7 24 25 26 7 34 , 25 14 15 24 1 2 1 10 ->= 25 20 17 26 7 16 2 25 18 1 10 , 29 16 5 10 12 13 30 31 ->= 0 0 3 15 34 12 13 13 18 3 32 , 29 8 4 10 33 8 23 30 ->= 29 24 3 32 27 6 16 17 26 16 10 , 3 4 10 35 23 18 25 30 ->= 0 25 13 13 18 29 24 29 8 23 30 , 0 0 1 17 -> 3 4 2 0 3 4 5 6 7 8 23 , 1 10 11 1 17 -> 1 10 12 13 14 15 16 17 13 13 13 , 0 1 2 1 17 -> 0 1 6 19 20 21 22 23 14 23 13 , 0 1 6 24 25 -> 0 25 26 7 19 14 22 15 16 2 25 , 25 18 1 10 12 -> 25 26 8 22 23 20 17 26 16 10 12 , 1 2 1 17 18 25 -> 25 13 20 5 5 21 4 2 25 18 25 , 0 1 10 27 2 25 -> 28 27 17 13 26 8 4 17 20 2 25 , 29 24 1 10 12 13 -> 25 18 3 4 17 30 31 12 13 26 19 , 3 22 32 33 16 17 -> 3 15 24 0 29 19 20 6 7 16 17 , 1 6 34 31 12 20 17 -> 25 13 20 2 25 20 5 17 26 8 23 , 0 1 5 6 34 35 23 -> 0 1 6 7 8 9 29 7 8 22 23 , 0 28 33 16 6 24 25 -> 0 25 13 18 29 16 21 22 15 24 25 , 0 28 35 9 25 30 12 -> 0 3 22 4 17 14 23 20 6 34 12 , 29 16 21 32 11 1 17 -> 3 9 3 23 26 8 22 23 14 4 17 , 29 16 10 33 19 30 12 -> 3 15 24 0 29 7 19 20 5 10 12 , 29 16 10 33 8 9 25 -> 3 23 14 15 16 6 24 0 3 9 25 , 3 9 25 18 0 1 17 -> 3 32 33 7 16 2 0 3 4 17 13 , 3 22 22 32 27 10 12 -> 29 8 15 7 19 14 23 14 9 3 23 , 28 12 20 21 32 11 25 -> 28 12 13 13 26 24 1 21 4 6 19 , 1 10 35 32 33 16 10 12 -> 1 21 23 14 22 22 15 16 5 10 12 , 0 1 10 31 33 19 30 12 -> 29 34 31 33 7 16 17 20 21 32 12 , 29 16 10 33 34 33 16 17 -> 0 0 25 14 9 25 20 2 3 4 17 , 29 24 1 2 28 31 11 25 -> 25 14 9 0 29 7 7 7 24 0 25 , 29 19 30 33 16 2 1 17 -> 25 14 9 25 26 8 15 24 0 25 13 , 29 7 34 33 8 32 33 19 -> 1 17 13 14 23 13 18 0 0 25 13 , 29 8 23 30 27 17 18 25 -> 29 16 21 15 19 14 22 4 5 2 25 , 29 8 15 19 18 3 22 23 -> 29 8 15 8 15 16 6 7 16 17 13 , 29 34 12 26 34 33 8 23 -> 29 34 11 1 6 16 5 17 14 23 13 , 3 22 32 33 19 18 1 17 -> 3 4 10 35 9 25 13 13 26 16 17 , 3 32 11 1 5 10 11 25 -> 28 31 12 13 13 30 31 31 11 3 23 , 3 32 11 29 24 25 26 19 -> 28 35 9 0 0 25 26 8 4 17 13 , 28 11 3 32 12 30 33 19 -> 28 31 11 3 23 26 16 5 6 8 23 , 28 11 28 35 23 30 11 25 -> 28 31 12 26 16 6 8 23 18 1 17 , 28 35 32 27 10 12 26 19 -> 28 11 0 3 23 26 16 2 29 16 17 , 1 2 25 ->= 25 26 7 19 13 26 7 8 22 23 13 , 29 16 17 ->= 0 3 23 13 13 20 6 16 5 17 13 , 0 1 6 19 ->= 0 28 12 13 26 24 29 16 17 20 17 , 25 20 10 12 ->= 25 14 15 19 26 19 14 15 19 18 25 , 25 18 28 12 ->= 25 13 14 4 5 17 14 4 2 28 12 , 25 26 8 23 ->= 25 26 8 15 19 14 4 21 22 23 13 , 29 16 5 17 ->= 29 7 8 23 14 22 22 23 26 19 13 , 28 35 23 13 ->= 28 35 22 23 13 20 17 13 14 15 19 , 1 5 6 24 25 ->= 1 6 8 23 13 26 16 5 2 0 25 , 1 10 35 4 17 ->= 25 30 31 31 12 26 7 7 19 26 19 , 0 1 2 25 13 ->= 0 25 13 13 30 31 12 13 26 8 23 , 25 20 10 27 17 ->= 25 14 9 29 8 15 8 9 28 33 19 , 25 14 23 30 12 ->= 25 26 8 4 5 17 20 5 6 34 12 , 29 16 10 33 19 ->= 0 29 19 20 21 4 6 16 6 8 23 , 28 12 20 5 17 ->= 28 35 4 6 16 21 23 13 26 16 17 , 1 17 18 1 6 19 ->= 1 17 18 25 26 8 15 19 26 16 17 , 25 14 9 28 11 25 ->= 29 7 19 13 14 22 9 29 7 24 25 , 28 11 0 28 27 17 ->= 28 31 12 13 20 5 2 3 9 29 19 , 0 0 0 0 3 32 12 ->= 0 3 4 6 8 15 19 13 18 29 19 , 0 3 32 11 3 23 13 ->= 0 1 21 15 8 15 19 26 8 23 13 , 25 14 32 12 26 34 12 ->= 25 14 22 4 5 2 0 0 25 18 25 , 0 1 6 34 31 33 7 19 ->= 29 34 12 26 7 7 24 25 26 7 19 , 25 14 15 24 1 2 1 17 ->= 25 20 17 26 7 16 2 25 18 1 17 , 29 16 5 10 12 13 30 12 ->= 0 0 3 15 34 12 13 13 18 3 23 , 29 8 4 10 33 8 23 13 ->= 29 24 3 32 27 6 16 17 26 16 17 , 3 4 10 35 23 18 25 13 ->= 0 25 13 13 18 29 24 29 8 23 13 , 2 0 1 2 -> 21 4 2 0 3 4 5 6 7 8 9 , 5 10 11 1 2 -> 5 10 12 13 14 15 16 17 13 13 18 , 2 1 2 1 2 -> 2 1 6 19 20 21 22 23 14 23 18 , 2 1 6 24 0 -> 2 25 26 7 19 14 22 15 16 2 0 , 17 18 1 10 11 -> 17 26 8 22 23 20 17 26 16 10 11 , 5 2 1 17 18 0 -> 17 13 20 5 5 21 4 2 25 18 0 , 2 1 10 27 2 0 -> 10 27 17 13 26 8 4 17 20 2 0 , 6 24 1 10 12 18 -> 17 18 3 4 17 30 31 12 13 26 24 , 21 22 32 33 16 2 -> 21 15 24 0 29 19 20 6 7 16 2 , 5 6 34 31 12 20 2 -> 17 13 20 2 25 20 5 17 26 8 9 , 2 1 5 6 34 35 9 -> 2 1 6 7 8 9 29 7 8 22 9 , 2 28 33 16 6 24 0 -> 2 25 13 18 29 16 21 22 15 24 0 , 2 28 35 9 25 30 11 -> 2 3 22 4 17 14 23 20 6 34 11 , 6 16 21 32 11 1 2 -> 21 9 3 23 26 8 22 23 14 4 2 , 6 16 10 33 19 30 11 -> 21 15 24 0 29 7 19 20 5 10 11 , 6 16 10 33 8 9 0 -> 21 23 14 15 16 6 24 0 3 9 0 , 21 9 25 18 0 1 2 -> 21 32 33 7 16 2 0 3 4 17 18 , 21 22 22 32 27 10 11 -> 6 8 15 7 19 14 23 14 9 3 9 , 10 12 20 21 32 11 0 -> 10 12 13 13 26 24 1 21 4 6 24 , 5 10 35 32 33 16 10 11 -> 5 21 23 14 22 22 15 16 5 10 11 , 2 1 10 31 33 19 30 11 -> 6 34 31 33 7 16 17 20 21 32 11 , 6 16 10 33 34 33 16 2 -> 2 0 25 14 9 25 20 2 3 4 2 , 6 24 1 2 28 31 11 0 -> 17 14 9 0 29 7 7 7 24 0 0 , 6 19 30 33 16 2 1 2 -> 17 14 9 25 26 8 15 24 0 25 18 , 6 7 34 33 8 32 33 24 -> 5 17 13 14 23 13 18 0 0 25 18 , 6 8 23 30 27 17 18 0 -> 6 16 21 15 19 14 22 4 5 2 0 , 6 8 15 19 18 3 22 9 -> 6 8 15 8 15 16 6 7 16 17 18 , 6 34 12 26 34 33 8 9 -> 6 34 11 1 6 16 5 17 14 23 18 , 21 22 32 33 19 18 1 2 -> 21 4 10 35 9 25 13 13 26 16 2 , 21 32 11 1 5 10 11 0 -> 10 31 12 13 13 30 31 31 11 3 9 , 21 32 11 29 24 25 26 24 -> 10 35 9 0 0 25 26 8 4 17 18 , 10 11 3 32 12 30 33 24 -> 10 31 11 3 23 26 16 5 6 8 9 , 10 11 28 35 23 30 11 0 -> 10 31 12 26 16 6 8 23 18 1 2 , 10 35 32 27 10 12 26 24 -> 10 11 0 3 23 26 16 2 29 16 2 , 5 2 0 ->= 17 26 7 19 13 26 7 8 22 23 18 , 6 16 2 ->= 2 3 23 13 13 20 6 16 5 17 18 , 2 1 6 24 ->= 2 28 12 13 26 24 29 16 17 20 2 , 17 20 10 11 ->= 17 14 15 19 26 19 14 15 19 18 0 , 17 18 28 11 ->= 17 13 14 4 5 17 14 4 2 28 11 , 17 26 8 9 ->= 17 26 8 15 19 14 4 21 22 23 18 , 6 16 5 2 ->= 6 7 8 23 14 22 22 23 26 19 18 , 10 35 23 18 ->= 10 35 22 23 13 20 17 13 14 15 24 , 5 5 6 24 0 ->= 5 6 8 23 13 26 16 5 2 0 0 , 5 10 35 4 2 ->= 17 30 31 31 12 26 7 7 19 26 24 , 2 1 2 25 18 ->= 2 25 13 13 30 31 12 13 26 8 9 , 17 20 10 27 2 ->= 17 14 9 29 8 15 8 9 28 33 24 , 17 14 23 30 11 ->= 17 26 8 4 5 17 20 5 6 34 11 , 6 16 10 33 24 ->= 2 29 19 20 21 4 6 16 6 8 9 , 10 12 20 5 2 ->= 10 35 4 6 16 21 23 13 26 16 2 , 5 17 18 1 6 24 ->= 5 17 18 25 26 8 15 19 26 16 2 , 17 14 9 28 11 0 ->= 6 7 19 13 14 22 9 29 7 24 0 , 10 11 0 28 27 2 ->= 10 31 12 13 20 5 2 3 9 29 24 , 2 0 0 0 3 32 11 ->= 2 3 4 6 8 15 19 13 18 29 24 , 2 3 32 11 3 23 18 ->= 2 1 21 15 8 15 19 26 8 23 18 , 17 14 32 12 26 34 11 ->= 17 14 22 4 5 2 0 0 25 18 0 , 2 1 6 34 31 33 7 24 ->= 6 34 12 26 7 7 24 25 26 7 24 , 17 14 15 24 1 2 1 2 ->= 17 20 17 26 7 16 2 25 18 1 2 , 6 16 5 10 12 13 30 11 ->= 2 0 3 15 34 12 13 13 18 3 9 , 6 8 4 10 33 8 23 18 ->= 6 24 3 32 27 6 16 17 26 16 2 , 21 4 10 35 23 18 25 18 ->= 2 25 13 13 18 29 24 29 8 23 18 , 2 0 1 5 -> 21 4 2 0 3 4 5 6 7 8 4 , 5 10 11 1 5 -> 5 10 12 13 14 15 16 17 13 13 20 , 2 1 2 1 5 -> 2 1 6 19 20 21 22 23 14 23 20 , 2 1 6 24 1 -> 2 25 26 7 19 14 22 15 16 2 1 , 17 18 1 10 27 -> 17 26 8 22 23 20 17 26 16 10 27 , 5 2 1 17 18 1 -> 17 13 20 5 5 21 4 2 25 18 1 , 2 1 10 27 2 1 -> 10 27 17 13 26 8 4 17 20 2 1 , 6 24 1 10 12 20 -> 17 18 3 4 17 30 31 12 13 26 16 , 21 22 32 33 16 5 -> 21 15 24 0 29 19 20 6 7 16 5 , 5 6 34 31 12 20 5 -> 17 13 20 2 25 20 5 17 26 8 4 , 2 1 5 6 34 35 4 -> 2 1 6 7 8 9 29 7 8 22 4 , 2 28 33 16 6 24 1 -> 2 25 13 18 29 16 21 22 15 24 1 , 2 28 35 9 25 30 27 -> 2 3 22 4 17 14 23 20 6 34 27 , 6 16 21 32 11 1 5 -> 21 9 3 23 26 8 22 23 14 4 5 , 6 16 10 33 19 30 27 -> 21 15 24 0 29 7 19 20 5 10 27 , 6 16 10 33 8 9 1 -> 21 23 14 15 16 6 24 0 3 9 1 , 21 9 25 18 0 1 5 -> 21 32 33 7 16 2 0 3 4 17 20 , 21 22 22 32 27 10 27 -> 6 8 15 7 19 14 23 14 9 3 4 , 10 12 20 21 32 11 1 -> 10 12 13 13 26 24 1 21 4 6 16 , 5 10 35 32 33 16 10 27 -> 5 21 23 14 22 22 15 16 5 10 27 , 2 1 10 31 33 19 30 27 -> 6 34 31 33 7 16 17 20 21 32 27 , 6 16 10 33 34 33 16 5 -> 2 0 25 14 9 25 20 2 3 4 5 , 6 24 1 2 28 31 11 1 -> 17 14 9 0 29 7 7 7 24 0 1 , 6 19 30 33 16 2 1 5 -> 17 14 9 25 26 8 15 24 0 25 20 , 6 7 34 33 8 32 33 16 -> 5 17 13 14 23 13 18 0 0 25 20 , 6 8 23 30 27 17 18 1 -> 6 16 21 15 19 14 22 4 5 2 1 , 6 8 15 19 18 3 22 4 -> 6 8 15 8 15 16 6 7 16 17 20 , 6 34 12 26 34 33 8 4 -> 6 34 11 1 6 16 5 17 14 23 20 , 21 22 32 33 19 18 1 5 -> 21 4 10 35 9 25 13 13 26 16 5 , 21 32 11 1 5 10 11 1 -> 10 31 12 13 13 30 31 31 11 3 4 , 21 32 11 29 24 25 26 16 -> 10 35 9 0 0 25 26 8 4 17 20 , 10 11 3 32 12 30 33 16 -> 10 31 11 3 23 26 16 5 6 8 4 , 10 11 28 35 23 30 11 1 -> 10 31 12 26 16 6 8 23 18 1 5 , 10 35 32 27 10 12 26 16 -> 10 11 0 3 23 26 16 2 29 16 5 , 5 2 1 ->= 17 26 7 19 13 26 7 8 22 23 20 , 6 16 5 ->= 2 3 23 13 13 20 6 16 5 17 20 , 2 1 6 16 ->= 2 28 12 13 26 24 29 16 17 20 5 , 17 20 10 27 ->= 17 14 15 19 26 19 14 15 19 18 1 , 17 18 28 27 ->= 17 13 14 4 5 17 14 4 2 28 27 , 17 26 8 4 ->= 17 26 8 15 19 14 4 21 22 23 20 , 6 16 5 5 ->= 6 7 8 23 14 22 22 23 26 19 20 , 10 35 23 20 ->= 10 35 22 23 13 20 17 13 14 15 16 , 5 5 6 24 1 ->= 5 6 8 23 13 26 16 5 2 0 1 , 5 10 35 4 5 ->= 17 30 31 31 12 26 7 7 19 26 16 , 2 1 2 25 20 ->= 2 25 13 13 30 31 12 13 26 8 4 , 17 20 10 27 5 ->= 17 14 9 29 8 15 8 9 28 33 16 , 17 14 23 30 27 ->= 17 26 8 4 5 17 20 5 6 34 27 , 6 16 10 33 16 ->= 2 29 19 20 21 4 6 16 6 8 4 , 10 12 20 5 5 ->= 10 35 4 6 16 21 23 13 26 16 5 , 5 17 18 1 6 16 ->= 5 17 18 25 26 8 15 19 26 16 5 , 17 14 9 28 11 1 ->= 6 7 19 13 14 22 9 29 7 24 1 , 10 11 0 28 27 5 ->= 10 31 12 13 20 5 2 3 9 29 16 , 2 0 0 0 3 32 27 ->= 2 3 4 6 8 15 19 13 18 29 16 , 2 3 32 11 3 23 20 ->= 2 1 21 15 8 15 19 26 8 23 20 , 17 14 32 12 26 34 27 ->= 17 14 22 4 5 2 0 0 25 18 1 , 2 1 6 34 31 33 7 16 ->= 6 34 12 26 7 7 24 25 26 7 16 , 17 14 15 24 1 2 1 5 ->= 17 20 17 26 7 16 2 25 18 1 5 , 6 16 5 10 12 13 30 27 ->= 2 0 3 15 34 12 13 13 18 3 4 , 6 8 4 10 33 8 23 20 ->= 6 24 3 32 27 6 16 17 26 16 5 , 21 4 10 35 23 18 25 20 ->= 2 25 13 13 18 29 24 29 8 23 20 , 2 0 1 21 -> 21 4 2 0 3 4 5 6 7 8 22 , 5 10 11 1 21 -> 5 10 12 13 14 15 16 17 13 13 14 , 2 1 2 1 21 -> 2 1 6 19 20 21 22 23 14 23 14 , 2 1 6 24 3 -> 2 25 26 7 19 14 22 15 16 2 3 , 17 18 1 10 35 -> 17 26 8 22 23 20 17 26 16 10 35 , 5 2 1 17 18 3 -> 17 13 20 5 5 21 4 2 25 18 3 , 2 1 10 27 2 3 -> 10 27 17 13 26 8 4 17 20 2 3 , 6 24 1 10 12 14 -> 17 18 3 4 17 30 31 12 13 26 8 , 21 22 32 33 16 21 -> 21 15 24 0 29 19 20 6 7 16 21 , 5 6 34 31 12 20 21 -> 17 13 20 2 25 20 5 17 26 8 22 , 2 1 5 6 34 35 22 -> 2 1 6 7 8 9 29 7 8 22 22 , 2 28 33 16 6 24 3 -> 2 25 13 18 29 16 21 22 15 24 3 , 2 28 35 9 25 30 35 -> 2 3 22 4 17 14 23 20 6 34 35 , 6 16 21 32 11 1 21 -> 21 9 3 23 26 8 22 23 14 4 21 , 6 16 10 33 19 30 35 -> 21 15 24 0 29 7 19 20 5 10 35 , 6 16 10 33 8 9 3 -> 21 23 14 15 16 6 24 0 3 9 3 , 21 9 25 18 0 1 21 -> 21 32 33 7 16 2 0 3 4 17 14 , 21 22 22 32 27 10 35 -> 6 8 15 7 19 14 23 14 9 3 22 , 10 12 20 21 32 11 3 -> 10 12 13 13 26 24 1 21 4 6 8 , 5 10 35 32 33 16 10 35 -> 5 21 23 14 22 22 15 16 5 10 35 , 2 1 10 31 33 19 30 35 -> 6 34 31 33 7 16 17 20 21 32 35 , 6 16 10 33 34 33 16 21 -> 2 0 25 14 9 25 20 2 3 4 21 , 6 24 1 2 28 31 11 3 -> 17 14 9 0 29 7 7 7 24 0 3 , 6 19 30 33 16 2 1 21 -> 17 14 9 25 26 8 15 24 0 25 14 , 6 7 34 33 8 32 33 8 -> 5 17 13 14 23 13 18 0 0 25 14 , 6 8 23 30 27 17 18 3 -> 6 16 21 15 19 14 22 4 5 2 3 , 6 8 15 19 18 3 22 22 -> 6 8 15 8 15 16 6 7 16 17 14 , 6 34 12 26 34 33 8 22 -> 6 34 11 1 6 16 5 17 14 23 14 , 21 22 32 33 19 18 1 21 -> 21 4 10 35 9 25 13 13 26 16 21 , 21 32 11 1 5 10 11 3 -> 10 31 12 13 13 30 31 31 11 3 22 , 21 32 11 29 24 25 26 8 -> 10 35 9 0 0 25 26 8 4 17 14 , 10 11 3 32 12 30 33 8 -> 10 31 11 3 23 26 16 5 6 8 22 , 10 11 28 35 23 30 11 3 -> 10 31 12 26 16 6 8 23 18 1 21 , 10 35 32 27 10 12 26 8 -> 10 11 0 3 23 26 16 2 29 16 21 , 5 2 3 ->= 17 26 7 19 13 26 7 8 22 23 14 , 6 16 21 ->= 2 3 23 13 13 20 6 16 5 17 14 , 2 1 6 8 ->= 2 28 12 13 26 24 29 16 17 20 21 , 17 20 10 35 ->= 17 14 15 19 26 19 14 15 19 18 3 , 17 18 28 35 ->= 17 13 14 4 5 17 14 4 2 28 35 , 17 26 8 22 ->= 17 26 8 15 19 14 4 21 22 23 14 , 6 16 5 21 ->= 6 7 8 23 14 22 22 23 26 19 14 , 10 35 23 14 ->= 10 35 22 23 13 20 17 13 14 15 8 , 5 5 6 24 3 ->= 5 6 8 23 13 26 16 5 2 0 3 , 5 10 35 4 21 ->= 17 30 31 31 12 26 7 7 19 26 8 , 2 1 2 25 14 ->= 2 25 13 13 30 31 12 13 26 8 22 , 17 20 10 27 21 ->= 17 14 9 29 8 15 8 9 28 33 8 , 17 14 23 30 35 ->= 17 26 8 4 5 17 20 5 6 34 35 , 6 16 10 33 8 ->= 2 29 19 20 21 4 6 16 6 8 22 , 10 12 20 5 21 ->= 10 35 4 6 16 21 23 13 26 16 21 , 5 17 18 1 6 8 ->= 5 17 18 25 26 8 15 19 26 16 21 , 17 14 9 28 11 3 ->= 6 7 19 13 14 22 9 29 7 24 3 , 10 11 0 28 27 21 ->= 10 31 12 13 20 5 2 3 9 29 8 , 2 0 0 0 3 32 35 ->= 2 3 4 6 8 15 19 13 18 29 8 , 2 3 32 11 3 23 14 ->= 2 1 21 15 8 15 19 26 8 23 14 , 17 14 32 12 26 34 35 ->= 17 14 22 4 5 2 0 0 25 18 3 , 2 1 6 34 31 33 7 8 ->= 6 34 12 26 7 7 24 25 26 7 8 , 17 14 15 24 1 2 1 21 ->= 17 20 17 26 7 16 2 25 18 1 21 , 6 16 5 10 12 13 30 35 ->= 2 0 3 15 34 12 13 13 18 3 22 , 6 8 4 10 33 8 23 14 ->= 6 24 3 32 27 6 16 17 26 16 21 , 21 4 10 35 23 18 25 14 ->= 2 25 13 13 18 29 24 29 8 23 14 , 2 0 1 6 -> 21 4 2 0 3 4 5 6 7 8 15 , 5 10 11 1 6 -> 5 10 12 13 14 15 16 17 13 13 26 , 2 1 2 1 6 -> 2 1 6 19 20 21 22 23 14 23 26 , 2 1 6 24 29 -> 2 25 26 7 19 14 22 15 16 2 29 , 17 18 1 10 33 -> 17 26 8 22 23 20 17 26 16 10 33 , 5 2 1 17 18 29 -> 17 13 20 5 5 21 4 2 25 18 29 , 2 1 10 27 2 29 -> 10 27 17 13 26 8 4 17 20 2 29 , 6 24 1 10 12 26 -> 17 18 3 4 17 30 31 12 13 26 7 , 21 22 32 33 16 6 -> 21 15 24 0 29 19 20 6 7 16 6 , 5 6 34 31 12 20 6 -> 17 13 20 2 25 20 5 17 26 8 15 , 2 1 5 6 34 35 15 -> 2 1 6 7 8 9 29 7 8 22 15 , 2 28 33 16 6 24 29 -> 2 25 13 18 29 16 21 22 15 24 29 , 2 28 35 9 25 30 33 -> 2 3 22 4 17 14 23 20 6 34 33 , 6 16 21 32 11 1 6 -> 21 9 3 23 26 8 22 23 14 4 6 , 6 16 10 33 19 30 33 -> 21 15 24 0 29 7 19 20 5 10 33 , 6 16 10 33 8 9 29 -> 21 23 14 15 16 6 24 0 3 9 29 , 21 9 25 18 0 1 6 -> 21 32 33 7 16 2 0 3 4 17 26 , 21 22 22 32 27 10 33 -> 6 8 15 7 19 14 23 14 9 3 15 , 10 12 20 21 32 11 29 -> 10 12 13 13 26 24 1 21 4 6 7 , 5 10 35 32 33 16 10 33 -> 5 21 23 14 22 22 15 16 5 10 33 , 2 1 10 31 33 19 30 33 -> 6 34 31 33 7 16 17 20 21 32 33 , 6 16 10 33 34 33 16 6 -> 2 0 25 14 9 25 20 2 3 4 6 , 6 24 1 2 28 31 11 29 -> 17 14 9 0 29 7 7 7 24 0 29 , 6 19 30 33 16 2 1 6 -> 17 14 9 25 26 8 15 24 0 25 26 , 6 7 34 33 8 32 33 7 -> 5 17 13 14 23 13 18 0 0 25 26 , 6 8 23 30 27 17 18 29 -> 6 16 21 15 19 14 22 4 5 2 29 , 6 8 15 19 18 3 22 15 -> 6 8 15 8 15 16 6 7 16 17 26 , 6 34 12 26 34 33 8 15 -> 6 34 11 1 6 16 5 17 14 23 26 , 21 22 32 33 19 18 1 6 -> 21 4 10 35 9 25 13 13 26 16 6 , 21 32 11 1 5 10 11 29 -> 10 31 12 13 13 30 31 31 11 3 15 , 21 32 11 29 24 25 26 7 -> 10 35 9 0 0 25 26 8 4 17 26 , 10 11 3 32 12 30 33 7 -> 10 31 11 3 23 26 16 5 6 8 15 , 10 11 28 35 23 30 11 29 -> 10 31 12 26 16 6 8 23 18 1 6 , 10 35 32 27 10 12 26 7 -> 10 11 0 3 23 26 16 2 29 16 6 , 5 2 29 ->= 17 26 7 19 13 26 7 8 22 23 26 , 6 16 6 ->= 2 3 23 13 13 20 6 16 5 17 26 , 2 1 6 7 ->= 2 28 12 13 26 24 29 16 17 20 6 , 17 20 10 33 ->= 17 14 15 19 26 19 14 15 19 18 29 , 17 18 28 33 ->= 17 13 14 4 5 17 14 4 2 28 33 , 17 26 8 15 ->= 17 26 8 15 19 14 4 21 22 23 26 , 6 16 5 6 ->= 6 7 8 23 14 22 22 23 26 19 26 , 10 35 23 26 ->= 10 35 22 23 13 20 17 13 14 15 7 , 5 5 6 24 29 ->= 5 6 8 23 13 26 16 5 2 0 29 , 5 10 35 4 6 ->= 17 30 31 31 12 26 7 7 19 26 7 , 2 1 2 25 26 ->= 2 25 13 13 30 31 12 13 26 8 15 , 17 20 10 27 6 ->= 17 14 9 29 8 15 8 9 28 33 7 , 17 14 23 30 33 ->= 17 26 8 4 5 17 20 5 6 34 33 , 6 16 10 33 7 ->= 2 29 19 20 21 4 6 16 6 8 15 , 10 12 20 5 6 ->= 10 35 4 6 16 21 23 13 26 16 6 , 5 17 18 1 6 7 ->= 5 17 18 25 26 8 15 19 26 16 6 , 17 14 9 28 11 29 ->= 6 7 19 13 14 22 9 29 7 24 29 , 10 11 0 28 27 6 ->= 10 31 12 13 20 5 2 3 9 29 7 , 2 0 0 0 3 32 33 ->= 2 3 4 6 8 15 19 13 18 29 7 , 2 3 32 11 3 23 26 ->= 2 1 21 15 8 15 19 26 8 23 26 , 17 14 32 12 26 34 33 ->= 17 14 22 4 5 2 0 0 25 18 29 , 2 1 6 34 31 33 7 7 ->= 6 34 12 26 7 7 24 25 26 7 7 , 17 14 15 24 1 2 1 6 ->= 17 20 17 26 7 16 2 25 18 1 6 , 6 16 5 10 12 13 30 33 ->= 2 0 3 15 34 12 13 13 18 3 15 , 6 8 4 10 33 8 23 26 ->= 6 24 3 32 27 6 16 17 26 16 6 , 21 4 10 35 23 18 25 26 ->= 2 25 13 13 18 29 24 29 8 23 26 , 2 0 1 10 -> 21 4 2 0 3 4 5 6 7 8 32 , 5 10 11 1 10 -> 5 10 12 13 14 15 16 17 13 13 30 , 2 1 2 1 10 -> 2 1 6 19 20 21 22 23 14 23 30 , 2 1 6 24 28 -> 2 25 26 7 19 14 22 15 16 2 28 , 17 18 1 10 31 -> 17 26 8 22 23 20 17 26 16 10 31 , 5 2 1 17 18 28 -> 17 13 20 5 5 21 4 2 25 18 28 , 2 1 10 27 2 28 -> 10 27 17 13 26 8 4 17 20 2 28 , 6 24 1 10 12 30 -> 17 18 3 4 17 30 31 12 13 26 34 , 21 22 32 33 16 10 -> 21 15 24 0 29 19 20 6 7 16 10 , 5 6 34 31 12 20 10 -> 17 13 20 2 25 20 5 17 26 8 32 , 2 1 5 6 34 35 32 -> 2 1 6 7 8 9 29 7 8 22 32 , 2 28 33 16 6 24 28 -> 2 25 13 18 29 16 21 22 15 24 28 , 2 28 35 9 25 30 31 -> 2 3 22 4 17 14 23 20 6 34 31 , 6 16 21 32 11 1 10 -> 21 9 3 23 26 8 22 23 14 4 10 , 6 16 10 33 19 30 31 -> 21 15 24 0 29 7 19 20 5 10 31 , 6 16 10 33 8 9 28 -> 21 23 14 15 16 6 24 0 3 9 28 , 21 9 25 18 0 1 10 -> 21 32 33 7 16 2 0 3 4 17 30 , 21 22 22 32 27 10 31 -> 6 8 15 7 19 14 23 14 9 3 32 , 10 12 20 21 32 11 28 -> 10 12 13 13 26 24 1 21 4 6 34 , 5 10 35 32 33 16 10 31 -> 5 21 23 14 22 22 15 16 5 10 31 , 2 1 10 31 33 19 30 31 -> 6 34 31 33 7 16 17 20 21 32 31 , 6 16 10 33 34 33 16 10 -> 2 0 25 14 9 25 20 2 3 4 10 , 6 24 1 2 28 31 11 28 -> 17 14 9 0 29 7 7 7 24 0 28 , 6 19 30 33 16 2 1 10 -> 17 14 9 25 26 8 15 24 0 25 30 , 6 7 34 33 8 32 33 34 -> 5 17 13 14 23 13 18 0 0 25 30 , 6 8 23 30 27 17 18 28 -> 6 16 21 15 19 14 22 4 5 2 28 , 6 8 15 19 18 3 22 32 -> 6 8 15 8 15 16 6 7 16 17 30 , 6 34 12 26 34 33 8 32 -> 6 34 11 1 6 16 5 17 14 23 30 , 21 22 32 33 19 18 1 10 -> 21 4 10 35 9 25 13 13 26 16 10 , 21 32 11 1 5 10 11 28 -> 10 31 12 13 13 30 31 31 11 3 32 , 21 32 11 29 24 25 26 34 -> 10 35 9 0 0 25 26 8 4 17 30 , 10 11 3 32 12 30 33 34 -> 10 31 11 3 23 26 16 5 6 8 32 , 10 11 28 35 23 30 11 28 -> 10 31 12 26 16 6 8 23 18 1 10 , 10 35 32 27 10 12 26 34 -> 10 11 0 3 23 26 16 2 29 16 10 , 5 2 28 ->= 17 26 7 19 13 26 7 8 22 23 30 , 6 16 10 ->= 2 3 23 13 13 20 6 16 5 17 30 , 2 1 6 34 ->= 2 28 12 13 26 24 29 16 17 20 10 , 17 20 10 31 ->= 17 14 15 19 26 19 14 15 19 18 28 , 17 18 28 31 ->= 17 13 14 4 5 17 14 4 2 28 31 , 17 26 8 32 ->= 17 26 8 15 19 14 4 21 22 23 30 , 6 16 5 10 ->= 6 7 8 23 14 22 22 23 26 19 30 , 10 35 23 30 ->= 10 35 22 23 13 20 17 13 14 15 34 , 5 5 6 24 28 ->= 5 6 8 23 13 26 16 5 2 0 28 , 5 10 35 4 10 ->= 17 30 31 31 12 26 7 7 19 26 34 , 2 1 2 25 30 ->= 2 25 13 13 30 31 12 13 26 8 32 , 17 20 10 27 10 ->= 17 14 9 29 8 15 8 9 28 33 34 , 17 14 23 30 31 ->= 17 26 8 4 5 17 20 5 6 34 31 , 6 16 10 33 34 ->= 2 29 19 20 21 4 6 16 6 8 32 , 10 12 20 5 10 ->= 10 35 4 6 16 21 23 13 26 16 10 , 5 17 18 1 6 34 ->= 5 17 18 25 26 8 15 19 26 16 10 , 17 14 9 28 11 28 ->= 6 7 19 13 14 22 9 29 7 24 28 , 10 11 0 28 27 10 ->= 10 31 12 13 20 5 2 3 9 29 34 , 2 0 0 0 3 32 31 ->= 2 3 4 6 8 15 19 13 18 29 34 , 2 3 32 11 3 23 30 ->= 2 1 21 15 8 15 19 26 8 23 30 , 17 14 32 12 26 34 31 ->= 17 14 22 4 5 2 0 0 25 18 28 , 2 1 6 34 31 33 7 34 ->= 6 34 12 26 7 7 24 25 26 7 34 , 17 14 15 24 1 2 1 10 ->= 17 20 17 26 7 16 2 25 18 1 10 , 6 16 5 10 12 13 30 31 ->= 2 0 3 15 34 12 13 13 18 3 32 , 6 8 4 10 33 8 23 30 ->= 6 24 3 32 27 6 16 17 26 16 10 , 21 4 10 35 23 18 25 30 ->= 2 25 13 13 18 29 24 29 8 23 30 , 2 0 1 17 -> 21 4 2 0 3 4 5 6 7 8 23 , 5 10 11 1 17 -> 5 10 12 13 14 15 16 17 13 13 13 , 2 1 2 1 17 -> 2 1 6 19 20 21 22 23 14 23 13 , 2 1 6 24 25 -> 2 25 26 7 19 14 22 15 16 2 25 , 17 18 1 10 12 -> 17 26 8 22 23 20 17 26 16 10 12 , 5 2 1 17 18 25 -> 17 13 20 5 5 21 4 2 25 18 25 , 2 1 10 27 2 25 -> 10 27 17 13 26 8 4 17 20 2 25 , 6 24 1 10 12 13 -> 17 18 3 4 17 30 31 12 13 26 19 , 21 22 32 33 16 17 -> 21 15 24 0 29 19 20 6 7 16 17 , 5 6 34 31 12 20 17 -> 17 13 20 2 25 20 5 17 26 8 23 , 2 1 5 6 34 35 23 -> 2 1 6 7 8 9 29 7 8 22 23 , 2 28 33 16 6 24 25 -> 2 25 13 18 29 16 21 22 15 24 25 , 2 28 35 9 25 30 12 -> 2 3 22 4 17 14 23 20 6 34 12 , 6 16 21 32 11 1 17 -> 21 9 3 23 26 8 22 23 14 4 17 , 6 16 10 33 19 30 12 -> 21 15 24 0 29 7 19 20 5 10 12 , 6 16 10 33 8 9 25 -> 21 23 14 15 16 6 24 0 3 9 25 , 21 9 25 18 0 1 17 -> 21 32 33 7 16 2 0 3 4 17 13 , 21 22 22 32 27 10 12 -> 6 8 15 7 19 14 23 14 9 3 23 , 10 12 20 21 32 11 25 -> 10 12 13 13 26 24 1 21 4 6 19 , 5 10 35 32 33 16 10 12 -> 5 21 23 14 22 22 15 16 5 10 12 , 2 1 10 31 33 19 30 12 -> 6 34 31 33 7 16 17 20 21 32 12 , 6 16 10 33 34 33 16 17 -> 2 0 25 14 9 25 20 2 3 4 17 , 6 24 1 2 28 31 11 25 -> 17 14 9 0 29 7 7 7 24 0 25 , 6 19 30 33 16 2 1 17 -> 17 14 9 25 26 8 15 24 0 25 13 , 6 7 34 33 8 32 33 19 -> 5 17 13 14 23 13 18 0 0 25 13 , 6 8 23 30 27 17 18 25 -> 6 16 21 15 19 14 22 4 5 2 25 , 6 8 15 19 18 3 22 23 -> 6 8 15 8 15 16 6 7 16 17 13 , 6 34 12 26 34 33 8 23 -> 6 34 11 1 6 16 5 17 14 23 13 , 21 22 32 33 19 18 1 17 -> 21 4 10 35 9 25 13 13 26 16 17 , 21 32 11 1 5 10 11 25 -> 10 31 12 13 13 30 31 31 11 3 23 , 21 32 11 29 24 25 26 19 -> 10 35 9 0 0 25 26 8 4 17 13 , 10 11 3 32 12 30 33 19 -> 10 31 11 3 23 26 16 5 6 8 23 , 10 11 28 35 23 30 11 25 -> 10 31 12 26 16 6 8 23 18 1 17 , 10 35 32 27 10 12 26 19 -> 10 11 0 3 23 26 16 2 29 16 17 , 5 2 25 ->= 17 26 7 19 13 26 7 8 22 23 13 , 6 16 17 ->= 2 3 23 13 13 20 6 16 5 17 13 , 2 1 6 19 ->= 2 28 12 13 26 24 29 16 17 20 17 , 17 20 10 12 ->= 17 14 15 19 26 19 14 15 19 18 25 , 17 18 28 12 ->= 17 13 14 4 5 17 14 4 2 28 12 , 17 26 8 23 ->= 17 26 8 15 19 14 4 21 22 23 13 , 6 16 5 17 ->= 6 7 8 23 14 22 22 23 26 19 13 , 10 35 23 13 ->= 10 35 22 23 13 20 17 13 14 15 19 , 5 5 6 24 25 ->= 5 6 8 23 13 26 16 5 2 0 25 , 5 10 35 4 17 ->= 17 30 31 31 12 26 7 7 19 26 19 , 2 1 2 25 13 ->= 2 25 13 13 30 31 12 13 26 8 23 , 17 20 10 27 17 ->= 17 14 9 29 8 15 8 9 28 33 19 , 17 14 23 30 12 ->= 17 26 8 4 5 17 20 5 6 34 12 , 6 16 10 33 19 ->= 2 29 19 20 21 4 6 16 6 8 23 , 10 12 20 5 17 ->= 10 35 4 6 16 21 23 13 26 16 17 , 5 17 18 1 6 19 ->= 5 17 18 25 26 8 15 19 26 16 17 , 17 14 9 28 11 25 ->= 6 7 19 13 14 22 9 29 7 24 25 , 10 11 0 28 27 17 ->= 10 31 12 13 20 5 2 3 9 29 19 , 2 0 0 0 3 32 12 ->= 2 3 4 6 8 15 19 13 18 29 19 , 2 3 32 11 3 23 13 ->= 2 1 21 15 8 15 19 26 8 23 13 , 17 14 32 12 26 34 12 ->= 17 14 22 4 5 2 0 0 25 18 25 , 2 1 6 34 31 33 7 19 ->= 6 34 12 26 7 7 24 25 26 7 19 , 17 14 15 24 1 2 1 17 ->= 17 20 17 26 7 16 2 25 18 1 17 , 6 16 5 10 12 13 30 12 ->= 2 0 3 15 34 12 13 13 18 3 23 , 6 8 4 10 33 8 23 13 ->= 6 24 3 32 27 6 16 17 26 16 17 , 21 4 10 35 23 18 25 13 ->= 2 25 13 13 18 29 24 29 8 23 13 , 9 0 1 2 -> 22 4 2 0 3 4 5 6 7 8 9 , 4 10 11 1 2 -> 4 10 12 13 14 15 16 17 13 13 18 , 9 1 2 1 2 -> 9 1 6 19 20 21 22 23 14 23 18 , 9 1 6 24 0 -> 9 25 26 7 19 14 22 15 16 2 0 , 23 18 1 10 11 -> 23 26 8 22 23 20 17 26 16 10 11 , 4 2 1 17 18 0 -> 23 13 20 5 5 21 4 2 25 18 0 , 9 1 10 27 2 0 -> 32 27 17 13 26 8 4 17 20 2 0 , 15 24 1 10 12 18 -> 23 18 3 4 17 30 31 12 13 26 24 , 22 22 32 33 16 2 -> 22 15 24 0 29 19 20 6 7 16 2 , 4 6 34 31 12 20 2 -> 23 13 20 2 25 20 5 17 26 8 9 , 9 1 5 6 34 35 9 -> 9 1 6 7 8 9 29 7 8 22 9 , 9 28 33 16 6 24 0 -> 9 25 13 18 29 16 21 22 15 24 0 , 9 28 35 9 25 30 11 -> 9 3 22 4 17 14 23 20 6 34 11 , 15 16 21 32 11 1 2 -> 22 9 3 23 26 8 22 23 14 4 2 , 15 16 10 33 19 30 11 -> 22 15 24 0 29 7 19 20 5 10 11 , 15 16 10 33 8 9 0 -> 22 23 14 15 16 6 24 0 3 9 0 , 22 9 25 18 0 1 2 -> 22 32 33 7 16 2 0 3 4 17 18 , 22 22 22 32 27 10 11 -> 15 8 15 7 19 14 23 14 9 3 9 , 32 12 20 21 32 11 0 -> 32 12 13 13 26 24 1 21 4 6 24 , 4 10 35 32 33 16 10 11 -> 4 21 23 14 22 22 15 16 5 10 11 , 9 1 10 31 33 19 30 11 -> 15 34 31 33 7 16 17 20 21 32 11 , 15 16 10 33 34 33 16 2 -> 9 0 25 14 9 25 20 2 3 4 2 , 15 24 1 2 28 31 11 0 -> 23 14 9 0 29 7 7 7 24 0 0 , 15 19 30 33 16 2 1 2 -> 23 14 9 25 26 8 15 24 0 25 18 , 15 7 34 33 8 32 33 24 -> 4 17 13 14 23 13 18 0 0 25 18 , 15 8 23 30 27 17 18 0 -> 15 16 21 15 19 14 22 4 5 2 0 , 15 8 15 19 18 3 22 9 -> 15 8 15 8 15 16 6 7 16 17 18 , 15 34 12 26 34 33 8 9 -> 15 34 11 1 6 16 5 17 14 23 18 , 22 22 32 33 19 18 1 2 -> 22 4 10 35 9 25 13 13 26 16 2 , 22 32 11 1 5 10 11 0 -> 32 31 12 13 13 30 31 31 11 3 9 , 22 32 11 29 24 25 26 24 -> 32 35 9 0 0 25 26 8 4 17 18 , 32 11 3 32 12 30 33 24 -> 32 31 11 3 23 26 16 5 6 8 9 , 32 11 28 35 23 30 11 0 -> 32 31 12 26 16 6 8 23 18 1 2 , 32 35 32 27 10 12 26 24 -> 32 11 0 3 23 26 16 2 29 16 2 , 4 2 0 ->= 23 26 7 19 13 26 7 8 22 23 18 , 15 16 2 ->= 9 3 23 13 13 20 6 16 5 17 18 , 9 1 6 24 ->= 9 28 12 13 26 24 29 16 17 20 2 , 23 20 10 11 ->= 23 14 15 19 26 19 14 15 19 18 0 , 23 18 28 11 ->= 23 13 14 4 5 17 14 4 2 28 11 , 23 26 8 9 ->= 23 26 8 15 19 14 4 21 22 23 18 , 15 16 5 2 ->= 15 7 8 23 14 22 22 23 26 19 18 , 32 35 23 18 ->= 32 35 22 23 13 20 17 13 14 15 24 , 4 5 6 24 0 ->= 4 6 8 23 13 26 16 5 2 0 0 , 4 10 35 4 2 ->= 23 30 31 31 12 26 7 7 19 26 24 , 9 1 2 25 18 ->= 9 25 13 13 30 31 12 13 26 8 9 , 23 20 10 27 2 ->= 23 14 9 29 8 15 8 9 28 33 24 , 23 14 23 30 11 ->= 23 26 8 4 5 17 20 5 6 34 11 , 15 16 10 33 24 ->= 9 29 19 20 21 4 6 16 6 8 9 , 32 12 20 5 2 ->= 32 35 4 6 16 21 23 13 26 16 2 , 4 17 18 1 6 24 ->= 4 17 18 25 26 8 15 19 26 16 2 , 23 14 9 28 11 0 ->= 15 7 19 13 14 22 9 29 7 24 0 , 32 11 0 28 27 2 ->= 32 31 12 13 20 5 2 3 9 29 24 , 9 0 0 0 3 32 11 ->= 9 3 4 6 8 15 19 13 18 29 24 , 9 3 32 11 3 23 18 ->= 9 1 21 15 8 15 19 26 8 23 18 , 23 14 32 12 26 34 11 ->= 23 14 22 4 5 2 0 0 25 18 0 , 9 1 6 34 31 33 7 24 ->= 15 34 12 26 7 7 24 25 26 7 24 , 23 14 15 24 1 2 1 2 ->= 23 20 17 26 7 16 2 25 18 1 2 , 15 16 5 10 12 13 30 11 ->= 9 0 3 15 34 12 13 13 18 3 9 , 15 8 4 10 33 8 23 18 ->= 15 24 3 32 27 6 16 17 26 16 2 , 22 4 10 35 23 18 25 18 ->= 9 25 13 13 18 29 24 29 8 23 18 , 9 0 1 5 -> 22 4 2 0 3 4 5 6 7 8 4 , 4 10 11 1 5 -> 4 10 12 13 14 15 16 17 13 13 20 , 9 1 2 1 5 -> 9 1 6 19 20 21 22 23 14 23 20 , 9 1 6 24 1 -> 9 25 26 7 19 14 22 15 16 2 1 , 23 18 1 10 27 -> 23 26 8 22 23 20 17 26 16 10 27 , 4 2 1 17 18 1 -> 23 13 20 5 5 21 4 2 25 18 1 , 9 1 10 27 2 1 -> 32 27 17 13 26 8 4 17 20 2 1 , 15 24 1 10 12 20 -> 23 18 3 4 17 30 31 12 13 26 16 , 22 22 32 33 16 5 -> 22 15 24 0 29 19 20 6 7 16 5 , 4 6 34 31 12 20 5 -> 23 13 20 2 25 20 5 17 26 8 4 , 9 1 5 6 34 35 4 -> 9 1 6 7 8 9 29 7 8 22 4 , 9 28 33 16 6 24 1 -> 9 25 13 18 29 16 21 22 15 24 1 , 9 28 35 9 25 30 27 -> 9 3 22 4 17 14 23 20 6 34 27 , 15 16 21 32 11 1 5 -> 22 9 3 23 26 8 22 23 14 4 5 , 15 16 10 33 19 30 27 -> 22 15 24 0 29 7 19 20 5 10 27 , 15 16 10 33 8 9 1 -> 22 23 14 15 16 6 24 0 3 9 1 , 22 9 25 18 0 1 5 -> 22 32 33 7 16 2 0 3 4 17 20 , 22 22 22 32 27 10 27 -> 15 8 15 7 19 14 23 14 9 3 4 , 32 12 20 21 32 11 1 -> 32 12 13 13 26 24 1 21 4 6 16 , 4 10 35 32 33 16 10 27 -> 4 21 23 14 22 22 15 16 5 10 27 , 9 1 10 31 33 19 30 27 -> 15 34 31 33 7 16 17 20 21 32 27 , 15 16 10 33 34 33 16 5 -> 9 0 25 14 9 25 20 2 3 4 5 , 15 24 1 2 28 31 11 1 -> 23 14 9 0 29 7 7 7 24 0 1 , 15 19 30 33 16 2 1 5 -> 23 14 9 25 26 8 15 24 0 25 20 , 15 7 34 33 8 32 33 16 -> 4 17 13 14 23 13 18 0 0 25 20 , 15 8 23 30 27 17 18 1 -> 15 16 21 15 19 14 22 4 5 2 1 , 15 8 15 19 18 3 22 4 -> 15 8 15 8 15 16 6 7 16 17 20 , 15 34 12 26 34 33 8 4 -> 15 34 11 1 6 16 5 17 14 23 20 , 22 22 32 33 19 18 1 5 -> 22 4 10 35 9 25 13 13 26 16 5 , 22 32 11 1 5 10 11 1 -> 32 31 12 13 13 30 31 31 11 3 4 , 22 32 11 29 24 25 26 16 -> 32 35 9 0 0 25 26 8 4 17 20 , 32 11 3 32 12 30 33 16 -> 32 31 11 3 23 26 16 5 6 8 4 , 32 11 28 35 23 30 11 1 -> 32 31 12 26 16 6 8 23 18 1 5 , 32 35 32 27 10 12 26 16 -> 32 11 0 3 23 26 16 2 29 16 5 , 4 2 1 ->= 23 26 7 19 13 26 7 8 22 23 20 , 15 16 5 ->= 9 3 23 13 13 20 6 16 5 17 20 , 9 1 6 16 ->= 9 28 12 13 26 24 29 16 17 20 5 , 23 20 10 27 ->= 23 14 15 19 26 19 14 15 19 18 1 , 23 18 28 27 ->= 23 13 14 4 5 17 14 4 2 28 27 , 23 26 8 4 ->= 23 26 8 15 19 14 4 21 22 23 20 , 15 16 5 5 ->= 15 7 8 23 14 22 22 23 26 19 20 , 32 35 23 20 ->= 32 35 22 23 13 20 17 13 14 15 16 , 4 5 6 24 1 ->= 4 6 8 23 13 26 16 5 2 0 1 , 4 10 35 4 5 ->= 23 30 31 31 12 26 7 7 19 26 16 , 9 1 2 25 20 ->= 9 25 13 13 30 31 12 13 26 8 4 , 23 20 10 27 5 ->= 23 14 9 29 8 15 8 9 28 33 16 , 23 14 23 30 27 ->= 23 26 8 4 5 17 20 5 6 34 27 , 15 16 10 33 16 ->= 9 29 19 20 21 4 6 16 6 8 4 , 32 12 20 5 5 ->= 32 35 4 6 16 21 23 13 26 16 5 , 4 17 18 1 6 16 ->= 4 17 18 25 26 8 15 19 26 16 5 , 23 14 9 28 11 1 ->= 15 7 19 13 14 22 9 29 7 24 1 , 32 11 0 28 27 5 ->= 32 31 12 13 20 5 2 3 9 29 16 , 9 0 0 0 3 32 27 ->= 9 3 4 6 8 15 19 13 18 29 16 , 9 3 32 11 3 23 20 ->= 9 1 21 15 8 15 19 26 8 23 20 , 23 14 32 12 26 34 27 ->= 23 14 22 4 5 2 0 0 25 18 1 , 9 1 6 34 31 33 7 16 ->= 15 34 12 26 7 7 24 25 26 7 16 , 23 14 15 24 1 2 1 5 ->= 23 20 17 26 7 16 2 25 18 1 5 , 15 16 5 10 12 13 30 27 ->= 9 0 3 15 34 12 13 13 18 3 4 , 15 8 4 10 33 8 23 20 ->= 15 24 3 32 27 6 16 17 26 16 5 , 22 4 10 35 23 18 25 20 ->= 9 25 13 13 18 29 24 29 8 23 20 , 9 0 1 21 -> 22 4 2 0 3 4 5 6 7 8 22 , 4 10 11 1 21 -> 4 10 12 13 14 15 16 17 13 13 14 , 9 1 2 1 21 -> 9 1 6 19 20 21 22 23 14 23 14 , 9 1 6 24 3 -> 9 25 26 7 19 14 22 15 16 2 3 , 23 18 1 10 35 -> 23 26 8 22 23 20 17 26 16 10 35 , 4 2 1 17 18 3 -> 23 13 20 5 5 21 4 2 25 18 3 , 9 1 10 27 2 3 -> 32 27 17 13 26 8 4 17 20 2 3 , 15 24 1 10 12 14 -> 23 18 3 4 17 30 31 12 13 26 8 , 22 22 32 33 16 21 -> 22 15 24 0 29 19 20 6 7 16 21 , 4 6 34 31 12 20 21 -> 23 13 20 2 25 20 5 17 26 8 22 , 9 1 5 6 34 35 22 -> 9 1 6 7 8 9 29 7 8 22 22 , 9 28 33 16 6 24 3 -> 9 25 13 18 29 16 21 22 15 24 3 , 9 28 35 9 25 30 35 -> 9 3 22 4 17 14 23 20 6 34 35 , 15 16 21 32 11 1 21 -> 22 9 3 23 26 8 22 23 14 4 21 , 15 16 10 33 19 30 35 -> 22 15 24 0 29 7 19 20 5 10 35 , 15 16 10 33 8 9 3 -> 22 23 14 15 16 6 24 0 3 9 3 , 22 9 25 18 0 1 21 -> 22 32 33 7 16 2 0 3 4 17 14 , 22 22 22 32 27 10 35 -> 15 8 15 7 19 14 23 14 9 3 22 , 32 12 20 21 32 11 3 -> 32 12 13 13 26 24 1 21 4 6 8 , 4 10 35 32 33 16 10 35 -> 4 21 23 14 22 22 15 16 5 10 35 , 9 1 10 31 33 19 30 35 -> 15 34 31 33 7 16 17 20 21 32 35 , 15 16 10 33 34 33 16 21 -> 9 0 25 14 9 25 20 2 3 4 21 , 15 24 1 2 28 31 11 3 -> 23 14 9 0 29 7 7 7 24 0 3 , 15 19 30 33 16 2 1 21 -> 23 14 9 25 26 8 15 24 0 25 14 , 15 7 34 33 8 32 33 8 -> 4 17 13 14 23 13 18 0 0 25 14 , 15 8 23 30 27 17 18 3 -> 15 16 21 15 19 14 22 4 5 2 3 , 15 8 15 19 18 3 22 22 -> 15 8 15 8 15 16 6 7 16 17 14 , 15 34 12 26 34 33 8 22 -> 15 34 11 1 6 16 5 17 14 23 14 , 22 22 32 33 19 18 1 21 -> 22 4 10 35 9 25 13 13 26 16 21 , 22 32 11 1 5 10 11 3 -> 32 31 12 13 13 30 31 31 11 3 22 , 22 32 11 29 24 25 26 8 -> 32 35 9 0 0 25 26 8 4 17 14 , 32 11 3 32 12 30 33 8 -> 32 31 11 3 23 26 16 5 6 8 22 , 32 11 28 35 23 30 11 3 -> 32 31 12 26 16 6 8 23 18 1 21 , 32 35 32 27 10 12 26 8 -> 32 11 0 3 23 26 16 2 29 16 21 , 4 2 3 ->= 23 26 7 19 13 26 7 8 22 23 14 , 15 16 21 ->= 9 3 23 13 13 20 6 16 5 17 14 , 9 1 6 8 ->= 9 28 12 13 26 24 29 16 17 20 21 , 23 20 10 35 ->= 23 14 15 19 26 19 14 15 19 18 3 , 23 18 28 35 ->= 23 13 14 4 5 17 14 4 2 28 35 , 23 26 8 22 ->= 23 26 8 15 19 14 4 21 22 23 14 , 15 16 5 21 ->= 15 7 8 23 14 22 22 23 26 19 14 , 32 35 23 14 ->= 32 35 22 23 13 20 17 13 14 15 8 , 4 5 6 24 3 ->= 4 6 8 23 13 26 16 5 2 0 3 , 4 10 35 4 21 ->= 23 30 31 31 12 26 7 7 19 26 8 , 9 1 2 25 14 ->= 9 25 13 13 30 31 12 13 26 8 22 , 23 20 10 27 21 ->= 23 14 9 29 8 15 8 9 28 33 8 , 23 14 23 30 35 ->= 23 26 8 4 5 17 20 5 6 34 35 , 15 16 10 33 8 ->= 9 29 19 20 21 4 6 16 6 8 22 , 32 12 20 5 21 ->= 32 35 4 6 16 21 23 13 26 16 21 , 4 17 18 1 6 8 ->= 4 17 18 25 26 8 15 19 26 16 21 , 23 14 9 28 11 3 ->= 15 7 19 13 14 22 9 29 7 24 3 , 32 11 0 28 27 21 ->= 32 31 12 13 20 5 2 3 9 29 8 , 9 0 0 0 3 32 35 ->= 9 3 4 6 8 15 19 13 18 29 8 , 9 3 32 11 3 23 14 ->= 9 1 21 15 8 15 19 26 8 23 14 , 23 14 32 12 26 34 35 ->= 23 14 22 4 5 2 0 0 25 18 3 , 9 1 6 34 31 33 7 8 ->= 15 34 12 26 7 7 24 25 26 7 8 , 23 14 15 24 1 2 1 21 ->= 23 20 17 26 7 16 2 25 18 1 21 , 15 16 5 10 12 13 30 35 ->= 9 0 3 15 34 12 13 13 18 3 22 , 15 8 4 10 33 8 23 14 ->= 15 24 3 32 27 6 16 17 26 16 21 , 22 4 10 35 23 18 25 14 ->= 9 25 13 13 18 29 24 29 8 23 14 , 9 0 1 6 -> 22 4 2 0 3 4 5 6 7 8 15 , 4 10 11 1 6 -> 4 10 12 13 14 15 16 17 13 13 26 , 9 1 2 1 6 -> 9 1 6 19 20 21 22 23 14 23 26 , 9 1 6 24 29 -> 9 25 26 7 19 14 22 15 16 2 29 , 23 18 1 10 33 -> 23 26 8 22 23 20 17 26 16 10 33 , 4 2 1 17 18 29 -> 23 13 20 5 5 21 4 2 25 18 29 , 9 1 10 27 2 29 -> 32 27 17 13 26 8 4 17 20 2 29 , 15 24 1 10 12 26 -> 23 18 3 4 17 30 31 12 13 26 7 , 22 22 32 33 16 6 -> 22 15 24 0 29 19 20 6 7 16 6 , 4 6 34 31 12 20 6 -> 23 13 20 2 25 20 5 17 26 8 15 , 9 1 5 6 34 35 15 -> 9 1 6 7 8 9 29 7 8 22 15 , 9 28 33 16 6 24 29 -> 9 25 13 18 29 16 21 22 15 24 29 , 9 28 35 9 25 30 33 -> 9 3 22 4 17 14 23 20 6 34 33 , 15 16 21 32 11 1 6 -> 22 9 3 23 26 8 22 23 14 4 6 , 15 16 10 33 19 30 33 -> 22 15 24 0 29 7 19 20 5 10 33 , 15 16 10 33 8 9 29 -> 22 23 14 15 16 6 24 0 3 9 29 , 22 9 25 18 0 1 6 -> 22 32 33 7 16 2 0 3 4 17 26 , 22 22 22 32 27 10 33 -> 15 8 15 7 19 14 23 14 9 3 15 , 32 12 20 21 32 11 29 -> 32 12 13 13 26 24 1 21 4 6 7 , 4 10 35 32 33 16 10 33 -> 4 21 23 14 22 22 15 16 5 10 33 , 9 1 10 31 33 19 30 33 -> 15 34 31 33 7 16 17 20 21 32 33 , 15 16 10 33 34 33 16 6 -> 9 0 25 14 9 25 20 2 3 4 6 , 15 24 1 2 28 31 11 29 -> 23 14 9 0 29 7 7 7 24 0 29 , 15 19 30 33 16 2 1 6 -> 23 14 9 25 26 8 15 24 0 25 26 , 15 7 34 33 8 32 33 7 -> 4 17 13 14 23 13 18 0 0 25 26 , 15 8 23 30 27 17 18 29 -> 15 16 21 15 19 14 22 4 5 2 29 , 15 8 15 19 18 3 22 15 -> 15 8 15 8 15 16 6 7 16 17 26 , 15 34 12 26 34 33 8 15 -> 15 34 11 1 6 16 5 17 14 23 26 , 22 22 32 33 19 18 1 6 -> 22 4 10 35 9 25 13 13 26 16 6 , 22 32 11 1 5 10 11 29 -> 32 31 12 13 13 30 31 31 11 3 15 , 22 32 11 29 24 25 26 7 -> 32 35 9 0 0 25 26 8 4 17 26 , 32 11 3 32 12 30 33 7 -> 32 31 11 3 23 26 16 5 6 8 15 , 32 11 28 35 23 30 11 29 -> 32 31 12 26 16 6 8 23 18 1 6 , 32 35 32 27 10 12 26 7 -> 32 11 0 3 23 26 16 2 29 16 6 , 4 2 29 ->= 23 26 7 19 13 26 7 8 22 23 26 , 15 16 6 ->= 9 3 23 13 13 20 6 16 5 17 26 , 9 1 6 7 ->= 9 28 12 13 26 24 29 16 17 20 6 , 23 20 10 33 ->= 23 14 15 19 26 19 14 15 19 18 29 , 23 18 28 33 ->= 23 13 14 4 5 17 14 4 2 28 33 , 23 26 8 15 ->= 23 26 8 15 19 14 4 21 22 23 26 , 15 16 5 6 ->= 15 7 8 23 14 22 22 23 26 19 26 , 32 35 23 26 ->= 32 35 22 23 13 20 17 13 14 15 7 , 4 5 6 24 29 ->= 4 6 8 23 13 26 16 5 2 0 29 , 4 10 35 4 6 ->= 23 30 31 31 12 26 7 7 19 26 7 , 9 1 2 25 26 ->= 9 25 13 13 30 31 12 13 26 8 15 , 23 20 10 27 6 ->= 23 14 9 29 8 15 8 9 28 33 7 , 23 14 23 30 33 ->= 23 26 8 4 5 17 20 5 6 34 33 , 15 16 10 33 7 ->= 9 29 19 20 21 4 6 16 6 8 15 , 32 12 20 5 6 ->= 32 35 4 6 16 21 23 13 26 16 6 , 4 17 18 1 6 7 ->= 4 17 18 25 26 8 15 19 26 16 6 , 23 14 9 28 11 29 ->= 15 7 19 13 14 22 9 29 7 24 29 , 32 11 0 28 27 6 ->= 32 31 12 13 20 5 2 3 9 29 7 , 9 0 0 0 3 32 33 ->= 9 3 4 6 8 15 19 13 18 29 7 , 9 3 32 11 3 23 26 ->= 9 1 21 15 8 15 19 26 8 23 26 , 23 14 32 12 26 34 33 ->= 23 14 22 4 5 2 0 0 25 18 29 , 9 1 6 34 31 33 7 7 ->= 15 34 12 26 7 7 24 25 26 7 7 , 23 14 15 24 1 2 1 6 ->= 23 20 17 26 7 16 2 25 18 1 6 , 15 16 5 10 12 13 30 33 ->= 9 0 3 15 34 12 13 13 18 3 15 , 15 8 4 10 33 8 23 26 ->= 15 24 3 32 27 6 16 17 26 16 6 , 22 4 10 35 23 18 25 26 ->= 9 25 13 13 18 29 24 29 8 23 26 , 9 0 1 10 -> 22 4 2 0 3 4 5 6 7 8 32 , 4 10 11 1 10 -> 4 10 12 13 14 15 16 17 13 13 30 , 9 1 2 1 10 -> 9 1 6 19 20 21 22 23 14 23 30 , 9 1 6 24 28 -> 9 25 26 7 19 14 22 15 16 2 28 , 23 18 1 10 31 -> 23 26 8 22 23 20 17 26 16 10 31 , 4 2 1 17 18 28 -> 23 13 20 5 5 21 4 2 25 18 28 , 9 1 10 27 2 28 -> 32 27 17 13 26 8 4 17 20 2 28 , 15 24 1 10 12 30 -> 23 18 3 4 17 30 31 12 13 26 34 , 22 22 32 33 16 10 -> 22 15 24 0 29 19 20 6 7 16 10 , 4 6 34 31 12 20 10 -> 23 13 20 2 25 20 5 17 26 8 32 , 9 1 5 6 34 35 32 -> 9 1 6 7 8 9 29 7 8 22 32 , 9 28 33 16 6 24 28 -> 9 25 13 18 29 16 21 22 15 24 28 , 9 28 35 9 25 30 31 -> 9 3 22 4 17 14 23 20 6 34 31 , 15 16 21 32 11 1 10 -> 22 9 3 23 26 8 22 23 14 4 10 , 15 16 10 33 19 30 31 -> 22 15 24 0 29 7 19 20 5 10 31 , 15 16 10 33 8 9 28 -> 22 23 14 15 16 6 24 0 3 9 28 , 22 9 25 18 0 1 10 -> 22 32 33 7 16 2 0 3 4 17 30 , 22 22 22 32 27 10 31 -> 15 8 15 7 19 14 23 14 9 3 32 , 32 12 20 21 32 11 28 -> 32 12 13 13 26 24 1 21 4 6 34 , 4 10 35 32 33 16 10 31 -> 4 21 23 14 22 22 15 16 5 10 31 , 9 1 10 31 33 19 30 31 -> 15 34 31 33 7 16 17 20 21 32 31 , 15 16 10 33 34 33 16 10 -> 9 0 25 14 9 25 20 2 3 4 10 , 15 24 1 2 28 31 11 28 -> 23 14 9 0 29 7 7 7 24 0 28 , 15 19 30 33 16 2 1 10 -> 23 14 9 25 26 8 15 24 0 25 30 , 15 7 34 33 8 32 33 34 -> 4 17 13 14 23 13 18 0 0 25 30 , 15 8 23 30 27 17 18 28 -> 15 16 21 15 19 14 22 4 5 2 28 , 15 8 15 19 18 3 22 32 -> 15 8 15 8 15 16 6 7 16 17 30 , 15 34 12 26 34 33 8 32 -> 15 34 11 1 6 16 5 17 14 23 30 , 22 22 32 33 19 18 1 10 -> 22 4 10 35 9 25 13 13 26 16 10 , 22 32 11 1 5 10 11 28 -> 32 31 12 13 13 30 31 31 11 3 32 , 22 32 11 29 24 25 26 34 -> 32 35 9 0 0 25 26 8 4 17 30 , 32 11 3 32 12 30 33 34 -> 32 31 11 3 23 26 16 5 6 8 32 , 32 11 28 35 23 30 11 28 -> 32 31 12 26 16 6 8 23 18 1 10 , 32 35 32 27 10 12 26 34 -> 32 11 0 3 23 26 16 2 29 16 10 , 4 2 28 ->= 23 26 7 19 13 26 7 8 22 23 30 , 15 16 10 ->= 9 3 23 13 13 20 6 16 5 17 30 , 9 1 6 34 ->= 9 28 12 13 26 24 29 16 17 20 10 , 23 20 10 31 ->= 23 14 15 19 26 19 14 15 19 18 28 , 23 18 28 31 ->= 23 13 14 4 5 17 14 4 2 28 31 , 23 26 8 32 ->= 23 26 8 15 19 14 4 21 22 23 30 , 15 16 5 10 ->= 15 7 8 23 14 22 22 23 26 19 30 , 32 35 23 30 ->= 32 35 22 23 13 20 17 13 14 15 34 , 4 5 6 24 28 ->= 4 6 8 23 13 26 16 5 2 0 28 , 4 10 35 4 10 ->= 23 30 31 31 12 26 7 7 19 26 34 , 9 1 2 25 30 ->= 9 25 13 13 30 31 12 13 26 8 32 , 23 20 10 27 10 ->= 23 14 9 29 8 15 8 9 28 33 34 , 23 14 23 30 31 ->= 23 26 8 4 5 17 20 5 6 34 31 , 15 16 10 33 34 ->= 9 29 19 20 21 4 6 16 6 8 32 , 32 12 20 5 10 ->= 32 35 4 6 16 21 23 13 26 16 10 , 4 17 18 1 6 34 ->= 4 17 18 25 26 8 15 19 26 16 10 , 23 14 9 28 11 28 ->= 15 7 19 13 14 22 9 29 7 24 28 , 32 11 0 28 27 10 ->= 32 31 12 13 20 5 2 3 9 29 34 , 9 0 0 0 3 32 31 ->= 9 3 4 6 8 15 19 13 18 29 34 , 9 3 32 11 3 23 30 ->= 9 1 21 15 8 15 19 26 8 23 30 , 23 14 32 12 26 34 31 ->= 23 14 22 4 5 2 0 0 25 18 28 , 9 1 6 34 31 33 7 34 ->= 15 34 12 26 7 7 24 25 26 7 34 , 23 14 15 24 1 2 1 10 ->= 23 20 17 26 7 16 2 25 18 1 10 , 15 16 5 10 12 13 30 31 ->= 9 0 3 15 34 12 13 13 18 3 32 , 15 8 4 10 33 8 23 30 ->= 15 24 3 32 27 6 16 17 26 16 10 , 22 4 10 35 23 18 25 30 ->= 9 25 13 13 18 29 24 29 8 23 30 , 9 0 1 17 -> 22 4 2 0 3 4 5 6 7 8 23 , 4 10 11 1 17 -> 4 10 12 13 14 15 16 17 13 13 13 , 9 1 2 1 17 -> 9 1 6 19 20 21 22 23 14 23 13 , 9 1 6 24 25 -> 9 25 26 7 19 14 22 15 16 2 25 , 23 18 1 10 12 -> 23 26 8 22 23 20 17 26 16 10 12 , 4 2 1 17 18 25 -> 23 13 20 5 5 21 4 2 25 18 25 , 9 1 10 27 2 25 -> 32 27 17 13 26 8 4 17 20 2 25 , 15 24 1 10 12 13 -> 23 18 3 4 17 30 31 12 13 26 19 , 22 22 32 33 16 17 -> 22 15 24 0 29 19 20 6 7 16 17 , 4 6 34 31 12 20 17 -> 23 13 20 2 25 20 5 17 26 8 23 , 9 1 5 6 34 35 23 -> 9 1 6 7 8 9 29 7 8 22 23 , 9 28 33 16 6 24 25 -> 9 25 13 18 29 16 21 22 15 24 25 , 9 28 35 9 25 30 12 -> 9 3 22 4 17 14 23 20 6 34 12 , 15 16 21 32 11 1 17 -> 22 9 3 23 26 8 22 23 14 4 17 , 15 16 10 33 19 30 12 -> 22 15 24 0 29 7 19 20 5 10 12 , 15 16 10 33 8 9 25 -> 22 23 14 15 16 6 24 0 3 9 25 , 22 9 25 18 0 1 17 -> 22 32 33 7 16 2 0 3 4 17 13 , 22 22 22 32 27 10 12 -> 15 8 15 7 19 14 23 14 9 3 23 , 32 12 20 21 32 11 25 -> 32 12 13 13 26 24 1 21 4 6 19 , 4 10 35 32 33 16 10 12 -> 4 21 23 14 22 22 15 16 5 10 12 , 9 1 10 31 33 19 30 12 -> 15 34 31 33 7 16 17 20 21 32 12 , 15 16 10 33 34 33 16 17 -> 9 0 25 14 9 25 20 2 3 4 17 , 15 24 1 2 28 31 11 25 -> 23 14 9 0 29 7 7 7 24 0 25 , 15 19 30 33 16 2 1 17 -> 23 14 9 25 26 8 15 24 0 25 13 , 15 7 34 33 8 32 33 19 -> 4 17 13 14 23 13 18 0 0 25 13 , 15 8 23 30 27 17 18 25 -> 15 16 21 15 19 14 22 4 5 2 25 , 15 8 15 19 18 3 22 23 -> 15 8 15 8 15 16 6 7 16 17 13 , 15 34 12 26 34 33 8 23 -> 15 34 11 1 6 16 5 17 14 23 13 , 22 22 32 33 19 18 1 17 -> 22 4 10 35 9 25 13 13 26 16 17 , 22 32 11 1 5 10 11 25 -> 32 31 12 13 13 30 31 31 11 3 23 , 22 32 11 29 24 25 26 19 -> 32 35 9 0 0 25 26 8 4 17 13 , 32 11 3 32 12 30 33 19 -> 32 31 11 3 23 26 16 5 6 8 23 , 32 11 28 35 23 30 11 25 -> 32 31 12 26 16 6 8 23 18 1 17 , 32 35 32 27 10 12 26 19 -> 32 11 0 3 23 26 16 2 29 16 17 , 4 2 25 ->= 23 26 7 19 13 26 7 8 22 23 13 , 15 16 17 ->= 9 3 23 13 13 20 6 16 5 17 13 , 9 1 6 19 ->= 9 28 12 13 26 24 29 16 17 20 17 , 23 20 10 12 ->= 23 14 15 19 26 19 14 15 19 18 25 , 23 18 28 12 ->= 23 13 14 4 5 17 14 4 2 28 12 , 23 26 8 23 ->= 23 26 8 15 19 14 4 21 22 23 13 , 15 16 5 17 ->= 15 7 8 23 14 22 22 23 26 19 13 , 32 35 23 13 ->= 32 35 22 23 13 20 17 13 14 15 19 , 4 5 6 24 25 ->= 4 6 8 23 13 26 16 5 2 0 25 , 4 10 35 4 17 ->= 23 30 31 31 12 26 7 7 19 26 19 , 9 1 2 25 13 ->= 9 25 13 13 30 31 12 13 26 8 23 , 23 20 10 27 17 ->= 23 14 9 29 8 15 8 9 28 33 19 , 23 14 23 30 12 ->= 23 26 8 4 5 17 20 5 6 34 12 , 15 16 10 33 19 ->= 9 29 19 20 21 4 6 16 6 8 23 , 32 12 20 5 17 ->= 32 35 4 6 16 21 23 13 26 16 17 , 4 17 18 1 6 19 ->= 4 17 18 25 26 8 15 19 26 16 17 , 23 14 9 28 11 25 ->= 15 7 19 13 14 22 9 29 7 24 25 , 32 11 0 28 27 17 ->= 32 31 12 13 20 5 2 3 9 29 19 , 9 0 0 0 3 32 12 ->= 9 3 4 6 8 15 19 13 18 29 19 , 9 3 32 11 3 23 13 ->= 9 1 21 15 8 15 19 26 8 23 13 , 23 14 32 12 26 34 12 ->= 23 14 22 4 5 2 0 0 25 18 25 , 9 1 6 34 31 33 7 19 ->= 15 34 12 26 7 7 24 25 26 7 19 , 23 14 15 24 1 2 1 17 ->= 23 20 17 26 7 16 2 25 18 1 17 , 15 16 5 10 12 13 30 12 ->= 9 0 3 15 34 12 13 13 18 3 23 , 15 8 4 10 33 8 23 13 ->= 15 24 3 32 27 6 16 17 26 16 17 , 22 4 10 35 23 18 25 13 ->= 9 25 13 13 18 29 24 29 8 23 13 , 24 0 1 2 -> 8 4 2 0 3 4 5 6 7 8 9 , 16 10 11 1 2 -> 16 10 12 13 14 15 16 17 13 13 18 , 24 1 2 1 2 -> 24 1 6 19 20 21 22 23 14 23 18 , 24 1 6 24 0 -> 24 25 26 7 19 14 22 15 16 2 0 , 19 18 1 10 11 -> 19 26 8 22 23 20 17 26 16 10 11 , 16 2 1 17 18 0 -> 19 13 20 5 5 21 4 2 25 18 0 , 24 1 10 27 2 0 -> 34 27 17 13 26 8 4 17 20 2 0 , 7 24 1 10 12 18 -> 19 18 3 4 17 30 31 12 13 26 24 , 8 22 32 33 16 2 -> 8 15 24 0 29 19 20 6 7 16 2 , 16 6 34 31 12 20 2 -> 19 13 20 2 25 20 5 17 26 8 9 , 24 1 5 6 34 35 9 -> 24 1 6 7 8 9 29 7 8 22 9 , 24 28 33 16 6 24 0 -> 24 25 13 18 29 16 21 22 15 24 0 , 24 28 35 9 25 30 11 -> 24 3 22 4 17 14 23 20 6 34 11 , 7 16 21 32 11 1 2 -> 8 9 3 23 26 8 22 23 14 4 2 , 7 16 10 33 19 30 11 -> 8 15 24 0 29 7 19 20 5 10 11 , 7 16 10 33 8 9 0 -> 8 23 14 15 16 6 24 0 3 9 0 , 8 9 25 18 0 1 2 -> 8 32 33 7 16 2 0 3 4 17 18 , 8 22 22 32 27 10 11 -> 7 8 15 7 19 14 23 14 9 3 9 , 34 12 20 21 32 11 0 -> 34 12 13 13 26 24 1 21 4 6 24 , 16 10 35 32 33 16 10 11 -> 16 21 23 14 22 22 15 16 5 10 11 , 24 1 10 31 33 19 30 11 -> 7 34 31 33 7 16 17 20 21 32 11 , 7 16 10 33 34 33 16 2 -> 24 0 25 14 9 25 20 2 3 4 2 , 7 24 1 2 28 31 11 0 -> 19 14 9 0 29 7 7 7 24 0 0 , 7 19 30 33 16 2 1 2 -> 19 14 9 25 26 8 15 24 0 25 18 , 7 7 34 33 8 32 33 24 -> 16 17 13 14 23 13 18 0 0 25 18 , 7 8 23 30 27 17 18 0 -> 7 16 21 15 19 14 22 4 5 2 0 , 7 8 15 19 18 3 22 9 -> 7 8 15 8 15 16 6 7 16 17 18 , 7 34 12 26 34 33 8 9 -> 7 34 11 1 6 16 5 17 14 23 18 , 8 22 32 33 19 18 1 2 -> 8 4 10 35 9 25 13 13 26 16 2 , 8 32 11 1 5 10 11 0 -> 34 31 12 13 13 30 31 31 11 3 9 , 8 32 11 29 24 25 26 24 -> 34 35 9 0 0 25 26 8 4 17 18 , 34 11 3 32 12 30 33 24 -> 34 31 11 3 23 26 16 5 6 8 9 , 34 11 28 35 23 30 11 0 -> 34 31 12 26 16 6 8 23 18 1 2 , 34 35 32 27 10 12 26 24 -> 34 11 0 3 23 26 16 2 29 16 2 , 16 2 0 ->= 19 26 7 19 13 26 7 8 22 23 18 , 7 16 2 ->= 24 3 23 13 13 20 6 16 5 17 18 , 24 1 6 24 ->= 24 28 12 13 26 24 29 16 17 20 2 , 19 20 10 11 ->= 19 14 15 19 26 19 14 15 19 18 0 , 19 18 28 11 ->= 19 13 14 4 5 17 14 4 2 28 11 , 19 26 8 9 ->= 19 26 8 15 19 14 4 21 22 23 18 , 7 16 5 2 ->= 7 7 8 23 14 22 22 23 26 19 18 , 34 35 23 18 ->= 34 35 22 23 13 20 17 13 14 15 24 , 16 5 6 24 0 ->= 16 6 8 23 13 26 16 5 2 0 0 , 16 10 35 4 2 ->= 19 30 31 31 12 26 7 7 19 26 24 , 24 1 2 25 18 ->= 24 25 13 13 30 31 12 13 26 8 9 , 19 20 10 27 2 ->= 19 14 9 29 8 15 8 9 28 33 24 , 19 14 23 30 11 ->= 19 26 8 4 5 17 20 5 6 34 11 , 7 16 10 33 24 ->= 24 29 19 20 21 4 6 16 6 8 9 , 34 12 20 5 2 ->= 34 35 4 6 16 21 23 13 26 16 2 , 16 17 18 1 6 24 ->= 16 17 18 25 26 8 15 19 26 16 2 , 19 14 9 28 11 0 ->= 7 7 19 13 14 22 9 29 7 24 0 , 34 11 0 28 27 2 ->= 34 31 12 13 20 5 2 3 9 29 24 , 24 0 0 0 3 32 11 ->= 24 3 4 6 8 15 19 13 18 29 24 , 24 3 32 11 3 23 18 ->= 24 1 21 15 8 15 19 26 8 23 18 , 19 14 32 12 26 34 11 ->= 19 14 22 4 5 2 0 0 25 18 0 , 24 1 6 34 31 33 7 24 ->= 7 34 12 26 7 7 24 25 26 7 24 , 19 14 15 24 1 2 1 2 ->= 19 20 17 26 7 16 2 25 18 1 2 , 7 16 5 10 12 13 30 11 ->= 24 0 3 15 34 12 13 13 18 3 9 , 7 8 4 10 33 8 23 18 ->= 7 24 3 32 27 6 16 17 26 16 2 , 8 4 10 35 23 18 25 18 ->= 24 25 13 13 18 29 24 29 8 23 18 , 24 0 1 5 -> 8 4 2 0 3 4 5 6 7 8 4 , 16 10 11 1 5 -> 16 10 12 13 14 15 16 17 13 13 20 , 24 1 2 1 5 -> 24 1 6 19 20 21 22 23 14 23 20 , 24 1 6 24 1 -> 24 25 26 7 19 14 22 15 16 2 1 , 19 18 1 10 27 -> 19 26 8 22 23 20 17 26 16 10 27 , 16 2 1 17 18 1 -> 19 13 20 5 5 21 4 2 25 18 1 , 24 1 10 27 2 1 -> 34 27 17 13 26 8 4 17 20 2 1 , 7 24 1 10 12 20 -> 19 18 3 4 17 30 31 12 13 26 16 , 8 22 32 33 16 5 -> 8 15 24 0 29 19 20 6 7 16 5 , 16 6 34 31 12 20 5 -> 19 13 20 2 25 20 5 17 26 8 4 , 24 1 5 6 34 35 4 -> 24 1 6 7 8 9 29 7 8 22 4 , 24 28 33 16 6 24 1 -> 24 25 13 18 29 16 21 22 15 24 1 , 24 28 35 9 25 30 27 -> 24 3 22 4 17 14 23 20 6 34 27 , 7 16 21 32 11 1 5 -> 8 9 3 23 26 8 22 23 14 4 5 , 7 16 10 33 19 30 27 -> 8 15 24 0 29 7 19 20 5 10 27 , 7 16 10 33 8 9 1 -> 8 23 14 15 16 6 24 0 3 9 1 , 8 9 25 18 0 1 5 -> 8 32 33 7 16 2 0 3 4 17 20 , 8 22 22 32 27 10 27 -> 7 8 15 7 19 14 23 14 9 3 4 , 34 12 20 21 32 11 1 -> 34 12 13 13 26 24 1 21 4 6 16 , 16 10 35 32 33 16 10 27 -> 16 21 23 14 22 22 15 16 5 10 27 , 24 1 10 31 33 19 30 27 -> 7 34 31 33 7 16 17 20 21 32 27 , 7 16 10 33 34 33 16 5 -> 24 0 25 14 9 25 20 2 3 4 5 , 7 24 1 2 28 31 11 1 -> 19 14 9 0 29 7 7 7 24 0 1 , 7 19 30 33 16 2 1 5 -> 19 14 9 25 26 8 15 24 0 25 20 , 7 7 34 33 8 32 33 16 -> 16 17 13 14 23 13 18 0 0 25 20 , 7 8 23 30 27 17 18 1 -> 7 16 21 15 19 14 22 4 5 2 1 , 7 8 15 19 18 3 22 4 -> 7 8 15 8 15 16 6 7 16 17 20 , 7 34 12 26 34 33 8 4 -> 7 34 11 1 6 16 5 17 14 23 20 , 8 22 32 33 19 18 1 5 -> 8 4 10 35 9 25 13 13 26 16 5 , 8 32 11 1 5 10 11 1 -> 34 31 12 13 13 30 31 31 11 3 4 , 8 32 11 29 24 25 26 16 -> 34 35 9 0 0 25 26 8 4 17 20 , 34 11 3 32 12 30 33 16 -> 34 31 11 3 23 26 16 5 6 8 4 , 34 11 28 35 23 30 11 1 -> 34 31 12 26 16 6 8 23 18 1 5 , 34 35 32 27 10 12 26 16 -> 34 11 0 3 23 26 16 2 29 16 5 , 16 2 1 ->= 19 26 7 19 13 26 7 8 22 23 20 , 7 16 5 ->= 24 3 23 13 13 20 6 16 5 17 20 , 24 1 6 16 ->= 24 28 12 13 26 24 29 16 17 20 5 , 19 20 10 27 ->= 19 14 15 19 26 19 14 15 19 18 1 , 19 18 28 27 ->= 19 13 14 4 5 17 14 4 2 28 27 , 19 26 8 4 ->= 19 26 8 15 19 14 4 21 22 23 20 , 7 16 5 5 ->= 7 7 8 23 14 22 22 23 26 19 20 , 34 35 23 20 ->= 34 35 22 23 13 20 17 13 14 15 16 , 16 5 6 24 1 ->= 16 6 8 23 13 26 16 5 2 0 1 , 16 10 35 4 5 ->= 19 30 31 31 12 26 7 7 19 26 16 , 24 1 2 25 20 ->= 24 25 13 13 30 31 12 13 26 8 4 , 19 20 10 27 5 ->= 19 14 9 29 8 15 8 9 28 33 16 , 19 14 23 30 27 ->= 19 26 8 4 5 17 20 5 6 34 27 , 7 16 10 33 16 ->= 24 29 19 20 21 4 6 16 6 8 4 , 34 12 20 5 5 ->= 34 35 4 6 16 21 23 13 26 16 5 , 16 17 18 1 6 16 ->= 16 17 18 25 26 8 15 19 26 16 5 , 19 14 9 28 11 1 ->= 7 7 19 13 14 22 9 29 7 24 1 , 34 11 0 28 27 5 ->= 34 31 12 13 20 5 2 3 9 29 16 , 24 0 0 0 3 32 27 ->= 24 3 4 6 8 15 19 13 18 29 16 , 24 3 32 11 3 23 20 ->= 24 1 21 15 8 15 19 26 8 23 20 , 19 14 32 12 26 34 27 ->= 19 14 22 4 5 2 0 0 25 18 1 , 24 1 6 34 31 33 7 16 ->= 7 34 12 26 7 7 24 25 26 7 16 , 19 14 15 24 1 2 1 5 ->= 19 20 17 26 7 16 2 25 18 1 5 , 7 16 5 10 12 13 30 27 ->= 24 0 3 15 34 12 13 13 18 3 4 , 7 8 4 10 33 8 23 20 ->= 7 24 3 32 27 6 16 17 26 16 5 , 8 4 10 35 23 18 25 20 ->= 24 25 13 13 18 29 24 29 8 23 20 , 24 0 1 21 -> 8 4 2 0 3 4 5 6 7 8 22 , 16 10 11 1 21 -> 16 10 12 13 14 15 16 17 13 13 14 , 24 1 2 1 21 -> 24 1 6 19 20 21 22 23 14 23 14 , 24 1 6 24 3 -> 24 25 26 7 19 14 22 15 16 2 3 , 19 18 1 10 35 -> 19 26 8 22 23 20 17 26 16 10 35 , 16 2 1 17 18 3 -> 19 13 20 5 5 21 4 2 25 18 3 , 24 1 10 27 2 3 -> 34 27 17 13 26 8 4 17 20 2 3 , 7 24 1 10 12 14 -> 19 18 3 4 17 30 31 12 13 26 8 , 8 22 32 33 16 21 -> 8 15 24 0 29 19 20 6 7 16 21 , 16 6 34 31 12 20 21 -> 19 13 20 2 25 20 5 17 26 8 22 , 24 1 5 6 34 35 22 -> 24 1 6 7 8 9 29 7 8 22 22 , 24 28 33 16 6 24 3 -> 24 25 13 18 29 16 21 22 15 24 3 , 24 28 35 9 25 30 35 -> 24 3 22 4 17 14 23 20 6 34 35 , 7 16 21 32 11 1 21 -> 8 9 3 23 26 8 22 23 14 4 21 , 7 16 10 33 19 30 35 -> 8 15 24 0 29 7 19 20 5 10 35 , 7 16 10 33 8 9 3 -> 8 23 14 15 16 6 24 0 3 9 3 , 8 9 25 18 0 1 21 -> 8 32 33 7 16 2 0 3 4 17 14 , 8 22 22 32 27 10 35 -> 7 8 15 7 19 14 23 14 9 3 22 , 34 12 20 21 32 11 3 -> 34 12 13 13 26 24 1 21 4 6 8 , 16 10 35 32 33 16 10 35 -> 16 21 23 14 22 22 15 16 5 10 35 , 24 1 10 31 33 19 30 35 -> 7 34 31 33 7 16 17 20 21 32 35 , 7 16 10 33 34 33 16 21 -> 24 0 25 14 9 25 20 2 3 4 21 , 7 24 1 2 28 31 11 3 -> 19 14 9 0 29 7 7 7 24 0 3 , 7 19 30 33 16 2 1 21 -> 19 14 9 25 26 8 15 24 0 25 14 , 7 7 34 33 8 32 33 8 -> 16 17 13 14 23 13 18 0 0 25 14 , 7 8 23 30 27 17 18 3 -> 7 16 21 15 19 14 22 4 5 2 3 , 7 8 15 19 18 3 22 22 -> 7 8 15 8 15 16 6 7 16 17 14 , 7 34 12 26 34 33 8 22 -> 7 34 11 1 6 16 5 17 14 23 14 , 8 22 32 33 19 18 1 21 -> 8 4 10 35 9 25 13 13 26 16 21 , 8 32 11 1 5 10 11 3 -> 34 31 12 13 13 30 31 31 11 3 22 , 8 32 11 29 24 25 26 8 -> 34 35 9 0 0 25 26 8 4 17 14 , 34 11 3 32 12 30 33 8 -> 34 31 11 3 23 26 16 5 6 8 22 , 34 11 28 35 23 30 11 3 -> 34 31 12 26 16 6 8 23 18 1 21 , 34 35 32 27 10 12 26 8 -> 34 11 0 3 23 26 16 2 29 16 21 , 16 2 3 ->= 19 26 7 19 13 26 7 8 22 23 14 , 7 16 21 ->= 24 3 23 13 13 20 6 16 5 17 14 , 24 1 6 8 ->= 24 28 12 13 26 24 29 16 17 20 21 , 19 20 10 35 ->= 19 14 15 19 26 19 14 15 19 18 3 , 19 18 28 35 ->= 19 13 14 4 5 17 14 4 2 28 35 , 19 26 8 22 ->= 19 26 8 15 19 14 4 21 22 23 14 , 7 16 5 21 ->= 7 7 8 23 14 22 22 23 26 19 14 , 34 35 23 14 ->= 34 35 22 23 13 20 17 13 14 15 8 , 16 5 6 24 3 ->= 16 6 8 23 13 26 16 5 2 0 3 , 16 10 35 4 21 ->= 19 30 31 31 12 26 7 7 19 26 8 , 24 1 2 25 14 ->= 24 25 13 13 30 31 12 13 26 8 22 , 19 20 10 27 21 ->= 19 14 9 29 8 15 8 9 28 33 8 , 19 14 23 30 35 ->= 19 26 8 4 5 17 20 5 6 34 35 , 7 16 10 33 8 ->= 24 29 19 20 21 4 6 16 6 8 22 , 34 12 20 5 21 ->= 34 35 4 6 16 21 23 13 26 16 21 , 16 17 18 1 6 8 ->= 16 17 18 25 26 8 15 19 26 16 21 , 19 14 9 28 11 3 ->= 7 7 19 13 14 22 9 29 7 24 3 , 34 11 0 28 27 21 ->= 34 31 12 13 20 5 2 3 9 29 8 , 24 0 0 0 3 32 35 ->= 24 3 4 6 8 15 19 13 18 29 8 , 24 3 32 11 3 23 14 ->= 24 1 21 15 8 15 19 26 8 23 14 , 19 14 32 12 26 34 35 ->= 19 14 22 4 5 2 0 0 25 18 3 , 24 1 6 34 31 33 7 8 ->= 7 34 12 26 7 7 24 25 26 7 8 , 19 14 15 24 1 2 1 21 ->= 19 20 17 26 7 16 2 25 18 1 21 , 7 16 5 10 12 13 30 35 ->= 24 0 3 15 34 12 13 13 18 3 22 , 7 8 4 10 33 8 23 14 ->= 7 24 3 32 27 6 16 17 26 16 21 , 8 4 10 35 23 18 25 14 ->= 24 25 13 13 18 29 24 29 8 23 14 , 24 0 1 6 -> 8 4 2 0 3 4 5 6 7 8 15 , 16 10 11 1 6 -> 16 10 12 13 14 15 16 17 13 13 26 , 24 1 2 1 6 -> 24 1 6 19 20 21 22 23 14 23 26 , 24 1 6 24 29 -> 24 25 26 7 19 14 22 15 16 2 29 , 19 18 1 10 33 -> 19 26 8 22 23 20 17 26 16 10 33 , 16 2 1 17 18 29 -> 19 13 20 5 5 21 4 2 25 18 29 , 24 1 10 27 2 29 -> 34 27 17 13 26 8 4 17 20 2 29 , 7 24 1 10 12 26 -> 19 18 3 4 17 30 31 12 13 26 7 , 8 22 32 33 16 6 -> 8 15 24 0 29 19 20 6 7 16 6 , 16 6 34 31 12 20 6 -> 19 13 20 2 25 20 5 17 26 8 15 , 24 1 5 6 34 35 15 -> 24 1 6 7 8 9 29 7 8 22 15 , 24 28 33 16 6 24 29 -> 24 25 13 18 29 16 21 22 15 24 29 , 24 28 35 9 25 30 33 -> 24 3 22 4 17 14 23 20 6 34 33 , 7 16 21 32 11 1 6 -> 8 9 3 23 26 8 22 23 14 4 6 , 7 16 10 33 19 30 33 -> 8 15 24 0 29 7 19 20 5 10 33 , 7 16 10 33 8 9 29 -> 8 23 14 15 16 6 24 0 3 9 29 , 8 9 25 18 0 1 6 -> 8 32 33 7 16 2 0 3 4 17 26 , 8 22 22 32 27 10 33 -> 7 8 15 7 19 14 23 14 9 3 15 , 34 12 20 21 32 11 29 -> 34 12 13 13 26 24 1 21 4 6 7 , 16 10 35 32 33 16 10 33 -> 16 21 23 14 22 22 15 16 5 10 33 , 24 1 10 31 33 19 30 33 -> 7 34 31 33 7 16 17 20 21 32 33 , 7 16 10 33 34 33 16 6 -> 24 0 25 14 9 25 20 2 3 4 6 , 7 24 1 2 28 31 11 29 -> 19 14 9 0 29 7 7 7 24 0 29 , 7 19 30 33 16 2 1 6 -> 19 14 9 25 26 8 15 24 0 25 26 , 7 7 34 33 8 32 33 7 -> 16 17 13 14 23 13 18 0 0 25 26 , 7 8 23 30 27 17 18 29 -> 7 16 21 15 19 14 22 4 5 2 29 , 7 8 15 19 18 3 22 15 -> 7 8 15 8 15 16 6 7 16 17 26 , 7 34 12 26 34 33 8 15 -> 7 34 11 1 6 16 5 17 14 23 26 , 8 22 32 33 19 18 1 6 -> 8 4 10 35 9 25 13 13 26 16 6 , 8 32 11 1 5 10 11 29 -> 34 31 12 13 13 30 31 31 11 3 15 , 8 32 11 29 24 25 26 7 -> 34 35 9 0 0 25 26 8 4 17 26 , 34 11 3 32 12 30 33 7 -> 34 31 11 3 23 26 16 5 6 8 15 , 34 11 28 35 23 30 11 29 -> 34 31 12 26 16 6 8 23 18 1 6 , 34 35 32 27 10 12 26 7 -> 34 11 0 3 23 26 16 2 29 16 6 , 16 2 29 ->= 19 26 7 19 13 26 7 8 22 23 26 , 7 16 6 ->= 24 3 23 13 13 20 6 16 5 17 26 , 24 1 6 7 ->= 24 28 12 13 26 24 29 16 17 20 6 , 19 20 10 33 ->= 19 14 15 19 26 19 14 15 19 18 29 , 19 18 28 33 ->= 19 13 14 4 5 17 14 4 2 28 33 , 19 26 8 15 ->= 19 26 8 15 19 14 4 21 22 23 26 , 7 16 5 6 ->= 7 7 8 23 14 22 22 23 26 19 26 , 34 35 23 26 ->= 34 35 22 23 13 20 17 13 14 15 7 , 16 5 6 24 29 ->= 16 6 8 23 13 26 16 5 2 0 29 , 16 10 35 4 6 ->= 19 30 31 31 12 26 7 7 19 26 7 , 24 1 2 25 26 ->= 24 25 13 13 30 31 12 13 26 8 15 , 19 20 10 27 6 ->= 19 14 9 29 8 15 8 9 28 33 7 , 19 14 23 30 33 ->= 19 26 8 4 5 17 20 5 6 34 33 , 7 16 10 33 7 ->= 24 29 19 20 21 4 6 16 6 8 15 , 34 12 20 5 6 ->= 34 35 4 6 16 21 23 13 26 16 6 , 16 17 18 1 6 7 ->= 16 17 18 25 26 8 15 19 26 16 6 , 19 14 9 28 11 29 ->= 7 7 19 13 14 22 9 29 7 24 29 , 34 11 0 28 27 6 ->= 34 31 12 13 20 5 2 3 9 29 7 , 24 0 0 0 3 32 33 ->= 24 3 4 6 8 15 19 13 18 29 7 , 24 3 32 11 3 23 26 ->= 24 1 21 15 8 15 19 26 8 23 26 , 19 14 32 12 26 34 33 ->= 19 14 22 4 5 2 0 0 25 18 29 , 24 1 6 34 31 33 7 7 ->= 7 34 12 26 7 7 24 25 26 7 7 , 19 14 15 24 1 2 1 6 ->= 19 20 17 26 7 16 2 25 18 1 6 , 7 16 5 10 12 13 30 33 ->= 24 0 3 15 34 12 13 13 18 3 15 , 7 8 4 10 33 8 23 26 ->= 7 24 3 32 27 6 16 17 26 16 6 , 8 4 10 35 23 18 25 26 ->= 24 25 13 13 18 29 24 29 8 23 26 , 24 0 1 10 -> 8 4 2 0 3 4 5 6 7 8 32 , 16 10 11 1 10 -> 16 10 12 13 14 15 16 17 13 13 30 , 24 1 2 1 10 -> 24 1 6 19 20 21 22 23 14 23 30 , 24 1 6 24 28 -> 24 25 26 7 19 14 22 15 16 2 28 , 19 18 1 10 31 -> 19 26 8 22 23 20 17 26 16 10 31 , 16 2 1 17 18 28 -> 19 13 20 5 5 21 4 2 25 18 28 , 24 1 10 27 2 28 -> 34 27 17 13 26 8 4 17 20 2 28 , 7 24 1 10 12 30 -> 19 18 3 4 17 30 31 12 13 26 34 , 8 22 32 33 16 10 -> 8 15 24 0 29 19 20 6 7 16 10 , 16 6 34 31 12 20 10 -> 19 13 20 2 25 20 5 17 26 8 32 , 24 1 5 6 34 35 32 -> 24 1 6 7 8 9 29 7 8 22 32 , 24 28 33 16 6 24 28 -> 24 25 13 18 29 16 21 22 15 24 28 , 24 28 35 9 25 30 31 -> 24 3 22 4 17 14 23 20 6 34 31 , 7 16 21 32 11 1 10 -> 8 9 3 23 26 8 22 23 14 4 10 , 7 16 10 33 19 30 31 -> 8 15 24 0 29 7 19 20 5 10 31 , 7 16 10 33 8 9 28 -> 8 23 14 15 16 6 24 0 3 9 28 , 8 9 25 18 0 1 10 -> 8 32 33 7 16 2 0 3 4 17 30 , 8 22 22 32 27 10 31 -> 7 8 15 7 19 14 23 14 9 3 32 , 34 12 20 21 32 11 28 -> 34 12 13 13 26 24 1 21 4 6 34 , 16 10 35 32 33 16 10 31 -> 16 21 23 14 22 22 15 16 5 10 31 , 24 1 10 31 33 19 30 31 -> 7 34 31 33 7 16 17 20 21 32 31 , 7 16 10 33 34 33 16 10 -> 24 0 25 14 9 25 20 2 3 4 10 , 7 24 1 2 28 31 11 28 -> 19 14 9 0 29 7 7 7 24 0 28 , 7 19 30 33 16 2 1 10 -> 19 14 9 25 26 8 15 24 0 25 30 , 7 7 34 33 8 32 33 34 -> 16 17 13 14 23 13 18 0 0 25 30 , 7 8 23 30 27 17 18 28 -> 7 16 21 15 19 14 22 4 5 2 28 , 7 8 15 19 18 3 22 32 -> 7 8 15 8 15 16 6 7 16 17 30 , 7 34 12 26 34 33 8 32 -> 7 34 11 1 6 16 5 17 14 23 30 , 8 22 32 33 19 18 1 10 -> 8 4 10 35 9 25 13 13 26 16 10 , 8 32 11 1 5 10 11 28 -> 34 31 12 13 13 30 31 31 11 3 32 , 8 32 11 29 24 25 26 34 -> 34 35 9 0 0 25 26 8 4 17 30 , 34 11 3 32 12 30 33 34 -> 34 31 11 3 23 26 16 5 6 8 32 , 34 11 28 35 23 30 11 28 -> 34 31 12 26 16 6 8 23 18 1 10 , 34 35 32 27 10 12 26 34 -> 34 11 0 3 23 26 16 2 29 16 10 , 16 2 28 ->= 19 26 7 19 13 26 7 8 22 23 30 , 7 16 10 ->= 24 3 23 13 13 20 6 16 5 17 30 , 24 1 6 34 ->= 24 28 12 13 26 24 29 16 17 20 10 , 19 20 10 31 ->= 19 14 15 19 26 19 14 15 19 18 28 , 19 18 28 31 ->= 19 13 14 4 5 17 14 4 2 28 31 , 19 26 8 32 ->= 19 26 8 15 19 14 4 21 22 23 30 , 7 16 5 10 ->= 7 7 8 23 14 22 22 23 26 19 30 , 34 35 23 30 ->= 34 35 22 23 13 20 17 13 14 15 34 , 16 5 6 24 28 ->= 16 6 8 23 13 26 16 5 2 0 28 , 16 10 35 4 10 ->= 19 30 31 31 12 26 7 7 19 26 34 , 24 1 2 25 30 ->= 24 25 13 13 30 31 12 13 26 8 32 , 19 20 10 27 10 ->= 19 14 9 29 8 15 8 9 28 33 34 , 19 14 23 30 31 ->= 19 26 8 4 5 17 20 5 6 34 31 , 7 16 10 33 34 ->= 24 29 19 20 21 4 6 16 6 8 32 , 34 12 20 5 10 ->= 34 35 4 6 16 21 23 13 26 16 10 , 16 17 18 1 6 34 ->= 16 17 18 25 26 8 15 19 26 16 10 , 19 14 9 28 11 28 ->= 7 7 19 13 14 22 9 29 7 24 28 , 34 11 0 28 27 10 ->= 34 31 12 13 20 5 2 3 9 29 34 , 24 0 0 0 3 32 31 ->= 24 3 4 6 8 15 19 13 18 29 34 , 24 3 32 11 3 23 30 ->= 24 1 21 15 8 15 19 26 8 23 30 , 19 14 32 12 26 34 31 ->= 19 14 22 4 5 2 0 0 25 18 28 , 24 1 6 34 31 33 7 34 ->= 7 34 12 26 7 7 24 25 26 7 34 , 19 14 15 24 1 2 1 10 ->= 19 20 17 26 7 16 2 25 18 1 10 , 7 16 5 10 12 13 30 31 ->= 24 0 3 15 34 12 13 13 18 3 32 , 7 8 4 10 33 8 23 30 ->= 7 24 3 32 27 6 16 17 26 16 10 , 8 4 10 35 23 18 25 30 ->= 24 25 13 13 18 29 24 29 8 23 30 , 24 0 1 17 -> 8 4 2 0 3 4 5 6 7 8 23 , 16 10 11 1 17 -> 16 10 12 13 14 15 16 17 13 13 13 , 24 1 2 1 17 -> 24 1 6 19 20 21 22 23 14 23 13 , 24 1 6 24 25 -> 24 25 26 7 19 14 22 15 16 2 25 , 19 18 1 10 12 -> 19 26 8 22 23 20 17 26 16 10 12 , 16 2 1 17 18 25 -> 19 13 20 5 5 21 4 2 25 18 25 , 24 1 10 27 2 25 -> 34 27 17 13 26 8 4 17 20 2 25 , 7 24 1 10 12 13 -> 19 18 3 4 17 30 31 12 13 26 19 , 8 22 32 33 16 17 -> 8 15 24 0 29 19 20 6 7 16 17 , 16 6 34 31 12 20 17 -> 19 13 20 2 25 20 5 17 26 8 23 , 24 1 5 6 34 35 23 -> 24 1 6 7 8 9 29 7 8 22 23 , 24 28 33 16 6 24 25 -> 24 25 13 18 29 16 21 22 15 24 25 , 24 28 35 9 25 30 12 -> 24 3 22 4 17 14 23 20 6 34 12 , 7 16 21 32 11 1 17 -> 8 9 3 23 26 8 22 23 14 4 17 , 7 16 10 33 19 30 12 -> 8 15 24 0 29 7 19 20 5 10 12 , 7 16 10 33 8 9 25 -> 8 23 14 15 16 6 24 0 3 9 25 , 8 9 25 18 0 1 17 -> 8 32 33 7 16 2 0 3 4 17 13 , 8 22 22 32 27 10 12 -> 7 8 15 7 19 14 23 14 9 3 23 , 34 12 20 21 32 11 25 -> 34 12 13 13 26 24 1 21 4 6 19 , 16 10 35 32 33 16 10 12 -> 16 21 23 14 22 22 15 16 5 10 12 , 24 1 10 31 33 19 30 12 -> 7 34 31 33 7 16 17 20 21 32 12 , 7 16 10 33 34 33 16 17 -> 24 0 25 14 9 25 20 2 3 4 17 , 7 24 1 2 28 31 11 25 -> 19 14 9 0 29 7 7 7 24 0 25 , 7 19 30 33 16 2 1 17 -> 19 14 9 25 26 8 15 24 0 25 13 , 7 7 34 33 8 32 33 19 -> 16 17 13 14 23 13 18 0 0 25 13 , 7 8 23 30 27 17 18 25 -> 7 16 21 15 19 14 22 4 5 2 25 , 7 8 15 19 18 3 22 23 -> 7 8 15 8 15 16 6 7 16 17 13 , 7 34 12 26 34 33 8 23 -> 7 34 11 1 6 16 5 17 14 23 13 , 8 22 32 33 19 18 1 17 -> 8 4 10 35 9 25 13 13 26 16 17 , 8 32 11 1 5 10 11 25 -> 34 31 12 13 13 30 31 31 11 3 23 , 8 32 11 29 24 25 26 19 -> 34 35 9 0 0 25 26 8 4 17 13 , 34 11 3 32 12 30 33 19 -> 34 31 11 3 23 26 16 5 6 8 23 , 34 11 28 35 23 30 11 25 -> 34 31 12 26 16 6 8 23 18 1 17 , 34 35 32 27 10 12 26 19 -> 34 11 0 3 23 26 16 2 29 16 17 , 16 2 25 ->= 19 26 7 19 13 26 7 8 22 23 13 , 7 16 17 ->= 24 3 23 13 13 20 6 16 5 17 13 , 24 1 6 19 ->= 24 28 12 13 26 24 29 16 17 20 17 , 19 20 10 12 ->= 19 14 15 19 26 19 14 15 19 18 25 , 19 18 28 12 ->= 19 13 14 4 5 17 14 4 2 28 12 , 19 26 8 23 ->= 19 26 8 15 19 14 4 21 22 23 13 , 7 16 5 17 ->= 7 7 8 23 14 22 22 23 26 19 13 , 34 35 23 13 ->= 34 35 22 23 13 20 17 13 14 15 19 , 16 5 6 24 25 ->= 16 6 8 23 13 26 16 5 2 0 25 , 16 10 35 4 17 ->= 19 30 31 31 12 26 7 7 19 26 19 , 24 1 2 25 13 ->= 24 25 13 13 30 31 12 13 26 8 23 , 19 20 10 27 17 ->= 19 14 9 29 8 15 8 9 28 33 19 , 19 14 23 30 12 ->= 19 26 8 4 5 17 20 5 6 34 12 , 7 16 10 33 19 ->= 24 29 19 20 21 4 6 16 6 8 23 , 34 12 20 5 17 ->= 34 35 4 6 16 21 23 13 26 16 17 , 16 17 18 1 6 19 ->= 16 17 18 25 26 8 15 19 26 16 17 , 19 14 9 28 11 25 ->= 7 7 19 13 14 22 9 29 7 24 25 , 34 11 0 28 27 17 ->= 34 31 12 13 20 5 2 3 9 29 19 , 24 0 0 0 3 32 12 ->= 24 3 4 6 8 15 19 13 18 29 19 , 24 3 32 11 3 23 13 ->= 24 1 21 15 8 15 19 26 8 23 13 , 19 14 32 12 26 34 12 ->= 19 14 22 4 5 2 0 0 25 18 25 , 24 1 6 34 31 33 7 19 ->= 7 34 12 26 7 7 24 25 26 7 19 , 19 14 15 24 1 2 1 17 ->= 19 20 17 26 7 16 2 25 18 1 17 , 7 16 5 10 12 13 30 12 ->= 24 0 3 15 34 12 13 13 18 3 23 , 7 8 4 10 33 8 23 13 ->= 7 24 3 32 27 6 16 17 26 16 17 , 8 4 10 35 23 18 25 13 ->= 24 25 13 13 18 29 24 29 8 23 13 , 11 0 1 2 -> 35 4 2 0 3 4 5 6 7 8 9 , 27 10 11 1 2 -> 27 10 12 13 14 15 16 17 13 13 18 , 11 1 2 1 2 -> 11 1 6 19 20 21 22 23 14 23 18 , 11 1 6 24 0 -> 11 25 26 7 19 14 22 15 16 2 0 , 12 18 1 10 11 -> 12 26 8 22 23 20 17 26 16 10 11 , 27 2 1 17 18 0 -> 12 13 20 5 5 21 4 2 25 18 0 , 11 1 10 27 2 0 -> 31 27 17 13 26 8 4 17 20 2 0 , 33 24 1 10 12 18 -> 12 18 3 4 17 30 31 12 13 26 24 , 35 22 32 33 16 2 -> 35 15 24 0 29 19 20 6 7 16 2 , 27 6 34 31 12 20 2 -> 12 13 20 2 25 20 5 17 26 8 9 , 11 1 5 6 34 35 9 -> 11 1 6 7 8 9 29 7 8 22 9 , 11 28 33 16 6 24 0 -> 11 25 13 18 29 16 21 22 15 24 0 , 11 28 35 9 25 30 11 -> 11 3 22 4 17 14 23 20 6 34 11 , 33 16 21 32 11 1 2 -> 35 9 3 23 26 8 22 23 14 4 2 , 33 16 10 33 19 30 11 -> 35 15 24 0 29 7 19 20 5 10 11 , 33 16 10 33 8 9 0 -> 35 23 14 15 16 6 24 0 3 9 0 , 35 9 25 18 0 1 2 -> 35 32 33 7 16 2 0 3 4 17 18 , 35 22 22 32 27 10 11 -> 33 8 15 7 19 14 23 14 9 3 9 , 31 12 20 21 32 11 0 -> 31 12 13 13 26 24 1 21 4 6 24 , 27 10 35 32 33 16 10 11 -> 27 21 23 14 22 22 15 16 5 10 11 , 11 1 10 31 33 19 30 11 -> 33 34 31 33 7 16 17 20 21 32 11 , 33 16 10 33 34 33 16 2 -> 11 0 25 14 9 25 20 2 3 4 2 , 33 24 1 2 28 31 11 0 -> 12 14 9 0 29 7 7 7 24 0 0 , 33 19 30 33 16 2 1 2 -> 12 14 9 25 26 8 15 24 0 25 18 , 33 7 34 33 8 32 33 24 -> 27 17 13 14 23 13 18 0 0 25 18 , 33 8 23 30 27 17 18 0 -> 33 16 21 15 19 14 22 4 5 2 0 , 33 8 15 19 18 3 22 9 -> 33 8 15 8 15 16 6 7 16 17 18 , 33 34 12 26 34 33 8 9 -> 33 34 11 1 6 16 5 17 14 23 18 , 35 22 32 33 19 18 1 2 -> 35 4 10 35 9 25 13 13 26 16 2 , 35 32 11 1 5 10 11 0 -> 31 31 12 13 13 30 31 31 11 3 9 , 35 32 11 29 24 25 26 24 -> 31 35 9 0 0 25 26 8 4 17 18 , 31 11 3 32 12 30 33 24 -> 31 31 11 3 23 26 16 5 6 8 9 , 31 11 28 35 23 30 11 0 -> 31 31 12 26 16 6 8 23 18 1 2 , 31 35 32 27 10 12 26 24 -> 31 11 0 3 23 26 16 2 29 16 2 , 27 2 0 ->= 12 26 7 19 13 26 7 8 22 23 18 , 33 16 2 ->= 11 3 23 13 13 20 6 16 5 17 18 , 11 1 6 24 ->= 11 28 12 13 26 24 29 16 17 20 2 , 12 20 10 11 ->= 12 14 15 19 26 19 14 15 19 18 0 , 12 18 28 11 ->= 12 13 14 4 5 17 14 4 2 28 11 , 12 26 8 9 ->= 12 26 8 15 19 14 4 21 22 23 18 , 33 16 5 2 ->= 33 7 8 23 14 22 22 23 26 19 18 , 31 35 23 18 ->= 31 35 22 23 13 20 17 13 14 15 24 , 27 5 6 24 0 ->= 27 6 8 23 13 26 16 5 2 0 0 , 27 10 35 4 2 ->= 12 30 31 31 12 26 7 7 19 26 24 , 11 1 2 25 18 ->= 11 25 13 13 30 31 12 13 26 8 9 , 12 20 10 27 2 ->= 12 14 9 29 8 15 8 9 28 33 24 , 12 14 23 30 11 ->= 12 26 8 4 5 17 20 5 6 34 11 , 33 16 10 33 24 ->= 11 29 19 20 21 4 6 16 6 8 9 , 31 12 20 5 2 ->= 31 35 4 6 16 21 23 13 26 16 2 , 27 17 18 1 6 24 ->= 27 17 18 25 26 8 15 19 26 16 2 , 12 14 9 28 11 0 ->= 33 7 19 13 14 22 9 29 7 24 0 , 31 11 0 28 27 2 ->= 31 31 12 13 20 5 2 3 9 29 24 , 11 0 0 0 3 32 11 ->= 11 3 4 6 8 15 19 13 18 29 24 , 11 3 32 11 3 23 18 ->= 11 1 21 15 8 15 19 26 8 23 18 , 12 14 32 12 26 34 11 ->= 12 14 22 4 5 2 0 0 25 18 0 , 11 1 6 34 31 33 7 24 ->= 33 34 12 26 7 7 24 25 26 7 24 , 12 14 15 24 1 2 1 2 ->= 12 20 17 26 7 16 2 25 18 1 2 , 33 16 5 10 12 13 30 11 ->= 11 0 3 15 34 12 13 13 18 3 9 , 33 8 4 10 33 8 23 18 ->= 33 24 3 32 27 6 16 17 26 16 2 , 35 4 10 35 23 18 25 18 ->= 11 25 13 13 18 29 24 29 8 23 18 , 11 0 1 5 -> 35 4 2 0 3 4 5 6 7 8 4 , 27 10 11 1 5 -> 27 10 12 13 14 15 16 17 13 13 20 , 11 1 2 1 5 -> 11 1 6 19 20 21 22 23 14 23 20 , 11 1 6 24 1 -> 11 25 26 7 19 14 22 15 16 2 1 , 12 18 1 10 27 -> 12 26 8 22 23 20 17 26 16 10 27 , 27 2 1 17 18 1 -> 12 13 20 5 5 21 4 2 25 18 1 , 11 1 10 27 2 1 -> 31 27 17 13 26 8 4 17 20 2 1 , 33 24 1 10 12 20 -> 12 18 3 4 17 30 31 12 13 26 16 , 35 22 32 33 16 5 -> 35 15 24 0 29 19 20 6 7 16 5 , 27 6 34 31 12 20 5 -> 12 13 20 2 25 20 5 17 26 8 4 , 11 1 5 6 34 35 4 -> 11 1 6 7 8 9 29 7 8 22 4 , 11 28 33 16 6 24 1 -> 11 25 13 18 29 16 21 22 15 24 1 , 11 28 35 9 25 30 27 -> 11 3 22 4 17 14 23 20 6 34 27 , 33 16 21 32 11 1 5 -> 35 9 3 23 26 8 22 23 14 4 5 , 33 16 10 33 19 30 27 -> 35 15 24 0 29 7 19 20 5 10 27 , 33 16 10 33 8 9 1 -> 35 23 14 15 16 6 24 0 3 9 1 , 35 9 25 18 0 1 5 -> 35 32 33 7 16 2 0 3 4 17 20 , 35 22 22 32 27 10 27 -> 33 8 15 7 19 14 23 14 9 3 4 , 31 12 20 21 32 11 1 -> 31 12 13 13 26 24 1 21 4 6 16 , 27 10 35 32 33 16 10 27 -> 27 21 23 14 22 22 15 16 5 10 27 , 11 1 10 31 33 19 30 27 -> 33 34 31 33 7 16 17 20 21 32 27 , 33 16 10 33 34 33 16 5 -> 11 0 25 14 9 25 20 2 3 4 5 , 33 24 1 2 28 31 11 1 -> 12 14 9 0 29 7 7 7 24 0 1 , 33 19 30 33 16 2 1 5 -> 12 14 9 25 26 8 15 24 0 25 20 , 33 7 34 33 8 32 33 16 -> 27 17 13 14 23 13 18 0 0 25 20 , 33 8 23 30 27 17 18 1 -> 33 16 21 15 19 14 22 4 5 2 1 , 33 8 15 19 18 3 22 4 -> 33 8 15 8 15 16 6 7 16 17 20 , 33 34 12 26 34 33 8 4 -> 33 34 11 1 6 16 5 17 14 23 20 , 35 22 32 33 19 18 1 5 -> 35 4 10 35 9 25 13 13 26 16 5 , 35 32 11 1 5 10 11 1 -> 31 31 12 13 13 30 31 31 11 3 4 , 35 32 11 29 24 25 26 16 -> 31 35 9 0 0 25 26 8 4 17 20 , 31 11 3 32 12 30 33 16 -> 31 31 11 3 23 26 16 5 6 8 4 , 31 11 28 35 23 30 11 1 -> 31 31 12 26 16 6 8 23 18 1 5 , 31 35 32 27 10 12 26 16 -> 31 11 0 3 23 26 16 2 29 16 5 , 27 2 1 ->= 12 26 7 19 13 26 7 8 22 23 20 , 33 16 5 ->= 11 3 23 13 13 20 6 16 5 17 20 , 11 1 6 16 ->= 11 28 12 13 26 24 29 16 17 20 5 , 12 20 10 27 ->= 12 14 15 19 26 19 14 15 19 18 1 , 12 18 28 27 ->= 12 13 14 4 5 17 14 4 2 28 27 , 12 26 8 4 ->= 12 26 8 15 19 14 4 21 22 23 20 , 33 16 5 5 ->= 33 7 8 23 14 22 22 23 26 19 20 , 31 35 23 20 ->= 31 35 22 23 13 20 17 13 14 15 16 , 27 5 6 24 1 ->= 27 6 8 23 13 26 16 5 2 0 1 , 27 10 35 4 5 ->= 12 30 31 31 12 26 7 7 19 26 16 , 11 1 2 25 20 ->= 11 25 13 13 30 31 12 13 26 8 4 , 12 20 10 27 5 ->= 12 14 9 29 8 15 8 9 28 33 16 , 12 14 23 30 27 ->= 12 26 8 4 5 17 20 5 6 34 27 , 33 16 10 33 16 ->= 11 29 19 20 21 4 6 16 6 8 4 , 31 12 20 5 5 ->= 31 35 4 6 16 21 23 13 26 16 5 , 27 17 18 1 6 16 ->= 27 17 18 25 26 8 15 19 26 16 5 , 12 14 9 28 11 1 ->= 33 7 19 13 14 22 9 29 7 24 1 , 31 11 0 28 27 5 ->= 31 31 12 13 20 5 2 3 9 29 16 , 11 0 0 0 3 32 27 ->= 11 3 4 6 8 15 19 13 18 29 16 , 11 3 32 11 3 23 20 ->= 11 1 21 15 8 15 19 26 8 23 20 , 12 14 32 12 26 34 27 ->= 12 14 22 4 5 2 0 0 25 18 1 , 11 1 6 34 31 33 7 16 ->= 33 34 12 26 7 7 24 25 26 7 16 , 12 14 15 24 1 2 1 5 ->= 12 20 17 26 7 16 2 25 18 1 5 , 33 16 5 10 12 13 30 27 ->= 11 0 3 15 34 12 13 13 18 3 4 , 33 8 4 10 33 8 23 20 ->= 33 24 3 32 27 6 16 17 26 16 5 , 35 4 10 35 23 18 25 20 ->= 11 25 13 13 18 29 24 29 8 23 20 , 11 0 1 21 -> 35 4 2 0 3 4 5 6 7 8 22 , 27 10 11 1 21 -> 27 10 12 13 14 15 16 17 13 13 14 , 11 1 2 1 21 -> 11 1 6 19 20 21 22 23 14 23 14 , 11 1 6 24 3 -> 11 25 26 7 19 14 22 15 16 2 3 , 12 18 1 10 35 -> 12 26 8 22 23 20 17 26 16 10 35 , 27 2 1 17 18 3 -> 12 13 20 5 5 21 4 2 25 18 3 , 11 1 10 27 2 3 -> 31 27 17 13 26 8 4 17 20 2 3 , 33 24 1 10 12 14 -> 12 18 3 4 17 30 31 12 13 26 8 , 35 22 32 33 16 21 -> 35 15 24 0 29 19 20 6 7 16 21 , 27 6 34 31 12 20 21 -> 12 13 20 2 25 20 5 17 26 8 22 , 11 1 5 6 34 35 22 -> 11 1 6 7 8 9 29 7 8 22 22 , 11 28 33 16 6 24 3 -> 11 25 13 18 29 16 21 22 15 24 3 , 11 28 35 9 25 30 35 -> 11 3 22 4 17 14 23 20 6 34 35 , 33 16 21 32 11 1 21 -> 35 9 3 23 26 8 22 23 14 4 21 , 33 16 10 33 19 30 35 -> 35 15 24 0 29 7 19 20 5 10 35 , 33 16 10 33 8 9 3 -> 35 23 14 15 16 6 24 0 3 9 3 , 35 9 25 18 0 1 21 -> 35 32 33 7 16 2 0 3 4 17 14 , 35 22 22 32 27 10 35 -> 33 8 15 7 19 14 23 14 9 3 22 , 31 12 20 21 32 11 3 -> 31 12 13 13 26 24 1 21 4 6 8 , 27 10 35 32 33 16 10 35 -> 27 21 23 14 22 22 15 16 5 10 35 , 11 1 10 31 33 19 30 35 -> 33 34 31 33 7 16 17 20 21 32 35 , 33 16 10 33 34 33 16 21 -> 11 0 25 14 9 25 20 2 3 4 21 , 33 24 1 2 28 31 11 3 -> 12 14 9 0 29 7 7 7 24 0 3 , 33 19 30 33 16 2 1 21 -> 12 14 9 25 26 8 15 24 0 25 14 , 33 7 34 33 8 32 33 8 -> 27 17 13 14 23 13 18 0 0 25 14 , 33 8 23 30 27 17 18 3 -> 33 16 21 15 19 14 22 4 5 2 3 , 33 8 15 19 18 3 22 22 -> 33 8 15 8 15 16 6 7 16 17 14 , 33 34 12 26 34 33 8 22 -> 33 34 11 1 6 16 5 17 14 23 14 , 35 22 32 33 19 18 1 21 -> 35 4 10 35 9 25 13 13 26 16 21 , 35 32 11 1 5 10 11 3 -> 31 31 12 13 13 30 31 31 11 3 22 , 35 32 11 29 24 25 26 8 -> 31 35 9 0 0 25 26 8 4 17 14 , 31 11 3 32 12 30 33 8 -> 31 31 11 3 23 26 16 5 6 8 22 , 31 11 28 35 23 30 11 3 -> 31 31 12 26 16 6 8 23 18 1 21 , 31 35 32 27 10 12 26 8 -> 31 11 0 3 23 26 16 2 29 16 21 , 27 2 3 ->= 12 26 7 19 13 26 7 8 22 23 14 , 33 16 21 ->= 11 3 23 13 13 20 6 16 5 17 14 , 11 1 6 8 ->= 11 28 12 13 26 24 29 16 17 20 21 , 12 20 10 35 ->= 12 14 15 19 26 19 14 15 19 18 3 , 12 18 28 35 ->= 12 13 14 4 5 17 14 4 2 28 35 , 12 26 8 22 ->= 12 26 8 15 19 14 4 21 22 23 14 , 33 16 5 21 ->= 33 7 8 23 14 22 22 23 26 19 14 , 31 35 23 14 ->= 31 35 22 23 13 20 17 13 14 15 8 , 27 5 6 24 3 ->= 27 6 8 23 13 26 16 5 2 0 3 , 27 10 35 4 21 ->= 12 30 31 31 12 26 7 7 19 26 8 , 11 1 2 25 14 ->= 11 25 13 13 30 31 12 13 26 8 22 , 12 20 10 27 21 ->= 12 14 9 29 8 15 8 9 28 33 8 , 12 14 23 30 35 ->= 12 26 8 4 5 17 20 5 6 34 35 , 33 16 10 33 8 ->= 11 29 19 20 21 4 6 16 6 8 22 , 31 12 20 5 21 ->= 31 35 4 6 16 21 23 13 26 16 21 , 27 17 18 1 6 8 ->= 27 17 18 25 26 8 15 19 26 16 21 , 12 14 9 28 11 3 ->= 33 7 19 13 14 22 9 29 7 24 3 , 31 11 0 28 27 21 ->= 31 31 12 13 20 5 2 3 9 29 8 , 11 0 0 0 3 32 35 ->= 11 3 4 6 8 15 19 13 18 29 8 , 11 3 32 11 3 23 14 ->= 11 1 21 15 8 15 19 26 8 23 14 , 12 14 32 12 26 34 35 ->= 12 14 22 4 5 2 0 0 25 18 3 , 11 1 6 34 31 33 7 8 ->= 33 34 12 26 7 7 24 25 26 7 8 , 12 14 15 24 1 2 1 21 ->= 12 20 17 26 7 16 2 25 18 1 21 , 33 16 5 10 12 13 30 35 ->= 11 0 3 15 34 12 13 13 18 3 22 , 33 8 4 10 33 8 23 14 ->= 33 24 3 32 27 6 16 17 26 16 21 , 35 4 10 35 23 18 25 14 ->= 11 25 13 13 18 29 24 29 8 23 14 , 11 0 1 6 -> 35 4 2 0 3 4 5 6 7 8 15 , 27 10 11 1 6 -> 27 10 12 13 14 15 16 17 13 13 26 , 11 1 2 1 6 -> 11 1 6 19 20 21 22 23 14 23 26 , 11 1 6 24 29 -> 11 25 26 7 19 14 22 15 16 2 29 , 12 18 1 10 33 -> 12 26 8 22 23 20 17 26 16 10 33 , 27 2 1 17 18 29 -> 12 13 20 5 5 21 4 2 25 18 29 , 11 1 10 27 2 29 -> 31 27 17 13 26 8 4 17 20 2 29 , 33 24 1 10 12 26 -> 12 18 3 4 17 30 31 12 13 26 7 , 35 22 32 33 16 6 -> 35 15 24 0 29 19 20 6 7 16 6 , 27 6 34 31 12 20 6 -> 12 13 20 2 25 20 5 17 26 8 15 , 11 1 5 6 34 35 15 -> 11 1 6 7 8 9 29 7 8 22 15 , 11 28 33 16 6 24 29 -> 11 25 13 18 29 16 21 22 15 24 29 , 11 28 35 9 25 30 33 -> 11 3 22 4 17 14 23 20 6 34 33 , 33 16 21 32 11 1 6 -> 35 9 3 23 26 8 22 23 14 4 6 , 33 16 10 33 19 30 33 -> 35 15 24 0 29 7 19 20 5 10 33 , 33 16 10 33 8 9 29 -> 35 23 14 15 16 6 24 0 3 9 29 , 35 9 25 18 0 1 6 -> 35 32 33 7 16 2 0 3 4 17 26 , 35 22 22 32 27 10 33 -> 33 8 15 7 19 14 23 14 9 3 15 , 31 12 20 21 32 11 29 -> 31 12 13 13 26 24 1 21 4 6 7 , 27 10 35 32 33 16 10 33 -> 27 21 23 14 22 22 15 16 5 10 33 , 11 1 10 31 33 19 30 33 -> 33 34 31 33 7 16 17 20 21 32 33 , 33 16 10 33 34 33 16 6 -> 11 0 25 14 9 25 20 2 3 4 6 , 33 24 1 2 28 31 11 29 -> 12 14 9 0 29 7 7 7 24 0 29 , 33 19 30 33 16 2 1 6 -> 12 14 9 25 26 8 15 24 0 25 26 , 33 7 34 33 8 32 33 7 -> 27 17 13 14 23 13 18 0 0 25 26 , 33 8 23 30 27 17 18 29 -> 33 16 21 15 19 14 22 4 5 2 29 , 33 8 15 19 18 3 22 15 -> 33 8 15 8 15 16 6 7 16 17 26 , 33 34 12 26 34 33 8 15 -> 33 34 11 1 6 16 5 17 14 23 26 , 35 22 32 33 19 18 1 6 -> 35 4 10 35 9 25 13 13 26 16 6 , 35 32 11 1 5 10 11 29 -> 31 31 12 13 13 30 31 31 11 3 15 , 35 32 11 29 24 25 26 7 -> 31 35 9 0 0 25 26 8 4 17 26 , 31 11 3 32 12 30 33 7 -> 31 31 11 3 23 26 16 5 6 8 15 , 31 11 28 35 23 30 11 29 -> 31 31 12 26 16 6 8 23 18 1 6 , 31 35 32 27 10 12 26 7 -> 31 11 0 3 23 26 16 2 29 16 6 , 27 2 29 ->= 12 26 7 19 13 26 7 8 22 23 26 , 33 16 6 ->= 11 3 23 13 13 20 6 16 5 17 26 , 11 1 6 7 ->= 11 28 12 13 26 24 29 16 17 20 6 , 12 20 10 33 ->= 12 14 15 19 26 19 14 15 19 18 29 , 12 18 28 33 ->= 12 13 14 4 5 17 14 4 2 28 33 , 12 26 8 15 ->= 12 26 8 15 19 14 4 21 22 23 26 , 33 16 5 6 ->= 33 7 8 23 14 22 22 23 26 19 26 , 31 35 23 26 ->= 31 35 22 23 13 20 17 13 14 15 7 , 27 5 6 24 29 ->= 27 6 8 23 13 26 16 5 2 0 29 , 27 10 35 4 6 ->= 12 30 31 31 12 26 7 7 19 26 7 , 11 1 2 25 26 ->= 11 25 13 13 30 31 12 13 26 8 15 , 12 20 10 27 6 ->= 12 14 9 29 8 15 8 9 28 33 7 , 12 14 23 30 33 ->= 12 26 8 4 5 17 20 5 6 34 33 , 33 16 10 33 7 ->= 11 29 19 20 21 4 6 16 6 8 15 , 31 12 20 5 6 ->= 31 35 4 6 16 21 23 13 26 16 6 , 27 17 18 1 6 7 ->= 27 17 18 25 26 8 15 19 26 16 6 , 12 14 9 28 11 29 ->= 33 7 19 13 14 22 9 29 7 24 29 , 31 11 0 28 27 6 ->= 31 31 12 13 20 5 2 3 9 29 7 , 11 0 0 0 3 32 33 ->= 11 3 4 6 8 15 19 13 18 29 7 , 11 3 32 11 3 23 26 ->= 11 1 21 15 8 15 19 26 8 23 26 , 12 14 32 12 26 34 33 ->= 12 14 22 4 5 2 0 0 25 18 29 , 11 1 6 34 31 33 7 7 ->= 33 34 12 26 7 7 24 25 26 7 7 , 12 14 15 24 1 2 1 6 ->= 12 20 17 26 7 16 2 25 18 1 6 , 33 16 5 10 12 13 30 33 ->= 11 0 3 15 34 12 13 13 18 3 15 , 33 8 4 10 33 8 23 26 ->= 33 24 3 32 27 6 16 17 26 16 6 , 35 4 10 35 23 18 25 26 ->= 11 25 13 13 18 29 24 29 8 23 26 , 11 0 1 10 -> 35 4 2 0 3 4 5 6 7 8 32 , 27 10 11 1 10 -> 27 10 12 13 14 15 16 17 13 13 30 , 11 1 2 1 10 -> 11 1 6 19 20 21 22 23 14 23 30 , 11 1 6 24 28 -> 11 25 26 7 19 14 22 15 16 2 28 , 12 18 1 10 31 -> 12 26 8 22 23 20 17 26 16 10 31 , 27 2 1 17 18 28 -> 12 13 20 5 5 21 4 2 25 18 28 , 11 1 10 27 2 28 -> 31 27 17 13 26 8 4 17 20 2 28 , 33 24 1 10 12 30 -> 12 18 3 4 17 30 31 12 13 26 34 , 35 22 32 33 16 10 -> 35 15 24 0 29 19 20 6 7 16 10 , 27 6 34 31 12 20 10 -> 12 13 20 2 25 20 5 17 26 8 32 , 11 1 5 6 34 35 32 -> 11 1 6 7 8 9 29 7 8 22 32 , 11 28 33 16 6 24 28 -> 11 25 13 18 29 16 21 22 15 24 28 , 11 28 35 9 25 30 31 -> 11 3 22 4 17 14 23 20 6 34 31 , 33 16 21 32 11 1 10 -> 35 9 3 23 26 8 22 23 14 4 10 , 33 16 10 33 19 30 31 -> 35 15 24 0 29 7 19 20 5 10 31 , 33 16 10 33 8 9 28 -> 35 23 14 15 16 6 24 0 3 9 28 , 35 9 25 18 0 1 10 -> 35 32 33 7 16 2 0 3 4 17 30 , 35 22 22 32 27 10 31 -> 33 8 15 7 19 14 23 14 9 3 32 , 31 12 20 21 32 11 28 -> 31 12 13 13 26 24 1 21 4 6 34 , 27 10 35 32 33 16 10 31 -> 27 21 23 14 22 22 15 16 5 10 31 , 11 1 10 31 33 19 30 31 -> 33 34 31 33 7 16 17 20 21 32 31 , 33 16 10 33 34 33 16 10 -> 11 0 25 14 9 25 20 2 3 4 10 , 33 24 1 2 28 31 11 28 -> 12 14 9 0 29 7 7 7 24 0 28 , 33 19 30 33 16 2 1 10 -> 12 14 9 25 26 8 15 24 0 25 30 , 33 7 34 33 8 32 33 34 -> 27 17 13 14 23 13 18 0 0 25 30 , 33 8 23 30 27 17 18 28 -> 33 16 21 15 19 14 22 4 5 2 28 , 33 8 15 19 18 3 22 32 -> 33 8 15 8 15 16 6 7 16 17 30 , 33 34 12 26 34 33 8 32 -> 33 34 11 1 6 16 5 17 14 23 30 , 35 22 32 33 19 18 1 10 -> 35 4 10 35 9 25 13 13 26 16 10 , 35 32 11 1 5 10 11 28 -> 31 31 12 13 13 30 31 31 11 3 32 , 35 32 11 29 24 25 26 34 -> 31 35 9 0 0 25 26 8 4 17 30 , 31 11 3 32 12 30 33 34 -> 31 31 11 3 23 26 16 5 6 8 32 , 31 11 28 35 23 30 11 28 -> 31 31 12 26 16 6 8 23 18 1 10 , 31 35 32 27 10 12 26 34 -> 31 11 0 3 23 26 16 2 29 16 10 , 27 2 28 ->= 12 26 7 19 13 26 7 8 22 23 30 , 33 16 10 ->= 11 3 23 13 13 20 6 16 5 17 30 , 11 1 6 34 ->= 11 28 12 13 26 24 29 16 17 20 10 , 12 20 10 31 ->= 12 14 15 19 26 19 14 15 19 18 28 , 12 18 28 31 ->= 12 13 14 4 5 17 14 4 2 28 31 , 12 26 8 32 ->= 12 26 8 15 19 14 4 21 22 23 30 , 33 16 5 10 ->= 33 7 8 23 14 22 22 23 26 19 30 , 31 35 23 30 ->= 31 35 22 23 13 20 17 13 14 15 34 , 27 5 6 24 28 ->= 27 6 8 23 13 26 16 5 2 0 28 , 27 10 35 4 10 ->= 12 30 31 31 12 26 7 7 19 26 34 , 11 1 2 25 30 ->= 11 25 13 13 30 31 12 13 26 8 32 , 12 20 10 27 10 ->= 12 14 9 29 8 15 8 9 28 33 34 , 12 14 23 30 31 ->= 12 26 8 4 5 17 20 5 6 34 31 , 33 16 10 33 34 ->= 11 29 19 20 21 4 6 16 6 8 32 , 31 12 20 5 10 ->= 31 35 4 6 16 21 23 13 26 16 10 , 27 17 18 1 6 34 ->= 27 17 18 25 26 8 15 19 26 16 10 , 12 14 9 28 11 28 ->= 33 7 19 13 14 22 9 29 7 24 28 , 31 11 0 28 27 10 ->= 31 31 12 13 20 5 2 3 9 29 34 , 11 0 0 0 3 32 31 ->= 11 3 4 6 8 15 19 13 18 29 34 , 11 3 32 11 3 23 30 ->= 11 1 21 15 8 15 19 26 8 23 30 , 12 14 32 12 26 34 31 ->= 12 14 22 4 5 2 0 0 25 18 28 , 11 1 6 34 31 33 7 34 ->= 33 34 12 26 7 7 24 25 26 7 34 , 12 14 15 24 1 2 1 10 ->= 12 20 17 26 7 16 2 25 18 1 10 , 33 16 5 10 12 13 30 31 ->= 11 0 3 15 34 12 13 13 18 3 32 , 33 8 4 10 33 8 23 30 ->= 33 24 3 32 27 6 16 17 26 16 10 , 35 4 10 35 23 18 25 30 ->= 11 25 13 13 18 29 24 29 8 23 30 , 11 0 1 17 -> 35 4 2 0 3 4 5 6 7 8 23 , 27 10 11 1 17 -> 27 10 12 13 14 15 16 17 13 13 13 , 11 1 2 1 17 -> 11 1 6 19 20 21 22 23 14 23 13 , 11 1 6 24 25 -> 11 25 26 7 19 14 22 15 16 2 25 , 12 18 1 10 12 -> 12 26 8 22 23 20 17 26 16 10 12 , 27 2 1 17 18 25 -> 12 13 20 5 5 21 4 2 25 18 25 , 11 1 10 27 2 25 -> 31 27 17 13 26 8 4 17 20 2 25 , 33 24 1 10 12 13 -> 12 18 3 4 17 30 31 12 13 26 19 , 35 22 32 33 16 17 -> 35 15 24 0 29 19 20 6 7 16 17 , 27 6 34 31 12 20 17 -> 12 13 20 2 25 20 5 17 26 8 23 , 11 1 5 6 34 35 23 -> 11 1 6 7 8 9 29 7 8 22 23 , 11 28 33 16 6 24 25 -> 11 25 13 18 29 16 21 22 15 24 25 , 11 28 35 9 25 30 12 -> 11 3 22 4 17 14 23 20 6 34 12 , 33 16 21 32 11 1 17 -> 35 9 3 23 26 8 22 23 14 4 17 , 33 16 10 33 19 30 12 -> 35 15 24 0 29 7 19 20 5 10 12 , 33 16 10 33 8 9 25 -> 35 23 14 15 16 6 24 0 3 9 25 , 35 9 25 18 0 1 17 -> 35 32 33 7 16 2 0 3 4 17 13 , 35 22 22 32 27 10 12 -> 33 8 15 7 19 14 23 14 9 3 23 , 31 12 20 21 32 11 25 -> 31 12 13 13 26 24 1 21 4 6 19 , 27 10 35 32 33 16 10 12 -> 27 21 23 14 22 22 15 16 5 10 12 , 11 1 10 31 33 19 30 12 -> 33 34 31 33 7 16 17 20 21 32 12 , 33 16 10 33 34 33 16 17 -> 11 0 25 14 9 25 20 2 3 4 17 , 33 24 1 2 28 31 11 25 -> 12 14 9 0 29 7 7 7 24 0 25 , 33 19 30 33 16 2 1 17 -> 12 14 9 25 26 8 15 24 0 25 13 , 33 7 34 33 8 32 33 19 -> 27 17 13 14 23 13 18 0 0 25 13 , 33 8 23 30 27 17 18 25 -> 33 16 21 15 19 14 22 4 5 2 25 , 33 8 15 19 18 3 22 23 -> 33 8 15 8 15 16 6 7 16 17 13 , 33 34 12 26 34 33 8 23 -> 33 34 11 1 6 16 5 17 14 23 13 , 35 22 32 33 19 18 1 17 -> 35 4 10 35 9 25 13 13 26 16 17 , 35 32 11 1 5 10 11 25 -> 31 31 12 13 13 30 31 31 11 3 23 , 35 32 11 29 24 25 26 19 -> 31 35 9 0 0 25 26 8 4 17 13 , 31 11 3 32 12 30 33 19 -> 31 31 11 3 23 26 16 5 6 8 23 , 31 11 28 35 23 30 11 25 -> 31 31 12 26 16 6 8 23 18 1 17 , 31 35 32 27 10 12 26 19 -> 31 11 0 3 23 26 16 2 29 16 17 , 27 2 25 ->= 12 26 7 19 13 26 7 8 22 23 13 , 33 16 17 ->= 11 3 23 13 13 20 6 16 5 17 13 , 11 1 6 19 ->= 11 28 12 13 26 24 29 16 17 20 17 , 12 20 10 12 ->= 12 14 15 19 26 19 14 15 19 18 25 , 12 18 28 12 ->= 12 13 14 4 5 17 14 4 2 28 12 , 12 26 8 23 ->= 12 26 8 15 19 14 4 21 22 23 13 , 33 16 5 17 ->= 33 7 8 23 14 22 22 23 26 19 13 , 31 35 23 13 ->= 31 35 22 23 13 20 17 13 14 15 19 , 27 5 6 24 25 ->= 27 6 8 23 13 26 16 5 2 0 25 , 27 10 35 4 17 ->= 12 30 31 31 12 26 7 7 19 26 19 , 11 1 2 25 13 ->= 11 25 13 13 30 31 12 13 26 8 23 , 12 20 10 27 17 ->= 12 14 9 29 8 15 8 9 28 33 19 , 12 14 23 30 12 ->= 12 26 8 4 5 17 20 5 6 34 12 , 33 16 10 33 19 ->= 11 29 19 20 21 4 6 16 6 8 23 , 31 12 20 5 17 ->= 31 35 4 6 16 21 23 13 26 16 17 , 27 17 18 1 6 19 ->= 27 17 18 25 26 8 15 19 26 16 17 , 12 14 9 28 11 25 ->= 33 7 19 13 14 22 9 29 7 24 25 , 31 11 0 28 27 17 ->= 31 31 12 13 20 5 2 3 9 29 19 , 11 0 0 0 3 32 12 ->= 11 3 4 6 8 15 19 13 18 29 19 , 11 3 32 11 3 23 13 ->= 11 1 21 15 8 15 19 26 8 23 13 , 12 14 32 12 26 34 12 ->= 12 14 22 4 5 2 0 0 25 18 25 , 11 1 6 34 31 33 7 19 ->= 33 34 12 26 7 7 24 25 26 7 19 , 12 14 15 24 1 2 1 17 ->= 12 20 17 26 7 16 2 25 18 1 17 , 33 16 5 10 12 13 30 12 ->= 11 0 3 15 34 12 13 13 18 3 23 , 33 8 4 10 33 8 23 13 ->= 33 24 3 32 27 6 16 17 26 16 17 , 35 4 10 35 23 18 25 13 ->= 11 25 13 13 18 29 24 29 8 23 13 , 18 0 1 2 -> 14 4 2 0 3 4 5 6 7 8 9 , 20 10 11 1 2 -> 20 10 12 13 14 15 16 17 13 13 18 , 18 1 2 1 2 -> 18 1 6 19 20 21 22 23 14 23 18 , 18 1 6 24 0 -> 18 25 26 7 19 14 22 15 16 2 0 , 13 18 1 10 11 -> 13 26 8 22 23 20 17 26 16 10 11 , 20 2 1 17 18 0 -> 13 13 20 5 5 21 4 2 25 18 0 , 18 1 10 27 2 0 -> 30 27 17 13 26 8 4 17 20 2 0 , 26 24 1 10 12 18 -> 13 18 3 4 17 30 31 12 13 26 24 , 14 22 32 33 16 2 -> 14 15 24 0 29 19 20 6 7 16 2 , 20 6 34 31 12 20 2 -> 13 13 20 2 25 20 5 17 26 8 9 , 18 1 5 6 34 35 9 -> 18 1 6 7 8 9 29 7 8 22 9 , 18 28 33 16 6 24 0 -> 18 25 13 18 29 16 21 22 15 24 0 , 18 28 35 9 25 30 11 -> 18 3 22 4 17 14 23 20 6 34 11 , 26 16 21 32 11 1 2 -> 14 9 3 23 26 8 22 23 14 4 2 , 26 16 10 33 19 30 11 -> 14 15 24 0 29 7 19 20 5 10 11 , 26 16 10 33 8 9 0 -> 14 23 14 15 16 6 24 0 3 9 0 , 14 9 25 18 0 1 2 -> 14 32 33 7 16 2 0 3 4 17 18 , 14 22 22 32 27 10 11 -> 26 8 15 7 19 14 23 14 9 3 9 , 30 12 20 21 32 11 0 -> 30 12 13 13 26 24 1 21 4 6 24 , 20 10 35 32 33 16 10 11 -> 20 21 23 14 22 22 15 16 5 10 11 , 18 1 10 31 33 19 30 11 -> 26 34 31 33 7 16 17 20 21 32 11 , 26 16 10 33 34 33 16 2 -> 18 0 25 14 9 25 20 2 3 4 2 , 26 24 1 2 28 31 11 0 -> 13 14 9 0 29 7 7 7 24 0 0 , 26 19 30 33 16 2 1 2 -> 13 14 9 25 26 8 15 24 0 25 18 , 26 7 34 33 8 32 33 24 -> 20 17 13 14 23 13 18 0 0 25 18 , 26 8 23 30 27 17 18 0 -> 26 16 21 15 19 14 22 4 5 2 0 , 26 8 15 19 18 3 22 9 -> 26 8 15 8 15 16 6 7 16 17 18 , 26 34 12 26 34 33 8 9 -> 26 34 11 1 6 16 5 17 14 23 18 , 14 22 32 33 19 18 1 2 -> 14 4 10 35 9 25 13 13 26 16 2 , 14 32 11 1 5 10 11 0 -> 30 31 12 13 13 30 31 31 11 3 9 , 14 32 11 29 24 25 26 24 -> 30 35 9 0 0 25 26 8 4 17 18 , 30 11 3 32 12 30 33 24 -> 30 31 11 3 23 26 16 5 6 8 9 , 30 11 28 35 23 30 11 0 -> 30 31 12 26 16 6 8 23 18 1 2 , 30 35 32 27 10 12 26 24 -> 30 11 0 3 23 26 16 2 29 16 2 , 20 2 0 ->= 13 26 7 19 13 26 7 8 22 23 18 , 26 16 2 ->= 18 3 23 13 13 20 6 16 5 17 18 , 18 1 6 24 ->= 18 28 12 13 26 24 29 16 17 20 2 , 13 20 10 11 ->= 13 14 15 19 26 19 14 15 19 18 0 , 13 18 28 11 ->= 13 13 14 4 5 17 14 4 2 28 11 , 13 26 8 9 ->= 13 26 8 15 19 14 4 21 22 23 18 , 26 16 5 2 ->= 26 7 8 23 14 22 22 23 26 19 18 , 30 35 23 18 ->= 30 35 22 23 13 20 17 13 14 15 24 , 20 5 6 24 0 ->= 20 6 8 23 13 26 16 5 2 0 0 , 20 10 35 4 2 ->= 13 30 31 31 12 26 7 7 19 26 24 , 18 1 2 25 18 ->= 18 25 13 13 30 31 12 13 26 8 9 , 13 20 10 27 2 ->= 13 14 9 29 8 15 8 9 28 33 24 , 13 14 23 30 11 ->= 13 26 8 4 5 17 20 5 6 34 11 , 26 16 10 33 24 ->= 18 29 19 20 21 4 6 16 6 8 9 , 30 12 20 5 2 ->= 30 35 4 6 16 21 23 13 26 16 2 , 20 17 18 1 6 24 ->= 20 17 18 25 26 8 15 19 26 16 2 , 13 14 9 28 11 0 ->= 26 7 19 13 14 22 9 29 7 24 0 , 30 11 0 28 27 2 ->= 30 31 12 13 20 5 2 3 9 29 24 , 18 0 0 0 3 32 11 ->= 18 3 4 6 8 15 19 13 18 29 24 , 18 3 32 11 3 23 18 ->= 18 1 21 15 8 15 19 26 8 23 18 , 13 14 32 12 26 34 11 ->= 13 14 22 4 5 2 0 0 25 18 0 , 18 1 6 34 31 33 7 24 ->= 26 34 12 26 7 7 24 25 26 7 24 , 13 14 15 24 1 2 1 2 ->= 13 20 17 26 7 16 2 25 18 1 2 , 26 16 5 10 12 13 30 11 ->= 18 0 3 15 34 12 13 13 18 3 9 , 26 8 4 10 33 8 23 18 ->= 26 24 3 32 27 6 16 17 26 16 2 , 14 4 10 35 23 18 25 18 ->= 18 25 13 13 18 29 24 29 8 23 18 , 18 0 1 5 -> 14 4 2 0 3 4 5 6 7 8 4 , 20 10 11 1 5 -> 20 10 12 13 14 15 16 17 13 13 20 , 18 1 2 1 5 -> 18 1 6 19 20 21 22 23 14 23 20 , 18 1 6 24 1 -> 18 25 26 7 19 14 22 15 16 2 1 , 13 18 1 10 27 -> 13 26 8 22 23 20 17 26 16 10 27 , 20 2 1 17 18 1 -> 13 13 20 5 5 21 4 2 25 18 1 , 18 1 10 27 2 1 -> 30 27 17 13 26 8 4 17 20 2 1 , 26 24 1 10 12 20 -> 13 18 3 4 17 30 31 12 13 26 16 , 14 22 32 33 16 5 -> 14 15 24 0 29 19 20 6 7 16 5 , 20 6 34 31 12 20 5 -> 13 13 20 2 25 20 5 17 26 8 4 , 18 1 5 6 34 35 4 -> 18 1 6 7 8 9 29 7 8 22 4 , 18 28 33 16 6 24 1 -> 18 25 13 18 29 16 21 22 15 24 1 , 18 28 35 9 25 30 27 -> 18 3 22 4 17 14 23 20 6 34 27 , 26 16 21 32 11 1 5 -> 14 9 3 23 26 8 22 23 14 4 5 , 26 16 10 33 19 30 27 -> 14 15 24 0 29 7 19 20 5 10 27 , 26 16 10 33 8 9 1 -> 14 23 14 15 16 6 24 0 3 9 1 , 14 9 25 18 0 1 5 -> 14 32 33 7 16 2 0 3 4 17 20 , 14 22 22 32 27 10 27 -> 26 8 15 7 19 14 23 14 9 3 4 , 30 12 20 21 32 11 1 -> 30 12 13 13 26 24 1 21 4 6 16 , 20 10 35 32 33 16 10 27 -> 20 21 23 14 22 22 15 16 5 10 27 , 18 1 10 31 33 19 30 27 -> 26 34 31 33 7 16 17 20 21 32 27 , 26 16 10 33 34 33 16 5 -> 18 0 25 14 9 25 20 2 3 4 5 , 26 24 1 2 28 31 11 1 -> 13 14 9 0 29 7 7 7 24 0 1 , 26 19 30 33 16 2 1 5 -> 13 14 9 25 26 8 15 24 0 25 20 , 26 7 34 33 8 32 33 16 -> 20 17 13 14 23 13 18 0 0 25 20 , 26 8 23 30 27 17 18 1 -> 26 16 21 15 19 14 22 4 5 2 1 , 26 8 15 19 18 3 22 4 -> 26 8 15 8 15 16 6 7 16 17 20 , 26 34 12 26 34 33 8 4 -> 26 34 11 1 6 16 5 17 14 23 20 , 14 22 32 33 19 18 1 5 -> 14 4 10 35 9 25 13 13 26 16 5 , 14 32 11 1 5 10 11 1 -> 30 31 12 13 13 30 31 31 11 3 4 , 14 32 11 29 24 25 26 16 -> 30 35 9 0 0 25 26 8 4 17 20 , 30 11 3 32 12 30 33 16 -> 30 31 11 3 23 26 16 5 6 8 4 , 30 11 28 35 23 30 11 1 -> 30 31 12 26 16 6 8 23 18 1 5 , 30 35 32 27 10 12 26 16 -> 30 11 0 3 23 26 16 2 29 16 5 , 20 2 1 ->= 13 26 7 19 13 26 7 8 22 23 20 , 26 16 5 ->= 18 3 23 13 13 20 6 16 5 17 20 , 18 1 6 16 ->= 18 28 12 13 26 24 29 16 17 20 5 , 13 20 10 27 ->= 13 14 15 19 26 19 14 15 19 18 1 , 13 18 28 27 ->= 13 13 14 4 5 17 14 4 2 28 27 , 13 26 8 4 ->= 13 26 8 15 19 14 4 21 22 23 20 , 26 16 5 5 ->= 26 7 8 23 14 22 22 23 26 19 20 , 30 35 23 20 ->= 30 35 22 23 13 20 17 13 14 15 16 , 20 5 6 24 1 ->= 20 6 8 23 13 26 16 5 2 0 1 , 20 10 35 4 5 ->= 13 30 31 31 12 26 7 7 19 26 16 , 18 1 2 25 20 ->= 18 25 13 13 30 31 12 13 26 8 4 , 13 20 10 27 5 ->= 13 14 9 29 8 15 8 9 28 33 16 , 13 14 23 30 27 ->= 13 26 8 4 5 17 20 5 6 34 27 , 26 16 10 33 16 ->= 18 29 19 20 21 4 6 16 6 8 4 , 30 12 20 5 5 ->= 30 35 4 6 16 21 23 13 26 16 5 , 20 17 18 1 6 16 ->= 20 17 18 25 26 8 15 19 26 16 5 , 13 14 9 28 11 1 ->= 26 7 19 13 14 22 9 29 7 24 1 , 30 11 0 28 27 5 ->= 30 31 12 13 20 5 2 3 9 29 16 , 18 0 0 0 3 32 27 ->= 18 3 4 6 8 15 19 13 18 29 16 , 18 3 32 11 3 23 20 ->= 18 1 21 15 8 15 19 26 8 23 20 , 13 14 32 12 26 34 27 ->= 13 14 22 4 5 2 0 0 25 18 1 , 18 1 6 34 31 33 7 16 ->= 26 34 12 26 7 7 24 25 26 7 16 , 13 14 15 24 1 2 1 5 ->= 13 20 17 26 7 16 2 25 18 1 5 , 26 16 5 10 12 13 30 27 ->= 18 0 3 15 34 12 13 13 18 3 4 , 26 8 4 10 33 8 23 20 ->= 26 24 3 32 27 6 16 17 26 16 5 , 14 4 10 35 23 18 25 20 ->= 18 25 13 13 18 29 24 29 8 23 20 , 18 0 1 21 -> 14 4 2 0 3 4 5 6 7 8 22 , 20 10 11 1 21 -> 20 10 12 13 14 15 16 17 13 13 14 , 18 1 2 1 21 -> 18 1 6 19 20 21 22 23 14 23 14 , 18 1 6 24 3 -> 18 25 26 7 19 14 22 15 16 2 3 , 13 18 1 10 35 -> 13 26 8 22 23 20 17 26 16 10 35 , 20 2 1 17 18 3 -> 13 13 20 5 5 21 4 2 25 18 3 , 18 1 10 27 2 3 -> 30 27 17 13 26 8 4 17 20 2 3 , 26 24 1 10 12 14 -> 13 18 3 4 17 30 31 12 13 26 8 , 14 22 32 33 16 21 -> 14 15 24 0 29 19 20 6 7 16 21 , 20 6 34 31 12 20 21 -> 13 13 20 2 25 20 5 17 26 8 22 , 18 1 5 6 34 35 22 -> 18 1 6 7 8 9 29 7 8 22 22 , 18 28 33 16 6 24 3 -> 18 25 13 18 29 16 21 22 15 24 3 , 18 28 35 9 25 30 35 -> 18 3 22 4 17 14 23 20 6 34 35 , 26 16 21 32 11 1 21 -> 14 9 3 23 26 8 22 23 14 4 21 , 26 16 10 33 19 30 35 -> 14 15 24 0 29 7 19 20 5 10 35 , 26 16 10 33 8 9 3 -> 14 23 14 15 16 6 24 0 3 9 3 , 14 9 25 18 0 1 21 -> 14 32 33 7 16 2 0 3 4 17 14 , 14 22 22 32 27 10 35 -> 26 8 15 7 19 14 23 14 9 3 22 , 30 12 20 21 32 11 3 -> 30 12 13 13 26 24 1 21 4 6 8 , 20 10 35 32 33 16 10 35 -> 20 21 23 14 22 22 15 16 5 10 35 , 18 1 10 31 33 19 30 35 -> 26 34 31 33 7 16 17 20 21 32 35 , 26 16 10 33 34 33 16 21 -> 18 0 25 14 9 25 20 2 3 4 21 , 26 24 1 2 28 31 11 3 -> 13 14 9 0 29 7 7 7 24 0 3 , 26 19 30 33 16 2 1 21 -> 13 14 9 25 26 8 15 24 0 25 14 , 26 7 34 33 8 32 33 8 -> 20 17 13 14 23 13 18 0 0 25 14 , 26 8 23 30 27 17 18 3 -> 26 16 21 15 19 14 22 4 5 2 3 , 26 8 15 19 18 3 22 22 -> 26 8 15 8 15 16 6 7 16 17 14 , 26 34 12 26 34 33 8 22 -> 26 34 11 1 6 16 5 17 14 23 14 , 14 22 32 33 19 18 1 21 -> 14 4 10 35 9 25 13 13 26 16 21 , 14 32 11 1 5 10 11 3 -> 30 31 12 13 13 30 31 31 11 3 22 , 14 32 11 29 24 25 26 8 -> 30 35 9 0 0 25 26 8 4 17 14 , 30 11 3 32 12 30 33 8 -> 30 31 11 3 23 26 16 5 6 8 22 , 30 11 28 35 23 30 11 3 -> 30 31 12 26 16 6 8 23 18 1 21 , 30 35 32 27 10 12 26 8 -> 30 11 0 3 23 26 16 2 29 16 21 , 20 2 3 ->= 13 26 7 19 13 26 7 8 22 23 14 , 26 16 21 ->= 18 3 23 13 13 20 6 16 5 17 14 , 18 1 6 8 ->= 18 28 12 13 26 24 29 16 17 20 21 , 13 20 10 35 ->= 13 14 15 19 26 19 14 15 19 18 3 , 13 18 28 35 ->= 13 13 14 4 5 17 14 4 2 28 35 , 13 26 8 22 ->= 13 26 8 15 19 14 4 21 22 23 14 , 26 16 5 21 ->= 26 7 8 23 14 22 22 23 26 19 14 , 30 35 23 14 ->= 30 35 22 23 13 20 17 13 14 15 8 , 20 5 6 24 3 ->= 20 6 8 23 13 26 16 5 2 0 3 , 20 10 35 4 21 ->= 13 30 31 31 12 26 7 7 19 26 8 , 18 1 2 25 14 ->= 18 25 13 13 30 31 12 13 26 8 22 , 13 20 10 27 21 ->= 13 14 9 29 8 15 8 9 28 33 8 , 13 14 23 30 35 ->= 13 26 8 4 5 17 20 5 6 34 35 , 26 16 10 33 8 ->= 18 29 19 20 21 4 6 16 6 8 22 , 30 12 20 5 21 ->= 30 35 4 6 16 21 23 13 26 16 21 , 20 17 18 1 6 8 ->= 20 17 18 25 26 8 15 19 26 16 21 , 13 14 9 28 11 3 ->= 26 7 19 13 14 22 9 29 7 24 3 , 30 11 0 28 27 21 ->= 30 31 12 13 20 5 2 3 9 29 8 , 18 0 0 0 3 32 35 ->= 18 3 4 6 8 15 19 13 18 29 8 , 18 3 32 11 3 23 14 ->= 18 1 21 15 8 15 19 26 8 23 14 , 13 14 32 12 26 34 35 ->= 13 14 22 4 5 2 0 0 25 18 3 , 18 1 6 34 31 33 7 8 ->= 26 34 12 26 7 7 24 25 26 7 8 , 13 14 15 24 1 2 1 21 ->= 13 20 17 26 7 16 2 25 18 1 21 , 26 16 5 10 12 13 30 35 ->= 18 0 3 15 34 12 13 13 18 3 22 , 26 8 4 10 33 8 23 14 ->= 26 24 3 32 27 6 16 17 26 16 21 , 14 4 10 35 23 18 25 14 ->= 18 25 13 13 18 29 24 29 8 23 14 , 18 0 1 6 -> 14 4 2 0 3 4 5 6 7 8 15 , 20 10 11 1 6 -> 20 10 12 13 14 15 16 17 13 13 26 , 18 1 2 1 6 -> 18 1 6 19 20 21 22 23 14 23 26 , 18 1 6 24 29 -> 18 25 26 7 19 14 22 15 16 2 29 , 13 18 1 10 33 -> 13 26 8 22 23 20 17 26 16 10 33 , 20 2 1 17 18 29 -> 13 13 20 5 5 21 4 2 25 18 29 , 18 1 10 27 2 29 -> 30 27 17 13 26 8 4 17 20 2 29 , 26 24 1 10 12 26 -> 13 18 3 4 17 30 31 12 13 26 7 , 14 22 32 33 16 6 -> 14 15 24 0 29 19 20 6 7 16 6 , 20 6 34 31 12 20 6 -> 13 13 20 2 25 20 5 17 26 8 15 , 18 1 5 6 34 35 15 -> 18 1 6 7 8 9 29 7 8 22 15 , 18 28 33 16 6 24 29 -> 18 25 13 18 29 16 21 22 15 24 29 , 18 28 35 9 25 30 33 -> 18 3 22 4 17 14 23 20 6 34 33 , 26 16 21 32 11 1 6 -> 14 9 3 23 26 8 22 23 14 4 6 , 26 16 10 33 19 30 33 -> 14 15 24 0 29 7 19 20 5 10 33 , 26 16 10 33 8 9 29 -> 14 23 14 15 16 6 24 0 3 9 29 , 14 9 25 18 0 1 6 -> 14 32 33 7 16 2 0 3 4 17 26 , 14 22 22 32 27 10 33 -> 26 8 15 7 19 14 23 14 9 3 15 , 30 12 20 21 32 11 29 -> 30 12 13 13 26 24 1 21 4 6 7 , 20 10 35 32 33 16 10 33 -> 20 21 23 14 22 22 15 16 5 10 33 , 18 1 10 31 33 19 30 33 -> 26 34 31 33 7 16 17 20 21 32 33 , 26 16 10 33 34 33 16 6 -> 18 0 25 14 9 25 20 2 3 4 6 , 26 24 1 2 28 31 11 29 -> 13 14 9 0 29 7 7 7 24 0 29 , 26 19 30 33 16 2 1 6 -> 13 14 9 25 26 8 15 24 0 25 26 , 26 7 34 33 8 32 33 7 -> 20 17 13 14 23 13 18 0 0 25 26 , 26 8 23 30 27 17 18 29 -> 26 16 21 15 19 14 22 4 5 2 29 , 26 8 15 19 18 3 22 15 -> 26 8 15 8 15 16 6 7 16 17 26 , 26 34 12 26 34 33 8 15 -> 26 34 11 1 6 16 5 17 14 23 26 , 14 22 32 33 19 18 1 6 -> 14 4 10 35 9 25 13 13 26 16 6 , 14 32 11 1 5 10 11 29 -> 30 31 12 13 13 30 31 31 11 3 15 , 14 32 11 29 24 25 26 7 -> 30 35 9 0 0 25 26 8 4 17 26 , 30 11 3 32 12 30 33 7 -> 30 31 11 3 23 26 16 5 6 8 15 , 30 11 28 35 23 30 11 29 -> 30 31 12 26 16 6 8 23 18 1 6 , 30 35 32 27 10 12 26 7 -> 30 11 0 3 23 26 16 2 29 16 6 , 20 2 29 ->= 13 26 7 19 13 26 7 8 22 23 26 , 26 16 6 ->= 18 3 23 13 13 20 6 16 5 17 26 , 18 1 6 7 ->= 18 28 12 13 26 24 29 16 17 20 6 , 13 20 10 33 ->= 13 14 15 19 26 19 14 15 19 18 29 , 13 18 28 33 ->= 13 13 14 4 5 17 14 4 2 28 33 , 13 26 8 15 ->= 13 26 8 15 19 14 4 21 22 23 26 , 26 16 5 6 ->= 26 7 8 23 14 22 22 23 26 19 26 , 30 35 23 26 ->= 30 35 22 23 13 20 17 13 14 15 7 , 20 5 6 24 29 ->= 20 6 8 23 13 26 16 5 2 0 29 , 20 10 35 4 6 ->= 13 30 31 31 12 26 7 7 19 26 7 , 18 1 2 25 26 ->= 18 25 13 13 30 31 12 13 26 8 15 , 13 20 10 27 6 ->= 13 14 9 29 8 15 8 9 28 33 7 , 13 14 23 30 33 ->= 13 26 8 4 5 17 20 5 6 34 33 , 26 16 10 33 7 ->= 18 29 19 20 21 4 6 16 6 8 15 , 30 12 20 5 6 ->= 30 35 4 6 16 21 23 13 26 16 6 , 20 17 18 1 6 7 ->= 20 17 18 25 26 8 15 19 26 16 6 , 13 14 9 28 11 29 ->= 26 7 19 13 14 22 9 29 7 24 29 , 30 11 0 28 27 6 ->= 30 31 12 13 20 5 2 3 9 29 7 , 18 0 0 0 3 32 33 ->= 18 3 4 6 8 15 19 13 18 29 7 , 18 3 32 11 3 23 26 ->= 18 1 21 15 8 15 19 26 8 23 26 , 13 14 32 12 26 34 33 ->= 13 14 22 4 5 2 0 0 25 18 29 , 18 1 6 34 31 33 7 7 ->= 26 34 12 26 7 7 24 25 26 7 7 , 13 14 15 24 1 2 1 6 ->= 13 20 17 26 7 16 2 25 18 1 6 , 26 16 5 10 12 13 30 33 ->= 18 0 3 15 34 12 13 13 18 3 15 , 26 8 4 10 33 8 23 26 ->= 26 24 3 32 27 6 16 17 26 16 6 , 14 4 10 35 23 18 25 26 ->= 18 25 13 13 18 29 24 29 8 23 26 , 18 0 1 10 -> 14 4 2 0 3 4 5 6 7 8 32 , 20 10 11 1 10 -> 20 10 12 13 14 15 16 17 13 13 30 , 18 1 2 1 10 -> 18 1 6 19 20 21 22 23 14 23 30 , 18 1 6 24 28 -> 18 25 26 7 19 14 22 15 16 2 28 , 13 18 1 10 31 -> 13 26 8 22 23 20 17 26 16 10 31 , 20 2 1 17 18 28 -> 13 13 20 5 5 21 4 2 25 18 28 , 18 1 10 27 2 28 -> 30 27 17 13 26 8 4 17 20 2 28 , 26 24 1 10 12 30 -> 13 18 3 4 17 30 31 12 13 26 34 , 14 22 32 33 16 10 -> 14 15 24 0 29 19 20 6 7 16 10 , 20 6 34 31 12 20 10 -> 13 13 20 2 25 20 5 17 26 8 32 , 18 1 5 6 34 35 32 -> 18 1 6 7 8 9 29 7 8 22 32 , 18 28 33 16 6 24 28 -> 18 25 13 18 29 16 21 22 15 24 28 , 18 28 35 9 25 30 31 -> 18 3 22 4 17 14 23 20 6 34 31 , 26 16 21 32 11 1 10 -> 14 9 3 23 26 8 22 23 14 4 10 , 26 16 10 33 19 30 31 -> 14 15 24 0 29 7 19 20 5 10 31 , 26 16 10 33 8 9 28 -> 14 23 14 15 16 6 24 0 3 9 28 , 14 9 25 18 0 1 10 -> 14 32 33 7 16 2 0 3 4 17 30 , 14 22 22 32 27 10 31 -> 26 8 15 7 19 14 23 14 9 3 32 , 30 12 20 21 32 11 28 -> 30 12 13 13 26 24 1 21 4 6 34 , 20 10 35 32 33 16 10 31 -> 20 21 23 14 22 22 15 16 5 10 31 , 18 1 10 31 33 19 30 31 -> 26 34 31 33 7 16 17 20 21 32 31 , 26 16 10 33 34 33 16 10 -> 18 0 25 14 9 25 20 2 3 4 10 , 26 24 1 2 28 31 11 28 -> 13 14 9 0 29 7 7 7 24 0 28 , 26 19 30 33 16 2 1 10 -> 13 14 9 25 26 8 15 24 0 25 30 , 26 7 34 33 8 32 33 34 -> 20 17 13 14 23 13 18 0 0 25 30 , 26 8 23 30 27 17 18 28 -> 26 16 21 15 19 14 22 4 5 2 28 , 26 8 15 19 18 3 22 32 -> 26 8 15 8 15 16 6 7 16 17 30 , 26 34 12 26 34 33 8 32 -> 26 34 11 1 6 16 5 17 14 23 30 , 14 22 32 33 19 18 1 10 -> 14 4 10 35 9 25 13 13 26 16 10 , 14 32 11 1 5 10 11 28 -> 30 31 12 13 13 30 31 31 11 3 32 , 14 32 11 29 24 25 26 34 -> 30 35 9 0 0 25 26 8 4 17 30 , 30 11 3 32 12 30 33 34 -> 30 31 11 3 23 26 16 5 6 8 32 , 30 11 28 35 23 30 11 28 -> 30 31 12 26 16 6 8 23 18 1 10 , 30 35 32 27 10 12 26 34 -> 30 11 0 3 23 26 16 2 29 16 10 , 20 2 28 ->= 13 26 7 19 13 26 7 8 22 23 30 , 26 16 10 ->= 18 3 23 13 13 20 6 16 5 17 30 , 18 1 6 34 ->= 18 28 12 13 26 24 29 16 17 20 10 , 13 20 10 31 ->= 13 14 15 19 26 19 14 15 19 18 28 , 13 18 28 31 ->= 13 13 14 4 5 17 14 4 2 28 31 , 13 26 8 32 ->= 13 26 8 15 19 14 4 21 22 23 30 , 26 16 5 10 ->= 26 7 8 23 14 22 22 23 26 19 30 , 30 35 23 30 ->= 30 35 22 23 13 20 17 13 14 15 34 , 20 5 6 24 28 ->= 20 6 8 23 13 26 16 5 2 0 28 , 20 10 35 4 10 ->= 13 30 31 31 12 26 7 7 19 26 34 , 18 1 2 25 30 ->= 18 25 13 13 30 31 12 13 26 8 32 , 13 20 10 27 10 ->= 13 14 9 29 8 15 8 9 28 33 34 , 13 14 23 30 31 ->= 13 26 8 4 5 17 20 5 6 34 31 , 26 16 10 33 34 ->= 18 29 19 20 21 4 6 16 6 8 32 , 30 12 20 5 10 ->= 30 35 4 6 16 21 23 13 26 16 10 , 20 17 18 1 6 34 ->= 20 17 18 25 26 8 15 19 26 16 10 , 13 14 9 28 11 28 ->= 26 7 19 13 14 22 9 29 7 24 28 , 30 11 0 28 27 10 ->= 30 31 12 13 20 5 2 3 9 29 34 , 18 0 0 0 3 32 31 ->= 18 3 4 6 8 15 19 13 18 29 34 , 18 3 32 11 3 23 30 ->= 18 1 21 15 8 15 19 26 8 23 30 , 13 14 32 12 26 34 31 ->= 13 14 22 4 5 2 0 0 25 18 28 , 18 1 6 34 31 33 7 34 ->= 26 34 12 26 7 7 24 25 26 7 34 , 13 14 15 24 1 2 1 10 ->= 13 20 17 26 7 16 2 25 18 1 10 , 26 16 5 10 12 13 30 31 ->= 18 0 3 15 34 12 13 13 18 3 32 , 26 8 4 10 33 8 23 30 ->= 26 24 3 32 27 6 16 17 26 16 10 , 14 4 10 35 23 18 25 30 ->= 18 25 13 13 18 29 24 29 8 23 30 , 18 0 1 17 -> 14 4 2 0 3 4 5 6 7 8 23 , 20 10 11 1 17 -> 20 10 12 13 14 15 16 17 13 13 13 , 18 1 2 1 17 -> 18 1 6 19 20 21 22 23 14 23 13 , 18 1 6 24 25 -> 18 25 26 7 19 14 22 15 16 2 25 , 13 18 1 10 12 -> 13 26 8 22 23 20 17 26 16 10 12 , 20 2 1 17 18 25 -> 13 13 20 5 5 21 4 2 25 18 25 , 18 1 10 27 2 25 -> 30 27 17 13 26 8 4 17 20 2 25 , 26 24 1 10 12 13 -> 13 18 3 4 17 30 31 12 13 26 19 , 14 22 32 33 16 17 -> 14 15 24 0 29 19 20 6 7 16 17 , 20 6 34 31 12 20 17 -> 13 13 20 2 25 20 5 17 26 8 23 , 18 1 5 6 34 35 23 -> 18 1 6 7 8 9 29 7 8 22 23 , 18 28 33 16 6 24 25 -> 18 25 13 18 29 16 21 22 15 24 25 , 18 28 35 9 25 30 12 -> 18 3 22 4 17 14 23 20 6 34 12 , 26 16 21 32 11 1 17 -> 14 9 3 23 26 8 22 23 14 4 17 , 26 16 10 33 19 30 12 -> 14 15 24 0 29 7 19 20 5 10 12 , 26 16 10 33 8 9 25 -> 14 23 14 15 16 6 24 0 3 9 25 , 14 9 25 18 0 1 17 -> 14 32 33 7 16 2 0 3 4 17 13 , 14 22 22 32 27 10 12 -> 26 8 15 7 19 14 23 14 9 3 23 , 30 12 20 21 32 11 25 -> 30 12 13 13 26 24 1 21 4 6 19 , 20 10 35 32 33 16 10 12 -> 20 21 23 14 22 22 15 16 5 10 12 , 18 1 10 31 33 19 30 12 -> 26 34 31 33 7 16 17 20 21 32 12 , 26 16 10 33 34 33 16 17 -> 18 0 25 14 9 25 20 2 3 4 17 , 26 24 1 2 28 31 11 25 -> 13 14 9 0 29 7 7 7 24 0 25 , 26 19 30 33 16 2 1 17 -> 13 14 9 25 26 8 15 24 0 25 13 , 26 7 34 33 8 32 33 19 -> 20 17 13 14 23 13 18 0 0 25 13 , 26 8 23 30 27 17 18 25 -> 26 16 21 15 19 14 22 4 5 2 25 , 26 8 15 19 18 3 22 23 -> 26 8 15 8 15 16 6 7 16 17 13 , 26 34 12 26 34 33 8 23 -> 26 34 11 1 6 16 5 17 14 23 13 , 14 22 32 33 19 18 1 17 -> 14 4 10 35 9 25 13 13 26 16 17 , 14 32 11 1 5 10 11 25 -> 30 31 12 13 13 30 31 31 11 3 23 , 14 32 11 29 24 25 26 19 -> 30 35 9 0 0 25 26 8 4 17 13 , 30 11 3 32 12 30 33 19 -> 30 31 11 3 23 26 16 5 6 8 23 , 30 11 28 35 23 30 11 25 -> 30 31 12 26 16 6 8 23 18 1 17 , 30 35 32 27 10 12 26 19 -> 30 11 0 3 23 26 16 2 29 16 17 , 20 2 25 ->= 13 26 7 19 13 26 7 8 22 23 13 , 26 16 17 ->= 18 3 23 13 13 20 6 16 5 17 13 , 18 1 6 19 ->= 18 28 12 13 26 24 29 16 17 20 17 , 13 20 10 12 ->= 13 14 15 19 26 19 14 15 19 18 25 , 13 18 28 12 ->= 13 13 14 4 5 17 14 4 2 28 12 , 13 26 8 23 ->= 13 26 8 15 19 14 4 21 22 23 13 , 26 16 5 17 ->= 26 7 8 23 14 22 22 23 26 19 13 , 30 35 23 13 ->= 30 35 22 23 13 20 17 13 14 15 19 , 20 5 6 24 25 ->= 20 6 8 23 13 26 16 5 2 0 25 , 20 10 35 4 17 ->= 13 30 31 31 12 26 7 7 19 26 19 , 18 1 2 25 13 ->= 18 25 13 13 30 31 12 13 26 8 23 , 13 20 10 27 17 ->= 13 14 9 29 8 15 8 9 28 33 19 , 13 14 23 30 12 ->= 13 26 8 4 5 17 20 5 6 34 12 , 26 16 10 33 19 ->= 18 29 19 20 21 4 6 16 6 8 23 , 30 12 20 5 17 ->= 30 35 4 6 16 21 23 13 26 16 17 , 20 17 18 1 6 19 ->= 20 17 18 25 26 8 15 19 26 16 17 , 13 14 9 28 11 25 ->= 26 7 19 13 14 22 9 29 7 24 25 , 30 11 0 28 27 17 ->= 30 31 12 13 20 5 2 3 9 29 19 , 18 0 0 0 3 32 12 ->= 18 3 4 6 8 15 19 13 18 29 19 , 18 3 32 11 3 23 13 ->= 18 1 21 15 8 15 19 26 8 23 13 , 13 14 32 12 26 34 12 ->= 13 14 22 4 5 2 0 0 25 18 25 , 18 1 6 34 31 33 7 19 ->= 26 34 12 26 7 7 24 25 26 7 19 , 13 14 15 24 1 2 1 17 ->= 13 20 17 26 7 16 2 25 18 1 17 , 26 16 5 10 12 13 30 12 ->= 18 0 3 15 34 12 13 13 18 3 23 , 26 8 4 10 33 8 23 13 ->= 26 24 3 32 27 6 16 17 26 16 17 , 14 4 10 35 23 18 25 13 ->= 18 25 13 13 18 29 24 29 8 23 13 } 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 24 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 19 | | 0 1 | \ / 11 is interpreted by / \ | 1 10 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 0 | | 0 1 | \ / 25 is interpreted by / \ | 1 14 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 19 | | 0 1 | \ / 28 is interpreted by / \ | 1 14 | | 0 1 | \ / 29 is interpreted by / \ | 1 1 | | 0 1 | \ / 30 is interpreted by / \ | 1 13 | | 0 1 | \ / 31 is interpreted by / \ | 1 2 | | 0 1 | \ / 32 is interpreted by / \ | 1 15 | | 0 1 | \ / 33 is interpreted by / \ | 1 22 | | 0 1 | \ / 34 is interpreted by / \ | 1 12 | | 0 1 | \ / 35 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { 29->0, 8->1, 15->2, 19->3, 18->4, 3->5, 22->6, 9->7, 16->8, 6->9, 7->10, 17->11, 25->12, 28->13, 11->14, 13->15, 14->16, 4->17, 5->18, 2->19, 26->20, 21->21, 23->22, 35->23, 20->24, 24->25, 1->26, 0->27, 27->28, 33->29, 31->30, 12->31, 10->32, 32->33, 34->34, 30->35 }, it remains to prove termination of the 220-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 4 13 14 ->= 12 15 16 17 18 11 16 17 19 13 14 , 12 20 1 7 ->= 12 20 1 2 3 16 17 21 6 22 4 , 0 8 18 19 ->= 0 10 1 22 16 6 6 22 20 3 4 , 13 23 22 4 ->= 13 23 6 22 15 24 11 15 16 2 25 , 26 18 9 25 27 ->= 26 9 1 22 15 20 8 18 19 27 27 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 24 , 12 4 13 28 ->= 12 15 16 17 18 11 16 17 19 13 28 , 12 20 1 17 ->= 12 20 1 2 3 16 17 21 6 22 24 , 0 8 18 18 ->= 0 10 1 22 16 6 6 22 20 3 24 , 13 23 22 24 ->= 13 23 6 22 15 24 11 15 16 2 8 , 26 18 9 25 26 ->= 26 9 1 22 15 20 8 18 19 27 26 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 16 , 12 4 13 23 ->= 12 15 16 17 18 11 16 17 19 13 23 , 12 20 1 6 ->= 12 20 1 2 3 16 17 21 6 22 16 , 0 8 18 21 ->= 0 10 1 22 16 6 6 22 20 3 16 , 13 23 22 16 ->= 13 23 6 22 15 24 11 15 16 2 1 , 26 18 9 25 5 ->= 26 9 1 22 15 20 8 18 19 27 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 20 , 12 4 13 29 ->= 12 15 16 17 18 11 16 17 19 13 29 , 12 20 1 2 ->= 12 20 1 2 3 16 17 21 6 22 20 , 0 8 18 9 ->= 0 10 1 22 16 6 6 22 20 3 20 , 13 23 22 20 ->= 13 23 6 22 15 24 11 15 16 2 10 , 26 18 9 25 0 ->= 26 9 1 22 15 20 8 18 19 27 0 , 12 4 13 30 ->= 12 15 16 17 18 11 16 17 19 13 30 , 26 18 9 25 13 ->= 26 9 1 22 15 20 8 18 19 27 13 , 0 1 2 3 4 5 6 22 -> 0 1 2 1 2 8 9 10 8 11 15 , 12 4 13 31 ->= 12 15 16 17 18 11 16 17 19 13 31 , 12 20 1 22 ->= 12 20 1 2 3 16 17 21 6 22 15 , 0 8 18 11 ->= 0 10 1 22 16 6 6 22 20 3 15 , 13 23 22 15 ->= 13 23 6 22 15 24 11 15 16 2 3 , 26 18 9 25 12 ->= 26 9 1 22 15 20 8 18 19 27 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 27 ->= 11 20 10 3 15 20 10 1 6 22 4 , 9 8 19 ->= 19 5 22 15 15 24 9 8 18 11 4 , 11 4 13 14 ->= 11 15 16 17 18 11 16 17 19 13 14 , 11 20 1 7 ->= 11 20 1 2 3 16 17 21 6 22 4 , 9 8 18 19 ->= 9 10 1 22 16 6 6 22 20 3 4 , 32 23 22 4 ->= 32 23 6 22 15 24 11 15 16 2 25 , 18 18 9 25 27 ->= 18 9 1 22 15 20 8 18 19 27 27 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 24 , 9 8 18 ->= 19 5 22 15 15 24 9 8 18 11 24 , 11 4 13 28 ->= 11 15 16 17 18 11 16 17 19 13 28 , 11 20 1 17 ->= 11 20 1 2 3 16 17 21 6 22 24 , 9 8 18 18 ->= 9 10 1 22 16 6 6 22 20 3 24 , 32 23 22 24 ->= 32 23 6 22 15 24 11 15 16 2 8 , 18 18 9 25 26 ->= 18 9 1 22 15 20 8 18 19 27 26 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 16 , 18 19 5 ->= 11 20 10 3 15 20 10 1 6 22 16 , 9 8 21 ->= 19 5 22 15 15 24 9 8 18 11 16 , 11 4 13 23 ->= 11 15 16 17 18 11 16 17 19 13 23 , 11 20 1 6 ->= 11 20 1 2 3 16 17 21 6 22 16 , 9 8 18 21 ->= 9 10 1 22 16 6 6 22 20 3 16 , 32 23 22 16 ->= 32 23 6 22 15 24 11 15 16 2 1 , 18 18 9 25 5 ->= 18 9 1 22 15 20 8 18 19 27 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 20 , 9 8 9 ->= 19 5 22 15 15 24 9 8 18 11 20 , 11 4 13 29 ->= 11 15 16 17 18 11 16 17 19 13 29 , 11 20 1 2 ->= 11 20 1 2 3 16 17 21 6 22 20 , 9 8 18 9 ->= 9 10 1 22 16 6 6 22 20 3 20 , 32 23 22 20 ->= 32 23 6 22 15 24 11 15 16 2 10 , 18 18 9 25 0 ->= 18 9 1 22 15 20 8 18 19 27 0 , 11 4 13 30 ->= 11 15 16 17 18 11 16 17 19 13 30 , 18 18 9 25 13 ->= 18 9 1 22 15 20 8 18 19 27 13 , 9 1 2 3 4 5 6 22 -> 9 1 2 1 2 8 9 10 8 11 15 , 9 8 11 ->= 19 5 22 15 15 24 9 8 18 11 15 , 11 4 13 31 ->= 11 15 16 17 18 11 16 17 19 13 31 , 11 20 1 22 ->= 11 20 1 2 3 16 17 21 6 22 15 , 9 8 18 11 ->= 9 10 1 22 16 6 6 22 20 3 15 , 32 23 22 15 ->= 32 23 6 22 15 24 11 15 16 2 3 , 18 18 9 25 12 ->= 18 9 1 22 15 20 8 18 19 27 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 17 19 27 ->= 22 20 10 3 15 20 10 1 6 22 4 , 2 8 19 ->= 7 5 22 15 15 24 9 8 18 11 4 , 22 4 13 14 ->= 22 15 16 17 18 11 16 17 19 13 14 , 22 20 1 7 ->= 22 20 1 2 3 16 17 21 6 22 4 , 2 8 18 19 ->= 2 10 1 22 16 6 6 22 20 3 4 , 33 23 22 4 ->= 33 23 6 22 15 24 11 15 16 2 25 , 17 18 9 25 27 ->= 17 9 1 22 15 20 8 18 19 27 27 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 24 , 2 8 18 ->= 7 5 22 15 15 24 9 8 18 11 24 , 22 4 13 28 ->= 22 15 16 17 18 11 16 17 19 13 28 , 22 20 1 17 ->= 22 20 1 2 3 16 17 21 6 22 24 , 2 8 18 18 ->= 2 10 1 22 16 6 6 22 20 3 24 , 33 23 22 24 ->= 33 23 6 22 15 24 11 15 16 2 8 , 17 18 9 25 26 ->= 17 9 1 22 15 20 8 18 19 27 26 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 16 , 17 19 5 ->= 22 20 10 3 15 20 10 1 6 22 16 , 2 8 21 ->= 7 5 22 15 15 24 9 8 18 11 16 , 22 4 13 23 ->= 22 15 16 17 18 11 16 17 19 13 23 , 22 20 1 6 ->= 22 20 1 2 3 16 17 21 6 22 16 , 2 8 18 21 ->= 2 10 1 22 16 6 6 22 20 3 16 , 33 23 22 16 ->= 33 23 6 22 15 24 11 15 16 2 1 , 17 18 9 25 5 ->= 17 9 1 22 15 20 8 18 19 27 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 20 , 2 8 9 ->= 7 5 22 15 15 24 9 8 18 11 20 , 22 4 13 29 ->= 22 15 16 17 18 11 16 17 19 13 29 , 22 20 1 2 ->= 22 20 1 2 3 16 17 21 6 22 20 , 2 8 18 9 ->= 2 10 1 22 16 6 6 22 20 3 20 , 33 23 22 20 ->= 33 23 6 22 15 24 11 15 16 2 10 , 17 18 9 25 0 ->= 17 9 1 22 15 20 8 18 19 27 0 , 22 4 13 30 ->= 22 15 16 17 18 11 16 17 19 13 30 , 17 18 9 25 13 ->= 17 9 1 22 15 20 8 18 19 27 13 , 2 1 2 3 4 5 6 22 -> 2 1 2 1 2 8 9 10 8 11 15 , 2 8 11 ->= 7 5 22 15 15 24 9 8 18 11 15 , 22 4 13 31 ->= 22 15 16 17 18 11 16 17 19 13 31 , 22 20 1 22 ->= 22 20 1 2 3 16 17 21 6 22 15 , 2 8 18 11 ->= 2 10 1 22 16 6 6 22 20 3 15 , 33 23 22 15 ->= 33 23 6 22 15 24 11 15 16 2 3 , 17 18 9 25 12 ->= 17 9 1 22 15 20 8 18 19 27 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 27 ->= 3 20 10 3 15 20 10 1 6 22 4 , 10 8 19 ->= 25 5 22 15 15 24 9 8 18 11 4 , 3 4 13 14 ->= 3 15 16 17 18 11 16 17 19 13 14 , 3 20 1 7 ->= 3 20 1 2 3 16 17 21 6 22 4 , 10 8 18 19 ->= 10 10 1 22 16 6 6 22 20 3 4 , 34 23 22 4 ->= 34 23 6 22 15 24 11 15 16 2 25 , 8 18 9 25 27 ->= 8 9 1 22 15 20 8 18 19 27 27 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 24 , 10 8 18 ->= 25 5 22 15 15 24 9 8 18 11 24 , 3 4 13 28 ->= 3 15 16 17 18 11 16 17 19 13 28 , 3 20 1 17 ->= 3 20 1 2 3 16 17 21 6 22 24 , 10 8 18 18 ->= 10 10 1 22 16 6 6 22 20 3 24 , 34 23 22 24 ->= 34 23 6 22 15 24 11 15 16 2 8 , 8 18 9 25 26 ->= 8 9 1 22 15 20 8 18 19 27 26 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 16 , 8 19 5 ->= 3 20 10 3 15 20 10 1 6 22 16 , 10 8 21 ->= 25 5 22 15 15 24 9 8 18 11 16 , 3 4 13 23 ->= 3 15 16 17 18 11 16 17 19 13 23 , 3 20 1 6 ->= 3 20 1 2 3 16 17 21 6 22 16 , 10 8 18 21 ->= 10 10 1 22 16 6 6 22 20 3 16 , 34 23 22 16 ->= 34 23 6 22 15 24 11 15 16 2 1 , 8 18 9 25 5 ->= 8 9 1 22 15 20 8 18 19 27 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 20 , 10 8 9 ->= 25 5 22 15 15 24 9 8 18 11 20 , 3 4 13 29 ->= 3 15 16 17 18 11 16 17 19 13 29 , 3 20 1 2 ->= 3 20 1 2 3 16 17 21 6 22 20 , 10 8 18 9 ->= 10 10 1 22 16 6 6 22 20 3 20 , 34 23 22 20 ->= 34 23 6 22 15 24 11 15 16 2 10 , 8 18 9 25 0 ->= 8 9 1 22 15 20 8 18 19 27 0 , 3 4 13 30 ->= 3 15 16 17 18 11 16 17 19 13 30 , 8 18 9 25 13 ->= 8 9 1 22 15 20 8 18 19 27 13 , 10 1 2 3 4 5 6 22 -> 10 1 2 1 2 8 9 10 8 11 15 , 10 8 11 ->= 25 5 22 15 15 24 9 8 18 11 15 , 3 4 13 31 ->= 3 15 16 17 18 11 16 17 19 13 31 , 3 20 1 22 ->= 3 20 1 2 3 16 17 21 6 22 15 , 10 8 18 11 ->= 10 10 1 22 16 6 6 22 20 3 15 , 34 23 22 15 ->= 34 23 6 22 15 24 11 15 16 2 3 , 8 18 9 25 12 ->= 8 9 1 22 15 20 8 18 19 27 12 , 29 1 2 3 4 5 6 7 -> 29 1 2 1 2 8 9 10 8 11 4 , 31 4 13 14 ->= 31 15 16 17 18 11 16 17 19 13 14 , 31 20 1 7 ->= 31 20 1 2 3 16 17 21 6 22 4 , 29 8 18 19 ->= 29 10 1 22 16 6 6 22 20 3 4 , 30 23 22 4 ->= 30 23 6 22 15 24 11 15 16 2 25 , 28 18 9 25 27 ->= 28 9 1 22 15 20 8 18 19 27 27 , 29 1 2 3 4 5 6 17 -> 29 1 2 1 2 8 9 10 8 11 24 , 31 4 13 28 ->= 31 15 16 17 18 11 16 17 19 13 28 , 31 20 1 17 ->= 31 20 1 2 3 16 17 21 6 22 24 , 29 8 18 18 ->= 29 10 1 22 16 6 6 22 20 3 24 , 30 23 22 24 ->= 30 23 6 22 15 24 11 15 16 2 8 , 28 18 9 25 26 ->= 28 9 1 22 15 20 8 18 19 27 26 , 29 1 2 3 4 5 6 6 -> 29 1 2 1 2 8 9 10 8 11 16 , 31 4 13 23 ->= 31 15 16 17 18 11 16 17 19 13 23 , 31 20 1 6 ->= 31 20 1 2 3 16 17 21 6 22 16 , 29 8 18 21 ->= 29 10 1 22 16 6 6 22 20 3 16 , 30 23 22 16 ->= 30 23 6 22 15 24 11 15 16 2 1 , 28 18 9 25 5 ->= 28 9 1 22 15 20 8 18 19 27 5 , 29 1 2 3 4 5 6 2 -> 29 1 2 1 2 8 9 10 8 11 20 , 31 4 13 29 ->= 31 15 16 17 18 11 16 17 19 13 29 , 31 20 1 2 ->= 31 20 1 2 3 16 17 21 6 22 20 , 29 8 18 9 ->= 29 10 1 22 16 6 6 22 20 3 20 , 30 23 22 20 ->= 30 23 6 22 15 24 11 15 16 2 10 , 28 18 9 25 0 ->= 28 9 1 22 15 20 8 18 19 27 0 , 31 4 13 30 ->= 31 15 16 17 18 11 16 17 19 13 30 , 28 18 9 25 13 ->= 28 9 1 22 15 20 8 18 19 27 13 , 29 1 2 3 4 5 6 22 -> 29 1 2 1 2 8 9 10 8 11 15 , 31 4 13 31 ->= 31 15 16 17 18 11 16 17 19 13 31 , 31 20 1 22 ->= 31 20 1 2 3 16 17 21 6 22 15 , 29 8 18 11 ->= 29 10 1 22 16 6 6 22 20 3 15 , 30 23 22 15 ->= 30 23 6 22 15 24 11 15 16 2 3 , 28 18 9 25 12 ->= 28 9 1 22 15 20 8 18 19 27 12 , 20 1 2 3 4 5 6 7 -> 20 1 2 1 2 8 9 10 8 11 4 , 24 19 27 ->= 15 20 10 3 15 20 10 1 6 22 4 , 20 8 19 ->= 4 5 22 15 15 24 9 8 18 11 4 , 15 4 13 14 ->= 15 15 16 17 18 11 16 17 19 13 14 , 15 20 1 7 ->= 15 20 1 2 3 16 17 21 6 22 4 , 20 8 18 19 ->= 20 10 1 22 16 6 6 22 20 3 4 , 35 23 22 4 ->= 35 23 6 22 15 24 11 15 16 2 25 , 24 18 9 25 27 ->= 24 9 1 22 15 20 8 18 19 27 27 , 20 1 2 3 4 5 6 17 -> 20 1 2 1 2 8 9 10 8 11 24 , 20 8 18 ->= 4 5 22 15 15 24 9 8 18 11 24 , 15 4 13 28 ->= 15 15 16 17 18 11 16 17 19 13 28 , 15 20 1 17 ->= 15 20 1 2 3 16 17 21 6 22 24 , 20 8 18 18 ->= 20 10 1 22 16 6 6 22 20 3 24 , 35 23 22 24 ->= 35 23 6 22 15 24 11 15 16 2 8 , 24 18 9 25 26 ->= 24 9 1 22 15 20 8 18 19 27 26 , 20 1 2 3 4 5 6 6 -> 20 1 2 1 2 8 9 10 8 11 16 , 24 19 5 ->= 15 20 10 3 15 20 10 1 6 22 16 , 20 8 21 ->= 4 5 22 15 15 24 9 8 18 11 16 , 15 4 13 23 ->= 15 15 16 17 18 11 16 17 19 13 23 , 15 20 1 6 ->= 15 20 1 2 3 16 17 21 6 22 16 , 20 8 18 21 ->= 20 10 1 22 16 6 6 22 20 3 16 , 35 23 22 16 ->= 35 23 6 22 15 24 11 15 16 2 1 , 24 18 9 25 5 ->= 24 9 1 22 15 20 8 18 19 27 5 , 20 1 2 3 4 5 6 2 -> 20 1 2 1 2 8 9 10 8 11 20 , 20 8 9 ->= 4 5 22 15 15 24 9 8 18 11 20 , 15 4 13 29 ->= 15 15 16 17 18 11 16 17 19 13 29 , 15 20 1 2 ->= 15 20 1 2 3 16 17 21 6 22 20 , 20 8 18 9 ->= 20 10 1 22 16 6 6 22 20 3 20 , 35 23 22 20 ->= 35 23 6 22 15 24 11 15 16 2 10 , 24 18 9 25 0 ->= 24 9 1 22 15 20 8 18 19 27 0 , 15 4 13 30 ->= 15 15 16 17 18 11 16 17 19 13 30 , 24 18 9 25 13 ->= 24 9 1 22 15 20 8 18 19 27 13 , 20 1 2 3 4 5 6 22 -> 20 1 2 1 2 8 9 10 8 11 15 , 20 8 11 ->= 4 5 22 15 15 24 9 8 18 11 15 , 15 4 13 31 ->= 15 15 16 17 18 11 16 17 19 13 31 , 15 20 1 22 ->= 15 20 1 2 3 16 17 21 6 22 15 , 20 8 18 11 ->= 20 10 1 22 16 6 6 22 20 3 15 , 35 23 22 15 ->= 35 23 6 22 15 24 11 15 16 2 3 , 24 18 9 25 12 ->= 24 9 1 22 15 20 8 18 19 27 12 } 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 1 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 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 1 | | 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 20->13, 16->14, 17->15, 21->16, 22->17, 18->18, 19->19, 13->20, 23->21, 15->22, 24->23, 25->24, 26->25, 27->26, 28->27, 29->28, 30->29, 31->30, 14->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 219-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 26 ->= 25 9 1 17 22 13 8 18 19 26 26 , 0 1 2 3 4 5 6 15 -> 0 1 2 1 2 8 9 10 8 11 23 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 15 ->= 12 13 1 2 3 14 15 16 6 17 23 , 0 8 18 18 ->= 0 10 1 17 14 6 6 17 13 3 23 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 25 ->= 25 9 1 17 22 13 8 18 19 26 25 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 30 ->= 12 22 14 15 18 11 14 15 19 20 30 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 32 21 17 4 ->= 32 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 32 21 17 23 ->= 32 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 32 21 17 14 ->= 32 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 32 21 17 13 ->= 32 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 32 21 17 22 ->= 32 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 28 1 2 3 4 5 6 7 -> 28 1 2 1 2 8 9 10 8 11 4 , 30 4 20 31 ->= 30 22 14 15 18 11 14 15 19 20 31 , 30 13 1 7 ->= 30 13 1 2 3 14 15 16 6 17 4 , 28 8 18 19 ->= 28 10 1 17 14 6 6 17 13 3 4 , 29 21 17 4 ->= 29 21 6 17 22 23 11 22 14 2 24 , 27 18 9 24 26 ->= 27 9 1 17 22 13 8 18 19 26 26 , 28 1 2 3 4 5 6 15 -> 28 1 2 1 2 8 9 10 8 11 23 , 30 4 20 27 ->= 30 22 14 15 18 11 14 15 19 20 27 , 30 13 1 15 ->= 30 13 1 2 3 14 15 16 6 17 23 , 28 8 18 18 ->= 28 10 1 17 14 6 6 17 13 3 23 , 29 21 17 23 ->= 29 21 6 17 22 23 11 22 14 2 8 , 27 18 9 24 25 ->= 27 9 1 17 22 13 8 18 19 26 25 , 28 1 2 3 4 5 6 6 -> 28 1 2 1 2 8 9 10 8 11 14 , 30 4 20 21 ->= 30 22 14 15 18 11 14 15 19 20 21 , 30 13 1 6 ->= 30 13 1 2 3 14 15 16 6 17 14 , 28 8 18 16 ->= 28 10 1 17 14 6 6 17 13 3 14 , 29 21 17 14 ->= 29 21 6 17 22 23 11 22 14 2 1 , 27 18 9 24 5 ->= 27 9 1 17 22 13 8 18 19 26 5 , 28 1 2 3 4 5 6 2 -> 28 1 2 1 2 8 9 10 8 11 13 , 30 4 20 28 ->= 30 22 14 15 18 11 14 15 19 20 28 , 30 13 1 2 ->= 30 13 1 2 3 14 15 16 6 17 13 , 28 8 18 9 ->= 28 10 1 17 14 6 6 17 13 3 13 , 29 21 17 13 ->= 29 21 6 17 22 23 11 22 14 2 10 , 27 18 9 24 0 ->= 27 9 1 17 22 13 8 18 19 26 0 , 30 4 20 29 ->= 30 22 14 15 18 11 14 15 19 20 29 , 27 18 9 24 20 ->= 27 9 1 17 22 13 8 18 19 26 20 , 28 1 2 3 4 5 6 17 -> 28 1 2 1 2 8 9 10 8 11 22 , 30 4 20 30 ->= 30 22 14 15 18 11 14 15 19 20 30 , 30 13 1 17 ->= 30 13 1 2 3 14 15 16 6 17 22 , 28 8 18 11 ->= 28 10 1 17 14 6 6 17 13 3 22 , 29 21 17 22 ->= 29 21 6 17 22 23 11 22 14 2 3 , 27 18 9 24 12 ->= 27 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19, 20->20, 21->21, 22->22, 23->23, 24->24, 27->25, 25->26, 26->27, 28->28, 29->29, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 218-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 0 1 2 3 4 5 6 15 -> 0 1 2 1 2 8 9 10 8 11 23 , 12 4 20 25 ->= 12 22 14 15 18 11 14 15 19 20 25 , 12 13 1 15 ->= 12 13 1 2 3 14 15 16 6 17 23 , 0 8 18 18 ->= 0 10 1 17 14 6 6 17 13 3 23 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 26 18 9 24 26 ->= 26 9 1 17 22 13 8 18 19 27 26 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 26 18 9 24 5 ->= 26 9 1 17 22 13 8 18 19 27 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 26 18 9 24 0 ->= 26 9 1 17 22 13 8 18 19 27 0 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 26 18 9 24 20 ->= 26 9 1 17 22 13 8 18 19 27 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 30 ->= 12 22 14 15 18 11 14 15 19 20 30 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 26 18 9 24 12 ->= 26 9 1 17 22 13 8 18 19 27 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 27 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 32 21 17 4 ->= 32 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 27 ->= 18 9 1 17 22 13 8 18 19 27 27 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 25 ->= 11 22 14 15 18 11 14 15 19 20 25 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 32 21 17 23 ->= 32 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 27 26 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 32 21 17 14 ->= 32 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 27 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 32 21 17 13 ->= 32 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 27 0 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 27 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 32 21 17 22 ->= 32 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 27 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 27 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 27 ->= 15 9 1 17 22 13 8 18 19 27 27 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 25 ->= 17 22 14 15 18 11 14 15 19 20 25 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 27 26 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 27 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 27 0 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 27 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 27 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 27 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 27 ->= 8 9 1 17 22 13 8 18 19 27 27 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 25 ->= 3 22 14 15 18 11 14 15 19 20 25 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 27 26 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 27 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 27 0 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 27 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 27 12 , 28 1 2 3 4 5 6 7 -> 28 1 2 1 2 8 9 10 8 11 4 , 30 4 20 31 ->= 30 22 14 15 18 11 14 15 19 20 31 , 30 13 1 7 ->= 30 13 1 2 3 14 15 16 6 17 4 , 28 8 18 19 ->= 28 10 1 17 14 6 6 17 13 3 4 , 29 21 17 4 ->= 29 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 27 ->= 25 9 1 17 22 13 8 18 19 27 27 , 28 1 2 3 4 5 6 15 -> 28 1 2 1 2 8 9 10 8 11 23 , 30 4 20 25 ->= 30 22 14 15 18 11 14 15 19 20 25 , 30 13 1 15 ->= 30 13 1 2 3 14 15 16 6 17 23 , 28 8 18 18 ->= 28 10 1 17 14 6 6 17 13 3 23 , 29 21 17 23 ->= 29 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 26 ->= 25 9 1 17 22 13 8 18 19 27 26 , 28 1 2 3 4 5 6 6 -> 28 1 2 1 2 8 9 10 8 11 14 , 30 4 20 21 ->= 30 22 14 15 18 11 14 15 19 20 21 , 30 13 1 6 ->= 30 13 1 2 3 14 15 16 6 17 14 , 28 8 18 16 ->= 28 10 1 17 14 6 6 17 13 3 14 , 29 21 17 14 ->= 29 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 27 5 , 28 1 2 3 4 5 6 2 -> 28 1 2 1 2 8 9 10 8 11 13 , 30 4 20 28 ->= 30 22 14 15 18 11 14 15 19 20 28 , 30 13 1 2 ->= 30 13 1 2 3 14 15 16 6 17 13 , 28 8 18 9 ->= 28 10 1 17 14 6 6 17 13 3 13 , 29 21 17 13 ->= 29 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 27 0 , 30 4 20 29 ->= 30 22 14 15 18 11 14 15 19 20 29 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 27 20 , 28 1 2 3 4 5 6 17 -> 28 1 2 1 2 8 9 10 8 11 22 , 30 4 20 30 ->= 30 22 14 15 18 11 14 15 19 20 30 , 30 13 1 17 ->= 30 13 1 2 3 14 15 16 6 17 22 , 28 8 18 11 ->= 28 10 1 17 14 6 6 17 13 3 22 , 29 21 17 22 ->= 29 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 27 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 27 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 27 ->= 23 9 1 17 22 13 8 18 19 27 27 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 25 ->= 22 22 14 15 18 11 14 15 19 20 25 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 27 26 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 27 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 27 0 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 27 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 27 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 217-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 12 4 20 25 ->= 12 22 14 15 18 11 14 15 19 20 25 , 12 13 1 15 ->= 12 13 1 2 3 14 15 16 6 17 23 , 0 8 18 18 ->= 0 10 1 17 14 6 6 17 13 3 23 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 26 18 9 24 26 ->= 26 9 1 17 22 13 8 18 19 27 26 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 26 18 9 24 5 ->= 26 9 1 17 22 13 8 18 19 27 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 26 18 9 24 0 ->= 26 9 1 17 22 13 8 18 19 27 0 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 26 18 9 24 20 ->= 26 9 1 17 22 13 8 18 19 27 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 30 ->= 12 22 14 15 18 11 14 15 19 20 30 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 26 18 9 24 12 ->= 26 9 1 17 22 13 8 18 19 27 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 27 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 32 21 17 4 ->= 32 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 27 ->= 18 9 1 17 22 13 8 18 19 27 27 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 25 ->= 11 22 14 15 18 11 14 15 19 20 25 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 32 21 17 23 ->= 32 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 27 26 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 32 21 17 14 ->= 32 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 27 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 32 21 17 13 ->= 32 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 27 0 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 27 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 32 21 17 22 ->= 32 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 27 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 27 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 27 ->= 15 9 1 17 22 13 8 18 19 27 27 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 25 ->= 17 22 14 15 18 11 14 15 19 20 25 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 27 26 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 27 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 27 0 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 27 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 27 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 27 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 27 ->= 8 9 1 17 22 13 8 18 19 27 27 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 25 ->= 3 22 14 15 18 11 14 15 19 20 25 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 27 26 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 27 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 27 0 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 27 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 27 12 , 28 1 2 3 4 5 6 7 -> 28 1 2 1 2 8 9 10 8 11 4 , 30 4 20 31 ->= 30 22 14 15 18 11 14 15 19 20 31 , 30 13 1 7 ->= 30 13 1 2 3 14 15 16 6 17 4 , 28 8 18 19 ->= 28 10 1 17 14 6 6 17 13 3 4 , 29 21 17 4 ->= 29 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 27 ->= 25 9 1 17 22 13 8 18 19 27 27 , 28 1 2 3 4 5 6 15 -> 28 1 2 1 2 8 9 10 8 11 23 , 30 4 20 25 ->= 30 22 14 15 18 11 14 15 19 20 25 , 30 13 1 15 ->= 30 13 1 2 3 14 15 16 6 17 23 , 28 8 18 18 ->= 28 10 1 17 14 6 6 17 13 3 23 , 29 21 17 23 ->= 29 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 26 ->= 25 9 1 17 22 13 8 18 19 27 26 , 28 1 2 3 4 5 6 6 -> 28 1 2 1 2 8 9 10 8 11 14 , 30 4 20 21 ->= 30 22 14 15 18 11 14 15 19 20 21 , 30 13 1 6 ->= 30 13 1 2 3 14 15 16 6 17 14 , 28 8 18 16 ->= 28 10 1 17 14 6 6 17 13 3 14 , 29 21 17 14 ->= 29 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 27 5 , 28 1 2 3 4 5 6 2 -> 28 1 2 1 2 8 9 10 8 11 13 , 30 4 20 28 ->= 30 22 14 15 18 11 14 15 19 20 28 , 30 13 1 2 ->= 30 13 1 2 3 14 15 16 6 17 13 , 28 8 18 9 ->= 28 10 1 17 14 6 6 17 13 3 13 , 29 21 17 13 ->= 29 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 27 0 , 30 4 20 29 ->= 30 22 14 15 18 11 14 15 19 20 29 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 27 20 , 28 1 2 3 4 5 6 17 -> 28 1 2 1 2 8 9 10 8 11 22 , 30 4 20 30 ->= 30 22 14 15 18 11 14 15 19 20 30 , 30 13 1 17 ->= 30 13 1 2 3 14 15 16 6 17 22 , 28 8 18 11 ->= 28 10 1 17 14 6 6 17 13 3 22 , 29 21 17 22 ->= 29 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 27 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 27 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 27 ->= 23 9 1 17 22 13 8 18 19 27 27 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 25 ->= 22 22 14 15 18 11 14 15 19 20 25 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 27 26 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 27 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 27 0 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 27 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 27 12 } 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 1 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 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 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 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 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 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 | \ / 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 27->26, 28->27, 29->28, 30->29, 31->30, 32->31, 25->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 216-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 12 13 1 15 ->= 12 13 1 2 3 14 15 16 6 17 23 , 0 8 18 18 ->= 0 10 1 17 14 6 6 17 13 3 23 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 25 ->= 25 9 1 17 22 13 8 18 19 26 25 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 0 0 | | 0 0 0 0 0 | | 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 215-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 0 8 18 18 ->= 0 10 1 17 14 6 6 17 13 3 23 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 25 ->= 25 9 1 17 22 13 8 18 19 26 25 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 | | 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 214-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 20 21 17 23 ->= 20 21 6 17 22 23 11 22 14 2 8 , 25 18 9 24 25 ->= 25 9 1 17 22 13 8 18 19 26 25 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 213-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 25 ->= 25 9 1 17 22 13 8 18 19 26 25 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 212-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 0 1 2 3 4 5 6 6 -> 0 1 2 1 2 8 9 10 8 11 14 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 211-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 12 4 20 21 ->= 12 22 14 15 18 11 14 15 19 20 21 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 210-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 12 13 1 6 ->= 12 13 1 2 3 14 15 16 6 17 14 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 209-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 0 8 18 16 ->= 0 10 1 17 14 6 6 17 13 3 14 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 | | 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 208-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 20 21 17 14 ->= 20 21 6 17 22 23 11 22 14 2 1 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 207-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 0 1 2 3 4 5 6 2 -> 0 1 2 1 2 8 9 10 8 11 13 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 206-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 29 ->= 12 22 14 15 18 11 14 15 19 20 29 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 27 1 2 3 4 5 6 7 -> 27 1 2 1 2 8 9 10 8 11 4 , 29 4 20 30 ->= 29 22 14 15 18 11 14 15 19 20 30 , 29 13 1 7 ->= 29 13 1 2 3 14 15 16 6 17 4 , 27 8 18 19 ->= 27 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 32 18 9 24 26 ->= 32 9 1 17 22 13 8 18 19 26 26 , 27 1 2 3 4 5 6 15 -> 27 1 2 1 2 8 9 10 8 11 23 , 29 4 20 32 ->= 29 22 14 15 18 11 14 15 19 20 32 , 29 13 1 15 ->= 29 13 1 2 3 14 15 16 6 17 23 , 27 8 18 18 ->= 27 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 32 18 9 24 25 ->= 32 9 1 17 22 13 8 18 19 26 25 , 27 1 2 3 4 5 6 6 -> 27 1 2 1 2 8 9 10 8 11 14 , 29 4 20 21 ->= 29 22 14 15 18 11 14 15 19 20 21 , 29 13 1 6 ->= 29 13 1 2 3 14 15 16 6 17 14 , 27 8 18 16 ->= 27 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 32 18 9 24 5 ->= 32 9 1 17 22 13 8 18 19 26 5 , 27 1 2 3 4 5 6 2 -> 27 1 2 1 2 8 9 10 8 11 13 , 29 4 20 27 ->= 29 22 14 15 18 11 14 15 19 20 27 , 29 13 1 2 ->= 29 13 1 2 3 14 15 16 6 17 13 , 27 8 18 9 ->= 27 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 32 18 9 24 0 ->= 32 9 1 17 22 13 8 18 19 26 0 , 29 4 20 28 ->= 29 22 14 15 18 11 14 15 19 20 28 , 32 18 9 24 20 ->= 32 9 1 17 22 13 8 18 19 26 20 , 27 1 2 3 4 5 6 17 -> 27 1 2 1 2 8 9 10 8 11 22 , 29 4 20 29 ->= 29 22 14 15 18 11 14 15 19 20 29 , 29 13 1 17 ->= 29 13 1 2 3 14 15 16 6 17 22 , 27 8 18 11 ->= 27 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 32 18 9 24 12 ->= 32 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 28->27, 29->28, 30->29, 31->30, 32->31, 27->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 205-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 0 ->= 25 9 1 17 22 13 8 18 19 26 0 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 30 21 17 4 ->= 30 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 30 21 17 23 ->= 30 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 30 21 17 14 ->= 30 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 30 21 17 13 ->= 30 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 30 21 17 22 ->= 30 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 32 1 2 3 4 5 6 7 -> 32 1 2 1 2 8 9 10 8 11 4 , 28 4 20 29 ->= 28 22 14 15 18 11 14 15 19 20 29 , 28 13 1 7 ->= 28 13 1 2 3 14 15 16 6 17 4 , 32 8 18 19 ->= 32 10 1 17 14 6 6 17 13 3 4 , 27 21 17 4 ->= 27 21 6 17 22 23 11 22 14 2 24 , 31 18 9 24 26 ->= 31 9 1 17 22 13 8 18 19 26 26 , 32 1 2 3 4 5 6 15 -> 32 1 2 1 2 8 9 10 8 11 23 , 28 4 20 31 ->= 28 22 14 15 18 11 14 15 19 20 31 , 28 13 1 15 ->= 28 13 1 2 3 14 15 16 6 17 23 , 32 8 18 18 ->= 32 10 1 17 14 6 6 17 13 3 23 , 27 21 17 23 ->= 27 21 6 17 22 23 11 22 14 2 8 , 31 18 9 24 25 ->= 31 9 1 17 22 13 8 18 19 26 25 , 32 1 2 3 4 5 6 6 -> 32 1 2 1 2 8 9 10 8 11 14 , 28 4 20 21 ->= 28 22 14 15 18 11 14 15 19 20 21 , 28 13 1 6 ->= 28 13 1 2 3 14 15 16 6 17 14 , 32 8 18 16 ->= 32 10 1 17 14 6 6 17 13 3 14 , 27 21 17 14 ->= 27 21 6 17 22 23 11 22 14 2 1 , 31 18 9 24 5 ->= 31 9 1 17 22 13 8 18 19 26 5 , 32 1 2 3 4 5 6 2 -> 32 1 2 1 2 8 9 10 8 11 13 , 28 4 20 32 ->= 28 22 14 15 18 11 14 15 19 20 32 , 28 13 1 2 ->= 28 13 1 2 3 14 15 16 6 17 13 , 32 8 18 9 ->= 32 10 1 17 14 6 6 17 13 3 13 , 27 21 17 13 ->= 27 21 6 17 22 23 11 22 14 2 10 , 31 18 9 24 0 ->= 31 9 1 17 22 13 8 18 19 26 0 , 28 4 20 27 ->= 28 22 14 15 18 11 14 15 19 20 27 , 31 18 9 24 20 ->= 31 9 1 17 22 13 8 18 19 26 20 , 32 1 2 3 4 5 6 17 -> 32 1 2 1 2 8 9 10 8 11 22 , 28 4 20 28 ->= 28 22 14 15 18 11 14 15 19 20 28 , 28 13 1 17 ->= 28 13 1 2 3 14 15 16 6 17 22 , 32 8 18 11 ->= 32 10 1 17 14 6 6 17 13 3 22 , 27 21 17 22 ->= 27 21 6 17 22 23 11 22 14 2 3 , 31 18 9 24 12 ->= 31 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 204-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 28 ->= 12 22 14 15 18 11 14 15 19 20 28 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 30 21 17 4 ->= 30 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 30 21 17 23 ->= 30 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 30 21 17 14 ->= 30 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 30 21 17 13 ->= 30 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 30 21 17 22 ->= 30 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 32 1 2 3 4 5 6 7 -> 32 1 2 1 2 8 9 10 8 11 4 , 28 4 20 29 ->= 28 22 14 15 18 11 14 15 19 20 29 , 28 13 1 7 ->= 28 13 1 2 3 14 15 16 6 17 4 , 32 8 18 19 ->= 32 10 1 17 14 6 6 17 13 3 4 , 27 21 17 4 ->= 27 21 6 17 22 23 11 22 14 2 24 , 31 18 9 24 26 ->= 31 9 1 17 22 13 8 18 19 26 26 , 32 1 2 3 4 5 6 15 -> 32 1 2 1 2 8 9 10 8 11 23 , 28 4 20 31 ->= 28 22 14 15 18 11 14 15 19 20 31 , 28 13 1 15 ->= 28 13 1 2 3 14 15 16 6 17 23 , 32 8 18 18 ->= 32 10 1 17 14 6 6 17 13 3 23 , 27 21 17 23 ->= 27 21 6 17 22 23 11 22 14 2 8 , 31 18 9 24 25 ->= 31 9 1 17 22 13 8 18 19 26 25 , 32 1 2 3 4 5 6 6 -> 32 1 2 1 2 8 9 10 8 11 14 , 28 4 20 21 ->= 28 22 14 15 18 11 14 15 19 20 21 , 28 13 1 6 ->= 28 13 1 2 3 14 15 16 6 17 14 , 32 8 18 16 ->= 32 10 1 17 14 6 6 17 13 3 14 , 27 21 17 14 ->= 27 21 6 17 22 23 11 22 14 2 1 , 31 18 9 24 5 ->= 31 9 1 17 22 13 8 18 19 26 5 , 32 1 2 3 4 5 6 2 -> 32 1 2 1 2 8 9 10 8 11 13 , 28 4 20 32 ->= 28 22 14 15 18 11 14 15 19 20 32 , 28 13 1 2 ->= 28 13 1 2 3 14 15 16 6 17 13 , 32 8 18 9 ->= 32 10 1 17 14 6 6 17 13 3 13 , 27 21 17 13 ->= 27 21 6 17 22 23 11 22 14 2 10 , 31 18 9 24 0 ->= 31 9 1 17 22 13 8 18 19 26 0 , 28 4 20 27 ->= 28 22 14 15 18 11 14 15 19 20 27 , 31 18 9 24 20 ->= 31 9 1 17 22 13 8 18 19 26 20 , 32 1 2 3 4 5 6 17 -> 32 1 2 1 2 8 9 10 8 11 22 , 28 4 20 28 ->= 28 22 14 15 18 11 14 15 19 20 28 , 28 13 1 17 ->= 28 13 1 2 3 14 15 16 6 17 22 , 32 8 18 11 ->= 32 10 1 17 14 6 6 17 13 3 22 , 27 21 17 22 ->= 27 21 6 17 22 23 11 22 14 2 3 , 31 18 9 24 12 ->= 31 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 28->27, 29->28, 30->29, 31->30, 32->31, 27->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 203-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 25 18 9 24 20 ->= 25 9 1 17 22 13 8 18 19 26 20 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 29 21 17 4 ->= 29 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 29 21 17 23 ->= 29 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 29 21 17 14 ->= 29 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 29 21 17 13 ->= 29 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 29 21 17 22 ->= 29 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 31 1 2 3 4 5 6 7 -> 31 1 2 1 2 8 9 10 8 11 4 , 27 4 20 28 ->= 27 22 14 15 18 11 14 15 19 20 28 , 27 13 1 7 ->= 27 13 1 2 3 14 15 16 6 17 4 , 31 8 18 19 ->= 31 10 1 17 14 6 6 17 13 3 4 , 32 21 17 4 ->= 32 21 6 17 22 23 11 22 14 2 24 , 30 18 9 24 26 ->= 30 9 1 17 22 13 8 18 19 26 26 , 31 1 2 3 4 5 6 15 -> 31 1 2 1 2 8 9 10 8 11 23 , 27 4 20 30 ->= 27 22 14 15 18 11 14 15 19 20 30 , 27 13 1 15 ->= 27 13 1 2 3 14 15 16 6 17 23 , 31 8 18 18 ->= 31 10 1 17 14 6 6 17 13 3 23 , 32 21 17 23 ->= 32 21 6 17 22 23 11 22 14 2 8 , 30 18 9 24 25 ->= 30 9 1 17 22 13 8 18 19 26 25 , 31 1 2 3 4 5 6 6 -> 31 1 2 1 2 8 9 10 8 11 14 , 27 4 20 21 ->= 27 22 14 15 18 11 14 15 19 20 21 , 27 13 1 6 ->= 27 13 1 2 3 14 15 16 6 17 14 , 31 8 18 16 ->= 31 10 1 17 14 6 6 17 13 3 14 , 32 21 17 14 ->= 32 21 6 17 22 23 11 22 14 2 1 , 30 18 9 24 5 ->= 30 9 1 17 22 13 8 18 19 26 5 , 31 1 2 3 4 5 6 2 -> 31 1 2 1 2 8 9 10 8 11 13 , 27 4 20 31 ->= 27 22 14 15 18 11 14 15 19 20 31 , 27 13 1 2 ->= 27 13 1 2 3 14 15 16 6 17 13 , 31 8 18 9 ->= 31 10 1 17 14 6 6 17 13 3 13 , 32 21 17 13 ->= 32 21 6 17 22 23 11 22 14 2 10 , 30 18 9 24 0 ->= 30 9 1 17 22 13 8 18 19 26 0 , 27 4 20 32 ->= 27 22 14 15 18 11 14 15 19 20 32 , 30 18 9 24 20 ->= 30 9 1 17 22 13 8 18 19 26 20 , 31 1 2 3 4 5 6 17 -> 31 1 2 1 2 8 9 10 8 11 22 , 27 4 20 27 ->= 27 22 14 15 18 11 14 15 19 20 27 , 27 13 1 17 ->= 27 13 1 2 3 14 15 16 6 17 22 , 31 8 18 11 ->= 31 10 1 17 14 6 6 17 13 3 22 , 32 21 17 22 ->= 32 21 6 17 22 23 11 22 14 2 3 , 30 18 9 24 12 ->= 30 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 202-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 4 20 27 ->= 12 22 14 15 18 11 14 15 19 20 27 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 28 ->= 11 22 14 15 18 11 14 15 19 20 28 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 29 21 17 4 ->= 29 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 29 21 17 23 ->= 29 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 29 21 17 14 ->= 29 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 29 21 17 13 ->= 29 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 29 21 17 22 ->= 29 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 28 ->= 17 22 14 15 18 11 14 15 19 20 28 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 28 ->= 3 22 14 15 18 11 14 15 19 20 28 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 31 1 2 3 4 5 6 7 -> 31 1 2 1 2 8 9 10 8 11 4 , 27 4 20 28 ->= 27 22 14 15 18 11 14 15 19 20 28 , 27 13 1 7 ->= 27 13 1 2 3 14 15 16 6 17 4 , 31 8 18 19 ->= 31 10 1 17 14 6 6 17 13 3 4 , 32 21 17 4 ->= 32 21 6 17 22 23 11 22 14 2 24 , 30 18 9 24 26 ->= 30 9 1 17 22 13 8 18 19 26 26 , 31 1 2 3 4 5 6 15 -> 31 1 2 1 2 8 9 10 8 11 23 , 27 4 20 30 ->= 27 22 14 15 18 11 14 15 19 20 30 , 27 13 1 15 ->= 27 13 1 2 3 14 15 16 6 17 23 , 31 8 18 18 ->= 31 10 1 17 14 6 6 17 13 3 23 , 32 21 17 23 ->= 32 21 6 17 22 23 11 22 14 2 8 , 30 18 9 24 25 ->= 30 9 1 17 22 13 8 18 19 26 25 , 31 1 2 3 4 5 6 6 -> 31 1 2 1 2 8 9 10 8 11 14 , 27 4 20 21 ->= 27 22 14 15 18 11 14 15 19 20 21 , 27 13 1 6 ->= 27 13 1 2 3 14 15 16 6 17 14 , 31 8 18 16 ->= 31 10 1 17 14 6 6 17 13 3 14 , 32 21 17 14 ->= 32 21 6 17 22 23 11 22 14 2 1 , 30 18 9 24 5 ->= 30 9 1 17 22 13 8 18 19 26 5 , 31 1 2 3 4 5 6 2 -> 31 1 2 1 2 8 9 10 8 11 13 , 27 4 20 31 ->= 27 22 14 15 18 11 14 15 19 20 31 , 27 13 1 2 ->= 27 13 1 2 3 14 15 16 6 17 13 , 31 8 18 9 ->= 31 10 1 17 14 6 6 17 13 3 13 , 32 21 17 13 ->= 32 21 6 17 22 23 11 22 14 2 10 , 30 18 9 24 0 ->= 30 9 1 17 22 13 8 18 19 26 0 , 27 4 20 32 ->= 27 22 14 15 18 11 14 15 19 20 32 , 30 18 9 24 20 ->= 30 9 1 17 22 13 8 18 19 26 20 , 31 1 2 3 4 5 6 17 -> 31 1 2 1 2 8 9 10 8 11 22 , 27 4 20 27 ->= 27 22 14 15 18 11 14 15 19 20 27 , 27 13 1 17 ->= 27 13 1 2 3 14 15 16 6 17 22 , 31 8 18 11 ->= 31 10 1 17 14 6 6 17 13 3 22 , 32 21 17 22 ->= 32 21 6 17 22 23 11 22 14 2 3 , 30 18 9 24 12 ->= 30 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 28 ->= 22 22 14 15 18 11 14 15 19 20 28 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 28->27, 29->28, 30->29, 31->30, 32->31, 27->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 201-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 25 18 9 24 12 ->= 25 9 1 17 22 13 8 18 19 26 12 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 200-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 18 18 9 24 26 ->= 18 9 1 17 22 13 8 18 19 26 26 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 199-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 1 2 3 4 5 6 15 -> 9 1 2 1 2 8 9 10 8 11 23 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 198-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 8 18 18 ->= 9 10 1 17 14 6 6 17 13 3 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 1 | | 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 197-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 28 21 17 23 ->= 28 21 6 17 22 23 11 22 14 2 8 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 196-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 18 9 24 25 ->= 18 9 1 17 22 13 8 18 19 26 25 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 195-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 9 1 2 3 4 5 6 6 -> 9 1 2 1 2 8 9 10 8 11 14 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 194-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 9 8 16 ->= 19 5 17 22 22 23 9 8 18 11 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 193-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 9 8 18 16 ->= 9 10 1 17 14 6 6 17 13 3 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 1 | | 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 192-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 28 21 17 14 ->= 28 21 6 17 22 23 11 22 14 2 1 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 191-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 1 2 3 4 5 6 2 -> 9 1 2 1 2 8 9 10 8 11 13 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 190-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 18 18 9 24 0 ->= 18 9 1 17 22 13 8 18 19 26 0 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 189-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 18 18 9 24 20 ->= 18 9 1 17 22 13 8 18 19 26 20 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 188-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 18 18 9 24 12 ->= 18 9 1 17 22 13 8 18 19 26 12 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 187-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 15 19 26 ->= 17 13 10 3 22 13 10 1 6 17 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 186-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 15 18 9 24 26 ->= 15 9 1 17 22 13 8 18 19 26 26 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 185-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 33 21 17 23 ->= 33 21 6 17 22 23 11 22 14 2 8 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 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 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 184-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 15 18 9 24 25 ->= 15 9 1 17 22 13 8 18 19 26 25 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 183-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 33 21 17 14 ->= 33 21 6 17 22 23 11 22 14 2 1 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 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 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 182-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 15 18 9 24 0 ->= 15 9 1 17 22 13 8 18 19 26 0 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 181-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 15 18 9 24 20 ->= 15 9 1 17 22 13 8 18 19 26 20 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 180-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 15 18 9 24 12 ->= 15 9 1 17 22 13 8 18 19 26 12 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 179-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 34 21 17 23 ->= 34 21 6 17 22 23 11 22 14 2 8 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 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 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 178-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 34 21 17 14 ->= 34 21 6 17 22 23 11 22 14 2 1 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 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 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 177-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 4 20 27 ->= 32 22 14 15 18 11 14 15 19 20 27 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 176-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 26 ->= 29 9 1 17 22 13 8 18 19 26 26 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 175-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 30 1 2 3 4 5 6 15 -> 30 1 2 1 2 8 9 10 8 11 23 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 174-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 32 4 20 29 ->= 32 22 14 15 18 11 14 15 19 20 29 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 1 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 173-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 32 13 1 15 ->= 32 13 1 2 3 14 15 16 6 17 23 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 172-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 30 8 18 18 ->= 30 10 1 17 14 6 6 17 13 3 23 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 1 | | 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 | \ / 30 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 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 171-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 31 21 17 23 ->= 31 21 6 17 22 23 11 22 14 2 8 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 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 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 170-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 25 ->= 29 9 1 17 22 13 8 18 19 26 25 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 169-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 30 1 2 3 4 5 6 6 -> 30 1 2 1 2 8 9 10 8 11 14 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 168-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 32 4 20 21 ->= 32 22 14 15 18 11 14 15 19 20 21 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 167-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 32 13 1 6 ->= 32 13 1 2 3 14 15 16 6 17 14 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 166-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 30 8 18 16 ->= 30 10 1 17 14 6 6 17 13 3 14 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 1 | | 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 | \ / 30 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 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 165-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 31 21 17 14 ->= 31 21 6 17 22 23 11 22 14 2 1 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 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 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 164-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 30 1 2 3 4 5 6 2 -> 30 1 2 1 2 8 9 10 8 11 13 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 163-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 4 20 30 ->= 32 22 14 15 18 11 14 15 19 20 30 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 | \ / 30 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 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 162-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 0 ->= 29 9 1 17 22 13 8 18 19 26 0 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 161-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 32 4 20 31 ->= 32 22 14 15 18 11 14 15 19 20 31 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 160-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 29 18 9 24 20 ->= 29 9 1 17 22 13 8 18 19 26 20 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 159-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 4 20 32 ->= 32 22 14 15 18 11 14 15 19 20 32 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 158-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 29 18 9 24 12 ->= 29 9 1 17 22 13 8 18 19 26 12 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 157-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 35 21 17 23 ->= 35 21 6 17 22 23 11 22 14 2 8 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 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 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 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 | \ / 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 156-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 2 8 18 19 ->= 2 10 1 17 14 6 6 17 13 3 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 2 8 18 ->= 7 5 17 22 22 23 9 8 18 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 8 18 18 ->= 2 10 1 17 14 6 6 17 13 3 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 2 8 18 16 ->= 2 10 1 17 14 6 6 17 13 3 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 2 8 18 9 ->= 2 10 1 17 14 6 6 17 13 3 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 2 8 18 11 ->= 2 10 1 17 14 6 6 17 13 3 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 150-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 2 8 16 ->= 7 5 17 22 22 23 9 8 18 11 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 149-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 8 19 26 ->= 3 13 10 3 22 13 10 1 6 17 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 148-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 8 18 9 24 26 ->= 8 9 1 17 22 13 8 18 19 26 26 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 147-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 8 18 9 24 25 ->= 8 9 1 17 22 13 8 18 19 26 25 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 146-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 8 18 9 24 0 ->= 8 9 1 17 22 13 8 18 19 26 0 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 145-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 8 18 9 24 20 ->= 8 9 1 17 22 13 8 18 19 26 20 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 144-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 8 18 9 24 12 ->= 8 9 1 17 22 13 8 18 19 26 12 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 143-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 35 21 17 14 ->= 35 21 6 17 22 23 11 22 14 2 1 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 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 | \ / 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 142-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 2 1 2 3 4 5 6 15 -> 2 1 2 1 2 8 9 10 8 11 23 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 141-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 2 1 2 3 4 5 6 6 -> 2 1 2 1 2 8 9 10 8 11 14 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 140-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 1 2 3 4 5 6 2 -> 2 1 2 1 2 8 9 10 8 11 13 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 139-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 9 ->= 0 10 1 17 14 6 6 17 13 3 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 1 | | 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 138-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 20 21 17 13 ->= 20 21 6 17 22 23 11 22 14 2 10 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 137-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 1 2 3 4 5 6 17 -> 0 1 2 1 2 8 9 10 8 11 22 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 136-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 12 13 1 17 ->= 12 13 1 2 3 14 15 16 6 17 22 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 0 0 | | 0 0 0 0 0 | | 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 135-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 9 8 9 ->= 19 5 17 22 22 23 9 8 18 11 13 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 9 8 18 9 ->= 9 10 1 17 14 6 6 17 13 3 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 1 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 133-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 28 21 17 13 ->= 28 21 6 17 22 23 11 22 14 2 10 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 132-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 1 2 3 4 5 6 17 -> 9 1 2 1 2 8 9 10 8 11 22 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 131-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 33 21 17 13 ->= 33 21 6 17 22 23 11 22 14 2 10 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 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 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 130-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 1 2 3 4 5 6 17 -> 2 1 2 1 2 8 9 10 8 11 22 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 129-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 34 21 17 13 ->= 34 21 6 17 22 23 11 22 14 2 10 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 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 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 128-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 9 ->= 30 10 1 17 14 6 6 17 13 3 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 1 1 | | 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 | \ / 30 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 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 127-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 31 21 17 13 ->= 31 21 6 17 22 23 11 22 14 2 10 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 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 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 126-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 1 2 3 4 5 6 15 -> 10 1 2 1 2 8 9 10 8 11 23 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 125-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 10 8 18 19 ->= 10 10 1 17 14 6 6 17 13 3 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 10 8 18 ->= 24 5 17 22 22 23 9 8 18 11 23 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 8 18 18 ->= 10 10 1 17 14 6 6 17 13 3 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 10 8 18 16 ->= 10 10 1 17 14 6 6 17 13 3 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 10 8 18 9 ->= 10 10 1 17 14 6 6 17 13 3 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 10 8 18 11 ->= 10 10 1 17 14 6 6 17 13 3 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 119-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 10 1 2 3 4 5 6 6 -> 10 1 2 1 2 8 9 10 8 11 14 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 118-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 10 8 16 ->= 24 5 17 22 22 23 9 8 18 11 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 117-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 1 2 3 4 5 6 2 -> 10 1 2 1 2 8 9 10 8 11 13 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 116-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 1 2 3 4 5 6 17 -> 30 1 2 1 2 8 9 10 8 11 22 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 115-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 32 13 1 17 ->= 32 13 1 2 3 14 15 16 6 17 22 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 | | 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 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 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 114-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 35 21 17 13 ->= 35 21 6 17 22 23 11 22 14 2 10 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 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 1 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 1 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 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 | \ / 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 113-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 10 8 9 ->= 24 5 17 22 22 23 9 8 18 11 13 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 112-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 1 2 3 4 5 6 17 -> 10 1 2 1 2 8 9 10 8 11 22 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 111-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 30 8 18 11 ->= 30 10 1 17 14 6 6 17 13 3 22 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } 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 1 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 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 1 | | 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 | \ / 30 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 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 110-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 2 8 11 ->= 7 5 17 22 22 23 9 8 18 11 22 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 109-rule system { 0 1 2 3 4 5 6 7 -> 0 1 2 1 2 8 9 10 8 11 4 , 12 13 1 7 ->= 12 13 1 2 3 14 15 16 6 17 4 , 0 8 18 19 ->= 0 10 1 17 14 6 6 17 13 3 4 , 20 21 17 4 ->= 20 21 6 17 22 23 11 22 14 2 24 , 25 18 9 24 5 ->= 25 9 1 17 22 13 8 18 19 26 5 , 12 13 1 2 ->= 12 13 1 2 3 14 15 16 6 17 13 , 0 8 18 11 ->= 0 10 1 17 14 6 6 17 13 3 22 , 20 21 17 22 ->= 20 21 6 17 22 23 11 22 14 2 3 , 9 1 2 3 4 5 6 7 -> 9 1 2 1 2 8 9 10 8 11 4 , 18 19 26 ->= 11 13 10 3 22 13 10 1 6 17 4 , 9 8 19 ->= 19 5 17 22 22 23 9 8 18 11 4 , 11 4 20 27 ->= 11 22 14 15 18 11 14 15 19 20 27 , 11 13 1 7 ->= 11 13 1 2 3 14 15 16 6 17 4 , 9 8 18 19 ->= 9 10 1 17 14 6 6 17 13 3 4 , 28 21 17 4 ->= 28 21 6 17 22 23 11 22 14 2 24 , 9 8 18 ->= 19 5 17 22 22 23 9 8 18 11 23 , 11 4 20 29 ->= 11 22 14 15 18 11 14 15 19 20 29 , 11 13 1 15 ->= 11 13 1 2 3 14 15 16 6 17 23 , 18 19 5 ->= 11 13 10 3 22 13 10 1 6 17 14 , 11 4 20 21 ->= 11 22 14 15 18 11 14 15 19 20 21 , 11 13 1 6 ->= 11 13 1 2 3 14 15 16 6 17 14 , 18 18 9 24 5 ->= 18 9 1 17 22 13 8 18 19 26 5 , 11 4 20 30 ->= 11 22 14 15 18 11 14 15 19 20 30 , 11 13 1 2 ->= 11 13 1 2 3 14 15 16 6 17 13 , 11 4 20 31 ->= 11 22 14 15 18 11 14 15 19 20 31 , 9 8 11 ->= 19 5 17 22 22 23 9 8 18 11 22 , 11 4 20 32 ->= 11 22 14 15 18 11 14 15 19 20 32 , 11 13 1 17 ->= 11 13 1 2 3 14 15 16 6 17 22 , 9 8 18 11 ->= 9 10 1 17 14 6 6 17 13 3 22 , 28 21 17 22 ->= 28 21 6 17 22 23 11 22 14 2 3 , 2 1 2 3 4 5 6 7 -> 2 1 2 1 2 8 9 10 8 11 4 , 2 8 19 ->= 7 5 17 22 22 23 9 8 18 11 4 , 17 4 20 27 ->= 17 22 14 15 18 11 14 15 19 20 27 , 17 13 1 7 ->= 17 13 1 2 3 14 15 16 6 17 4 , 33 21 17 4 ->= 33 21 6 17 22 23 11 22 14 2 24 , 17 4 20 29 ->= 17 22 14 15 18 11 14 15 19 20 29 , 17 13 1 15 ->= 17 13 1 2 3 14 15 16 6 17 23 , 15 19 5 ->= 17 13 10 3 22 13 10 1 6 17 14 , 17 4 20 21 ->= 17 22 14 15 18 11 14 15 19 20 21 , 17 13 1 6 ->= 17 13 1 2 3 14 15 16 6 17 14 , 15 18 9 24 5 ->= 15 9 1 17 22 13 8 18 19 26 5 , 2 8 9 ->= 7 5 17 22 22 23 9 8 18 11 13 , 17 4 20 30 ->= 17 22 14 15 18 11 14 15 19 20 30 , 17 13 1 2 ->= 17 13 1 2 3 14 15 16 6 17 13 , 17 4 20 31 ->= 17 22 14 15 18 11 14 15 19 20 31 , 17 4 20 32 ->= 17 22 14 15 18 11 14 15 19 20 32 , 17 13 1 17 ->= 17 13 1 2 3 14 15 16 6 17 22 , 33 21 17 22 ->= 33 21 6 17 22 23 11 22 14 2 3 , 10 1 2 3 4 5 6 7 -> 10 1 2 1 2 8 9 10 8 11 4 , 10 8 19 ->= 24 5 17 22 22 23 9 8 18 11 4 , 3 4 20 27 ->= 3 22 14 15 18 11 14 15 19 20 27 , 3 13 1 7 ->= 3 13 1 2 3 14 15 16 6 17 4 , 34 21 17 4 ->= 34 21 6 17 22 23 11 22 14 2 24 , 3 4 20 29 ->= 3 22 14 15 18 11 14 15 19 20 29 , 3 13 1 15 ->= 3 13 1 2 3 14 15 16 6 17 23 , 8 19 5 ->= 3 13 10 3 22 13 10 1 6 17 14 , 3 4 20 21 ->= 3 22 14 15 18 11 14 15 19 20 21 , 3 13 1 6 ->= 3 13 1 2 3 14 15 16 6 17 14 , 8 18 9 24 5 ->= 8 9 1 17 22 13 8 18 19 26 5 , 3 4 20 30 ->= 3 22 14 15 18 11 14 15 19 20 30 , 3 13 1 2 ->= 3 13 1 2 3 14 15 16 6 17 13 , 3 4 20 31 ->= 3 22 14 15 18 11 14 15 19 20 31 , 10 8 11 ->= 24 5 17 22 22 23 9 8 18 11 22 , 3 4 20 32 ->= 3 22 14 15 18 11 14 15 19 20 32 , 3 13 1 17 ->= 3 13 1 2 3 14 15 16 6 17 22 , 34 21 17 22 ->= 34 21 6 17 22 23 11 22 14 2 3 , 30 1 2 3 4 5 6 7 -> 30 1 2 1 2 8 9 10 8 11 4 , 32 13 1 7 ->= 32 13 1 2 3 14 15 16 6 17 4 , 30 8 18 19 ->= 30 10 1 17 14 6 6 17 13 3 4 , 31 21 17 4 ->= 31 21 6 17 22 23 11 22 14 2 24 , 29 18 9 24 5 ->= 29 9 1 17 22 13 8 18 19 26 5 , 32 13 1 2 ->= 32 13 1 2 3 14 15 16 6 17 13 , 31 21 17 22 ->= 31 21 6 17 22 23 11 22 14 2 3 , 13 1 2 3 4 5 6 7 -> 13 1 2 1 2 8 9 10 8 11 4 , 23 19 26 ->= 22 13 10 3 22 13 10 1 6 17 4 , 13 8 19 ->= 4 5 17 22 22 23 9 8 18 11 4 , 22 4 20 27 ->= 22 22 14 15 18 11 14 15 19 20 27 , 22 13 1 7 ->= 22 13 1 2 3 14 15 16 6 17 4 , 13 8 18 19 ->= 13 10 1 17 14 6 6 17 13 3 4 , 35 21 17 4 ->= 35 21 6 17 22 23 11 22 14 2 24 , 23 18 9 24 26 ->= 23 9 1 17 22 13 8 18 19 26 26 , 13 1 2 3 4 5 6 15 -> 13 1 2 1 2 8 9 10 8 11 23 , 13 8 18 ->= 4 5 17 22 22 23 9 8 18 11 23 , 22 4 20 29 ->= 22 22 14 15 18 11 14 15 19 20 29 , 22 13 1 15 ->= 22 13 1 2 3 14 15 16 6 17 23 , 13 8 18 18 ->= 13 10 1 17 14 6 6 17 13 3 23 , 23 18 9 24 25 ->= 23 9 1 17 22 13 8 18 19 26 25 , 13 1 2 3 4 5 6 6 -> 13 1 2 1 2 8 9 10 8 11 14 , 23 19 5 ->= 22 13 10 3 22 13 10 1 6 17 14 , 13 8 16 ->= 4 5 17 22 22 23 9 8 18 11 14 , 22 4 20 21 ->= 22 22 14 15 18 11 14 15 19 20 21 , 22 13 1 6 ->= 22 13 1 2 3 14 15 16 6 17 14 , 13 8 18 16 ->= 13 10 1 17 14 6 6 17 13 3 14 , 23 18 9 24 5 ->= 23 9 1 17 22 13 8 18 19 26 5 , 13 1 2 3 4 5 6 2 -> 13 1 2 1 2 8 9 10 8 11 13 , 13 8 9 ->= 4 5 17 22 22 23 9 8 18 11 13 , 22 4 20 30 ->= 22 22 14 15 18 11 14 15 19 20 30 , 22 13 1 2 ->= 22 13 1 2 3 14 15 16 6 17 13 , 13 8 18 9 ->= 13 10 1 17 14 6 6 17 13 3 13 , 23 18 9 24 0 ->= 23 9 1 17 22 13 8 18 19 26 0 , 22 4 20 31 ->= 22 22 14 15 18 11 14 15 19 20 31 , 23 18 9 24 20 ->= 23 9 1 17 22 13 8 18 19 26 20 , 13 1 2 3 4 5 6 17 -> 13 1 2 1 2 8 9 10 8 11 22 , 13 8 11 ->= 4 5 17 22 22 23 9 8 18 11 22 , 22 4 20 32 ->= 22 22 14 15 18 11 14 15 19 20 32 , 22 13 1 17 ->= 22 13 1 2 3 14 15 16 6 17 22 , 13 8 18 11 ->= 13 10 1 17 14 6 6 17 13 3 22 , 35 21 17 22 ->= 35 21 6 17 22 23 11 22 14 2 3 , 23 18 9 24 12 ->= 23 9 1 17 22 13 8 18 19 26 12 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 12->0, 13->1, 1->2, 7->3, 2->4, 3->5, 14->6, 15->7, 16->8, 6->9, 17->10, 4->11, 0->12, 8->13, 18->14, 19->15, 10->16, 20->17, 21->18, 22->19, 23->20, 11->21, 24->22, 25->23, 9->24, 5->25, 26->26, 27->27, 28->28, 29->29, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 108-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 12 13 14 21 ->= 12 16 2 10 6 9 9 10 1 5 19 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 24 2 4 5 11 25 9 3 -> 24 2 4 2 4 13 24 16 13 21 11 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 2 4 5 11 25 9 3 -> 4 2 4 2 4 13 24 16 13 21 11 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 2 4 5 11 25 9 3 -> 16 2 4 2 4 13 24 16 13 21 11 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 30 2 4 5 11 25 9 3 -> 30 2 4 2 4 13 24 16 13 21 11 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } 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 0 0 | | 0 0 0 0 0 | | 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 1 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 1 | | 0 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 107-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 24 2 4 5 11 25 9 3 -> 24 2 4 2 4 13 24 16 13 21 11 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 2 4 5 11 25 9 3 -> 4 2 4 2 4 13 24 16 13 21 11 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 2 4 5 11 25 9 3 -> 16 2 4 2 4 13 24 16 13 21 11 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 30 2 4 5 11 25 9 3 -> 30 2 4 2 4 13 24 16 13 21 11 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 106-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 24 2 4 5 11 25 9 3 -> 24 2 4 2 4 13 24 16 13 21 11 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 2 4 5 11 25 9 3 -> 4 2 4 2 4 13 24 16 13 21 11 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 30 2 4 5 11 25 9 3 -> 30 2 4 2 4 13 24 16 13 21 11 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 105-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 2 4 5 11 25 9 3 -> 4 2 4 2 4 13 24 16 13 21 11 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 30 2 4 5 11 25 9 3 -> 30 2 4 2 4 13 24 16 13 21 11 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 104-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 30 2 4 5 11 25 9 3 -> 30 2 4 2 4 13 24 16 13 21 11 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 103-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 14 15 ->= 12 16 2 10 6 9 9 10 1 5 11 , 17 18 10 11 ->= 17 18 9 10 19 20 21 19 6 4 22 , 23 14 24 22 25 ->= 23 24 2 10 19 1 13 14 15 26 25 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 17 18 10 19 ->= 17 18 9 10 19 20 21 19 6 4 5 , 14 15 26 ->= 21 1 16 5 19 1 16 2 9 10 11 , 24 13 15 ->= 15 25 10 19 19 20 24 13 14 21 11 , 21 11 17 27 ->= 21 19 6 7 14 21 6 7 15 17 27 , 21 1 2 3 ->= 21 1 2 4 5 6 7 8 9 10 11 , 24 13 14 15 ->= 24 16 2 10 6 9 9 10 1 5 11 , 28 18 10 11 ->= 28 18 9 10 19 20 21 19 6 4 22 , 24 13 14 ->= 15 25 10 19 19 20 24 13 14 21 20 , 21 11 17 29 ->= 21 19 6 7 14 21 6 7 15 17 29 , 21 1 2 7 ->= 21 1 2 4 5 6 7 8 9 10 20 , 14 15 25 ->= 21 1 16 5 19 1 16 2 9 10 6 , 21 11 17 18 ->= 21 19 6 7 14 21 6 7 15 17 18 , 21 1 2 9 ->= 21 1 2 4 5 6 7 8 9 10 6 , 14 14 24 22 25 ->= 14 24 2 10 19 1 13 14 15 26 25 , 21 11 17 30 ->= 21 19 6 7 14 21 6 7 15 17 30 , 21 1 2 4 ->= 21 1 2 4 5 6 7 8 9 10 1 , 21 11 17 31 ->= 21 19 6 7 14 21 6 7 15 17 31 , 24 13 21 ->= 15 25 10 19 19 20 24 13 14 21 19 , 21 11 17 32 ->= 21 19 6 7 14 21 6 7 15 17 32 , 21 1 2 10 ->= 21 1 2 4 5 6 7 8 9 10 19 , 24 13 14 21 ->= 24 16 2 10 6 9 9 10 1 5 19 , 28 18 10 19 ->= 28 18 9 10 19 20 21 19 6 4 5 , 4 13 15 ->= 3 25 10 19 19 20 24 13 14 21 11 , 10 11 17 27 ->= 10 19 6 7 14 21 6 7 15 17 27 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 33 18 10 11 ->= 33 18 9 10 19 20 21 19 6 4 22 , 10 11 17 29 ->= 10 19 6 7 14 21 6 7 15 17 29 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 20 , 7 15 25 ->= 10 1 16 5 19 1 16 2 9 10 6 , 10 11 17 18 ->= 10 19 6 7 14 21 6 7 15 17 18 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 14 24 22 25 ->= 7 24 2 10 19 1 13 14 15 26 25 , 4 13 24 ->= 3 25 10 19 19 20 24 13 14 21 1 , 10 11 17 30 ->= 10 19 6 7 14 21 6 7 15 17 30 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 17 31 ->= 10 19 6 7 14 21 6 7 15 17 31 , 10 11 17 32 ->= 10 19 6 7 14 21 6 7 15 17 32 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 19 , 33 18 10 19 ->= 33 18 9 10 19 20 21 19 6 4 5 , 16 13 15 ->= 22 25 10 19 19 20 24 13 14 21 11 , 5 11 17 27 ->= 5 19 6 7 14 21 6 7 15 17 27 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 34 18 10 11 ->= 34 18 9 10 19 20 21 19 6 4 22 , 5 11 17 29 ->= 5 19 6 7 14 21 6 7 15 17 29 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 20 , 13 15 25 ->= 5 1 16 5 19 1 16 2 9 10 6 , 5 11 17 18 ->= 5 19 6 7 14 21 6 7 15 17 18 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 13 14 24 22 25 ->= 13 24 2 10 19 1 13 14 15 26 25 , 5 11 17 30 ->= 5 19 6 7 14 21 6 7 15 17 30 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 17 31 ->= 5 19 6 7 14 21 6 7 15 17 31 , 16 13 21 ->= 22 25 10 19 19 20 24 13 14 21 19 , 5 11 17 32 ->= 5 19 6 7 14 21 6 7 15 17 32 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 19 , 34 18 10 19 ->= 34 18 9 10 19 20 21 19 6 4 5 , 32 1 2 3 ->= 32 1 2 4 5 6 7 8 9 10 11 , 30 13 14 15 ->= 30 16 2 10 6 9 9 10 1 5 11 , 31 18 10 11 ->= 31 18 9 10 19 20 21 19 6 4 22 , 29 14 24 22 25 ->= 29 24 2 10 19 1 13 14 15 26 25 , 32 1 2 4 ->= 32 1 2 4 5 6 7 8 9 10 1 , 31 18 10 19 ->= 31 18 9 10 19 20 21 19 6 4 5 , 1 2 4 5 11 25 9 3 -> 1 2 4 2 4 13 24 16 13 21 11 , 20 15 26 ->= 19 1 16 5 19 1 16 2 9 10 11 , 1 13 15 ->= 11 25 10 19 19 20 24 13 14 21 11 , 19 11 17 27 ->= 19 19 6 7 14 21 6 7 15 17 27 , 19 1 2 3 ->= 19 1 2 4 5 6 7 8 9 10 11 , 1 13 14 15 ->= 1 16 2 10 6 9 9 10 1 5 11 , 35 18 10 11 ->= 35 18 9 10 19 20 21 19 6 4 22 , 20 14 24 22 26 ->= 20 24 2 10 19 1 13 14 15 26 26 , 1 2 4 5 11 25 9 7 -> 1 2 4 2 4 13 24 16 13 21 20 , 1 13 14 ->= 11 25 10 19 19 20 24 13 14 21 20 , 19 11 17 29 ->= 19 19 6 7 14 21 6 7 15 17 29 , 19 1 2 7 ->= 19 1 2 4 5 6 7 8 9 10 20 , 1 13 14 14 ->= 1 16 2 10 6 9 9 10 1 5 20 , 20 14 24 22 23 ->= 20 24 2 10 19 1 13 14 15 26 23 , 1 2 4 5 11 25 9 9 -> 1 2 4 2 4 13 24 16 13 21 6 , 20 15 25 ->= 19 1 16 5 19 1 16 2 9 10 6 , 1 13 8 ->= 11 25 10 19 19 20 24 13 14 21 6 , 19 11 17 18 ->= 19 19 6 7 14 21 6 7 15 17 18 , 19 1 2 9 ->= 19 1 2 4 5 6 7 8 9 10 6 , 1 13 14 8 ->= 1 16 2 10 6 9 9 10 1 5 6 , 20 14 24 22 25 ->= 20 24 2 10 19 1 13 14 15 26 25 , 1 2 4 5 11 25 9 4 -> 1 2 4 2 4 13 24 16 13 21 1 , 1 13 24 ->= 11 25 10 19 19 20 24 13 14 21 1 , 19 11 17 30 ->= 19 19 6 7 14 21 6 7 15 17 30 , 19 1 2 4 ->= 19 1 2 4 5 6 7 8 9 10 1 , 1 13 14 24 ->= 1 16 2 10 6 9 9 10 1 5 1 , 20 14 24 22 12 ->= 20 24 2 10 19 1 13 14 15 26 12 , 19 11 17 31 ->= 19 19 6 7 14 21 6 7 15 17 31 , 20 14 24 22 17 ->= 20 24 2 10 19 1 13 14 15 26 17 , 1 2 4 5 11 25 9 10 -> 1 2 4 2 4 13 24 16 13 21 19 , 1 13 21 ->= 11 25 10 19 19 20 24 13 14 21 19 , 19 11 17 32 ->= 19 19 6 7 14 21 6 7 15 17 32 , 19 1 2 10 ->= 19 1 2 4 5 6 7 8 9 10 19 , 1 13 14 21 ->= 1 16 2 10 6 9 9 10 1 5 19 , 35 18 10 19 ->= 35 18 9 10 19 20 21 19 6 4 5 , 20 14 24 22 0 ->= 20 24 2 10 19 1 13 14 15 26 0 } 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 0 0 | | 0 0 0 0 0 | | 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 1 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 1 1 | | 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 1 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 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 17->12, 18->13, 19->14, 20->15, 21->16, 22->17, 23->18, 14->19, 24->20, 25->21, 13->22, 15->23, 26->24, 16->25, 27->26, 28->27, 29->28, 30->29, 31->30, 32->31, 33->32, 34->33, 35->34, 12->35 }, it remains to prove termination of the 102-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 10 11 ->= 12 13 9 10 14 15 16 14 6 4 17 , 18 19 20 17 21 ->= 18 20 2 10 14 1 22 19 23 24 21 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 12 13 10 14 ->= 12 13 9 10 14 15 16 14 6 4 5 , 19 23 24 ->= 16 1 25 5 14 1 25 2 9 10 11 , 20 22 23 ->= 23 21 10 14 14 15 20 22 19 16 11 , 16 11 12 26 ->= 16 14 6 7 19 16 6 7 23 12 26 , 16 1 2 3 ->= 16 1 2 4 5 6 7 8 9 10 11 , 20 22 19 23 ->= 20 25 2 10 6 9 9 10 1 5 11 , 27 13 10 11 ->= 27 13 9 10 14 15 16 14 6 4 17 , 20 22 19 ->= 23 21 10 14 14 15 20 22 19 16 15 , 16 11 12 28 ->= 16 14 6 7 19 16 6 7 23 12 28 , 16 1 2 7 ->= 16 1 2 4 5 6 7 8 9 10 15 , 19 23 21 ->= 16 1 25 5 14 1 25 2 9 10 6 , 16 11 12 13 ->= 16 14 6 7 19 16 6 7 23 12 13 , 16 1 2 9 ->= 16 1 2 4 5 6 7 8 9 10 6 , 19 19 20 17 21 ->= 19 20 2 10 14 1 22 19 23 24 21 , 16 11 12 29 ->= 16 14 6 7 19 16 6 7 23 12 29 , 16 1 2 4 ->= 16 1 2 4 5 6 7 8 9 10 1 , 16 11 12 30 ->= 16 14 6 7 19 16 6 7 23 12 30 , 20 22 16 ->= 23 21 10 14 14 15 20 22 19 16 14 , 16 11 12 31 ->= 16 14 6 7 19 16 6 7 23 12 31 , 16 1 2 10 ->= 16 1 2 4 5 6 7 8 9 10 14 , 20 22 19 16 ->= 20 25 2 10 6 9 9 10 1 5 14 , 27 13 10 14 ->= 27 13 9 10 14 15 16 14 6 4 5 , 4 22 23 ->= 3 21 10 14 14 15 20 22 19 16 11 , 10 11 12 26 ->= 10 14 6 7 19 16 6 7 23 12 26 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 32 13 10 11 ->= 32 13 9 10 14 15 16 14 6 4 17 , 10 11 12 28 ->= 10 14 6 7 19 16 6 7 23 12 28 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 15 , 7 23 21 ->= 10 1 25 5 14 1 25 2 9 10 6 , 10 11 12 13 ->= 10 14 6 7 19 16 6 7 23 12 13 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 19 20 17 21 ->= 7 20 2 10 14 1 22 19 23 24 21 , 4 22 20 ->= 3 21 10 14 14 15 20 22 19 16 1 , 10 11 12 29 ->= 10 14 6 7 19 16 6 7 23 12 29 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 12 30 ->= 10 14 6 7 19 16 6 7 23 12 30 , 10 11 12 31 ->= 10 14 6 7 19 16 6 7 23 12 31 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 14 , 32 13 10 14 ->= 32 13 9 10 14 15 16 14 6 4 5 , 25 22 23 ->= 17 21 10 14 14 15 20 22 19 16 11 , 5 11 12 26 ->= 5 14 6 7 19 16 6 7 23 12 26 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 33 13 10 11 ->= 33 13 9 10 14 15 16 14 6 4 17 , 5 11 12 28 ->= 5 14 6 7 19 16 6 7 23 12 28 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 15 , 22 23 21 ->= 5 1 25 5 14 1 25 2 9 10 6 , 5 11 12 13 ->= 5 14 6 7 19 16 6 7 23 12 13 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 22 19 20 17 21 ->= 22 20 2 10 14 1 22 19 23 24 21 , 5 11 12 29 ->= 5 14 6 7 19 16 6 7 23 12 29 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 12 30 ->= 5 14 6 7 19 16 6 7 23 12 30 , 25 22 16 ->= 17 21 10 14 14 15 20 22 19 16 14 , 5 11 12 31 ->= 5 14 6 7 19 16 6 7 23 12 31 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 14 , 33 13 10 14 ->= 33 13 9 10 14 15 16 14 6 4 5 , 31 1 2 3 ->= 31 1 2 4 5 6 7 8 9 10 11 , 29 22 19 23 ->= 29 25 2 10 6 9 9 10 1 5 11 , 30 13 10 11 ->= 30 13 9 10 14 15 16 14 6 4 17 , 28 19 20 17 21 ->= 28 20 2 10 14 1 22 19 23 24 21 , 31 1 2 4 ->= 31 1 2 4 5 6 7 8 9 10 1 , 30 13 10 14 ->= 30 13 9 10 14 15 16 14 6 4 5 , 1 2 4 5 11 21 9 3 -> 1 2 4 2 4 22 20 25 22 16 11 , 15 23 24 ->= 14 1 25 5 14 1 25 2 9 10 11 , 1 22 23 ->= 11 21 10 14 14 15 20 22 19 16 11 , 14 11 12 26 ->= 14 14 6 7 19 16 6 7 23 12 26 , 14 1 2 3 ->= 14 1 2 4 5 6 7 8 9 10 11 , 1 22 19 23 ->= 1 25 2 10 6 9 9 10 1 5 11 , 34 13 10 11 ->= 34 13 9 10 14 15 16 14 6 4 17 , 15 19 20 17 24 ->= 15 20 2 10 14 1 22 19 23 24 24 , 1 2 4 5 11 21 9 7 -> 1 2 4 2 4 22 20 25 22 16 15 , 1 22 19 ->= 11 21 10 14 14 15 20 22 19 16 15 , 14 11 12 28 ->= 14 14 6 7 19 16 6 7 23 12 28 , 14 1 2 7 ->= 14 1 2 4 5 6 7 8 9 10 15 , 1 22 19 19 ->= 1 25 2 10 6 9 9 10 1 5 15 , 15 19 20 17 18 ->= 15 20 2 10 14 1 22 19 23 24 18 , 1 2 4 5 11 21 9 9 -> 1 2 4 2 4 22 20 25 22 16 6 , 15 23 21 ->= 14 1 25 5 14 1 25 2 9 10 6 , 1 22 8 ->= 11 21 10 14 14 15 20 22 19 16 6 , 14 11 12 13 ->= 14 14 6 7 19 16 6 7 23 12 13 , 14 1 2 9 ->= 14 1 2 4 5 6 7 8 9 10 6 , 1 22 19 8 ->= 1 25 2 10 6 9 9 10 1 5 6 , 15 19 20 17 21 ->= 15 20 2 10 14 1 22 19 23 24 21 , 1 2 4 5 11 21 9 4 -> 1 2 4 2 4 22 20 25 22 16 1 , 1 22 20 ->= 11 21 10 14 14 15 20 22 19 16 1 , 14 11 12 29 ->= 14 14 6 7 19 16 6 7 23 12 29 , 14 1 2 4 ->= 14 1 2 4 5 6 7 8 9 10 1 , 1 22 19 20 ->= 1 25 2 10 6 9 9 10 1 5 1 , 15 19 20 17 35 ->= 15 20 2 10 14 1 22 19 23 24 35 , 14 11 12 30 ->= 14 14 6 7 19 16 6 7 23 12 30 , 15 19 20 17 12 ->= 15 20 2 10 14 1 22 19 23 24 12 , 1 2 4 5 11 21 9 10 -> 1 2 4 2 4 22 20 25 22 16 14 , 1 22 16 ->= 11 21 10 14 14 15 20 22 19 16 14 , 14 11 12 31 ->= 14 14 6 7 19 16 6 7 23 12 31 , 14 1 2 10 ->= 14 1 2 4 5 6 7 8 9 10 14 , 1 22 19 16 ->= 1 25 2 10 6 9 9 10 1 5 14 , 34 13 10 14 ->= 34 13 9 10 14 15 16 14 6 4 5 , 15 19 20 17 0 ->= 15 20 2 10 14 1 22 19 23 24 0 } 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 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 1 1 | | 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 0 | | 0 0 0 0 0 | \ / 22 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 | \ / 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 101-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 10 11 ->= 12 13 9 10 14 15 16 14 6 4 17 , 18 19 20 17 21 ->= 18 20 2 10 14 1 22 19 23 24 21 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 12 13 10 14 ->= 12 13 9 10 14 15 16 14 6 4 5 , 19 23 24 ->= 16 1 25 5 14 1 25 2 9 10 11 , 20 22 23 ->= 23 21 10 14 14 15 20 22 19 16 11 , 16 11 12 26 ->= 16 14 6 7 19 16 6 7 23 12 26 , 16 1 2 3 ->= 16 1 2 4 5 6 7 8 9 10 11 , 27 13 10 11 ->= 27 13 9 10 14 15 16 14 6 4 17 , 20 22 19 ->= 23 21 10 14 14 15 20 22 19 16 15 , 16 11 12 28 ->= 16 14 6 7 19 16 6 7 23 12 28 , 16 1 2 7 ->= 16 1 2 4 5 6 7 8 9 10 15 , 19 23 21 ->= 16 1 25 5 14 1 25 2 9 10 6 , 16 11 12 13 ->= 16 14 6 7 19 16 6 7 23 12 13 , 16 1 2 9 ->= 16 1 2 4 5 6 7 8 9 10 6 , 19 19 20 17 21 ->= 19 20 2 10 14 1 22 19 23 24 21 , 16 11 12 29 ->= 16 14 6 7 19 16 6 7 23 12 29 , 16 1 2 4 ->= 16 1 2 4 5 6 7 8 9 10 1 , 16 11 12 30 ->= 16 14 6 7 19 16 6 7 23 12 30 , 20 22 16 ->= 23 21 10 14 14 15 20 22 19 16 14 , 16 11 12 31 ->= 16 14 6 7 19 16 6 7 23 12 31 , 16 1 2 10 ->= 16 1 2 4 5 6 7 8 9 10 14 , 20 22 19 16 ->= 20 25 2 10 6 9 9 10 1 5 14 , 27 13 10 14 ->= 27 13 9 10 14 15 16 14 6 4 5 , 4 22 23 ->= 3 21 10 14 14 15 20 22 19 16 11 , 10 11 12 26 ->= 10 14 6 7 19 16 6 7 23 12 26 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 32 13 10 11 ->= 32 13 9 10 14 15 16 14 6 4 17 , 10 11 12 28 ->= 10 14 6 7 19 16 6 7 23 12 28 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 15 , 7 23 21 ->= 10 1 25 5 14 1 25 2 9 10 6 , 10 11 12 13 ->= 10 14 6 7 19 16 6 7 23 12 13 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 7 19 20 17 21 ->= 7 20 2 10 14 1 22 19 23 24 21 , 4 22 20 ->= 3 21 10 14 14 15 20 22 19 16 1 , 10 11 12 29 ->= 10 14 6 7 19 16 6 7 23 12 29 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 12 30 ->= 10 14 6 7 19 16 6 7 23 12 30 , 10 11 12 31 ->= 10 14 6 7 19 16 6 7 23 12 31 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 14 , 32 13 10 14 ->= 32 13 9 10 14 15 16 14 6 4 5 , 25 22 23 ->= 17 21 10 14 14 15 20 22 19 16 11 , 5 11 12 26 ->= 5 14 6 7 19 16 6 7 23 12 26 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 33 13 10 11 ->= 33 13 9 10 14 15 16 14 6 4 17 , 5 11 12 28 ->= 5 14 6 7 19 16 6 7 23 12 28 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 15 , 22 23 21 ->= 5 1 25 5 14 1 25 2 9 10 6 , 5 11 12 13 ->= 5 14 6 7 19 16 6 7 23 12 13 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 22 19 20 17 21 ->= 22 20 2 10 14 1 22 19 23 24 21 , 5 11 12 29 ->= 5 14 6 7 19 16 6 7 23 12 29 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 12 30 ->= 5 14 6 7 19 16 6 7 23 12 30 , 25 22 16 ->= 17 21 10 14 14 15 20 22 19 16 14 , 5 11 12 31 ->= 5 14 6 7 19 16 6 7 23 12 31 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 14 , 33 13 10 14 ->= 33 13 9 10 14 15 16 14 6 4 5 , 31 1 2 3 ->= 31 1 2 4 5 6 7 8 9 10 11 , 29 22 19 23 ->= 29 25 2 10 6 9 9 10 1 5 11 , 30 13 10 11 ->= 30 13 9 10 14 15 16 14 6 4 17 , 28 19 20 17 21 ->= 28 20 2 10 14 1 22 19 23 24 21 , 31 1 2 4 ->= 31 1 2 4 5 6 7 8 9 10 1 , 30 13 10 14 ->= 30 13 9 10 14 15 16 14 6 4 5 , 1 2 4 5 11 21 9 3 -> 1 2 4 2 4 22 20 25 22 16 11 , 15 23 24 ->= 14 1 25 5 14 1 25 2 9 10 11 , 1 22 23 ->= 11 21 10 14 14 15 20 22 19 16 11 , 14 11 12 26 ->= 14 14 6 7 19 16 6 7 23 12 26 , 14 1 2 3 ->= 14 1 2 4 5 6 7 8 9 10 11 , 1 22 19 23 ->= 1 25 2 10 6 9 9 10 1 5 11 , 34 13 10 11 ->= 34 13 9 10 14 15 16 14 6 4 17 , 15 19 20 17 24 ->= 15 20 2 10 14 1 22 19 23 24 24 , 1 2 4 5 11 21 9 7 -> 1 2 4 2 4 22 20 25 22 16 15 , 1 22 19 ->= 11 21 10 14 14 15 20 22 19 16 15 , 14 11 12 28 ->= 14 14 6 7 19 16 6 7 23 12 28 , 14 1 2 7 ->= 14 1 2 4 5 6 7 8 9 10 15 , 1 22 19 19 ->= 1 25 2 10 6 9 9 10 1 5 15 , 15 19 20 17 18 ->= 15 20 2 10 14 1 22 19 23 24 18 , 1 2 4 5 11 21 9 9 -> 1 2 4 2 4 22 20 25 22 16 6 , 15 23 21 ->= 14 1 25 5 14 1 25 2 9 10 6 , 1 22 8 ->= 11 21 10 14 14 15 20 22 19 16 6 , 14 11 12 13 ->= 14 14 6 7 19 16 6 7 23 12 13 , 14 1 2 9 ->= 14 1 2 4 5 6 7 8 9 10 6 , 1 22 19 8 ->= 1 25 2 10 6 9 9 10 1 5 6 , 15 19 20 17 21 ->= 15 20 2 10 14 1 22 19 23 24 21 , 1 2 4 5 11 21 9 4 -> 1 2 4 2 4 22 20 25 22 16 1 , 1 22 20 ->= 11 21 10 14 14 15 20 22 19 16 1 , 14 11 12 29 ->= 14 14 6 7 19 16 6 7 23 12 29 , 14 1 2 4 ->= 14 1 2 4 5 6 7 8 9 10 1 , 1 22 19 20 ->= 1 25 2 10 6 9 9 10 1 5 1 , 15 19 20 17 35 ->= 15 20 2 10 14 1 22 19 23 24 35 , 14 11 12 30 ->= 14 14 6 7 19 16 6 7 23 12 30 , 15 19 20 17 12 ->= 15 20 2 10 14 1 22 19 23 24 12 , 1 2 4 5 11 21 9 10 -> 1 2 4 2 4 22 20 25 22 16 14 , 1 22 16 ->= 11 21 10 14 14 15 20 22 19 16 14 , 14 11 12 31 ->= 14 14 6 7 19 16 6 7 23 12 31 , 14 1 2 10 ->= 14 1 2 4 5 6 7 8 9 10 14 , 1 22 19 16 ->= 1 25 2 10 6 9 9 10 1 5 14 , 34 13 10 14 ->= 34 13 9 10 14 15 16 14 6 4 5 , 15 19 20 17 0 ->= 15 20 2 10 14 1 22 19 23 24 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 100-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 10 11 ->= 12 13 9 10 14 15 16 14 6 4 17 , 18 19 20 17 21 ->= 18 20 2 10 14 1 22 19 23 24 21 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 12 13 10 14 ->= 12 13 9 10 14 15 16 14 6 4 5 , 19 23 24 ->= 16 1 25 5 14 1 25 2 9 10 11 , 20 22 23 ->= 23 21 10 14 14 15 20 22 19 16 11 , 16 11 12 26 ->= 16 14 6 7 19 16 6 7 23 12 26 , 16 1 2 3 ->= 16 1 2 4 5 6 7 8 9 10 11 , 27 13 10 11 ->= 27 13 9 10 14 15 16 14 6 4 17 , 20 22 19 ->= 23 21 10 14 14 15 20 22 19 16 15 , 16 11 12 28 ->= 16 14 6 7 19 16 6 7 23 12 28 , 16 1 2 7 ->= 16 1 2 4 5 6 7 8 9 10 15 , 19 23 21 ->= 16 1 25 5 14 1 25 2 9 10 6 , 16 11 12 13 ->= 16 14 6 7 19 16 6 7 23 12 13 , 16 1 2 9 ->= 16 1 2 4 5 6 7 8 9 10 6 , 19 19 20 17 21 ->= 19 20 2 10 14 1 22 19 23 24 21 , 16 11 12 29 ->= 16 14 6 7 19 16 6 7 23 12 29 , 16 1 2 4 ->= 16 1 2 4 5 6 7 8 9 10 1 , 16 11 12 30 ->= 16 14 6 7 19 16 6 7 23 12 30 , 20 22 16 ->= 23 21 10 14 14 15 20 22 19 16 14 , 16 11 12 31 ->= 16 14 6 7 19 16 6 7 23 12 31 , 16 1 2 10 ->= 16 1 2 4 5 6 7 8 9 10 14 , 20 22 19 16 ->= 20 25 2 10 6 9 9 10 1 5 14 , 27 13 10 14 ->= 27 13 9 10 14 15 16 14 6 4 5 , 4 22 23 ->= 3 21 10 14 14 15 20 22 19 16 11 , 10 11 12 26 ->= 10 14 6 7 19 16 6 7 23 12 26 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 32 13 10 11 ->= 32 13 9 10 14 15 16 14 6 4 17 , 10 11 12 28 ->= 10 14 6 7 19 16 6 7 23 12 28 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 15 , 7 23 21 ->= 10 1 25 5 14 1 25 2 9 10 6 , 10 11 12 13 ->= 10 14 6 7 19 16 6 7 23 12 13 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 4 22 20 ->= 3 21 10 14 14 15 20 22 19 16 1 , 10 11 12 29 ->= 10 14 6 7 19 16 6 7 23 12 29 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 12 30 ->= 10 14 6 7 19 16 6 7 23 12 30 , 10 11 12 31 ->= 10 14 6 7 19 16 6 7 23 12 31 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 14 , 32 13 10 14 ->= 32 13 9 10 14 15 16 14 6 4 5 , 25 22 23 ->= 17 21 10 14 14 15 20 22 19 16 11 , 5 11 12 26 ->= 5 14 6 7 19 16 6 7 23 12 26 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 33 13 10 11 ->= 33 13 9 10 14 15 16 14 6 4 17 , 5 11 12 28 ->= 5 14 6 7 19 16 6 7 23 12 28 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 15 , 22 23 21 ->= 5 1 25 5 14 1 25 2 9 10 6 , 5 11 12 13 ->= 5 14 6 7 19 16 6 7 23 12 13 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 22 19 20 17 21 ->= 22 20 2 10 14 1 22 19 23 24 21 , 5 11 12 29 ->= 5 14 6 7 19 16 6 7 23 12 29 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 12 30 ->= 5 14 6 7 19 16 6 7 23 12 30 , 25 22 16 ->= 17 21 10 14 14 15 20 22 19 16 14 , 5 11 12 31 ->= 5 14 6 7 19 16 6 7 23 12 31 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 14 , 33 13 10 14 ->= 33 13 9 10 14 15 16 14 6 4 5 , 31 1 2 3 ->= 31 1 2 4 5 6 7 8 9 10 11 , 29 22 19 23 ->= 29 25 2 10 6 9 9 10 1 5 11 , 30 13 10 11 ->= 30 13 9 10 14 15 16 14 6 4 17 , 28 19 20 17 21 ->= 28 20 2 10 14 1 22 19 23 24 21 , 31 1 2 4 ->= 31 1 2 4 5 6 7 8 9 10 1 , 30 13 10 14 ->= 30 13 9 10 14 15 16 14 6 4 5 , 1 2 4 5 11 21 9 3 -> 1 2 4 2 4 22 20 25 22 16 11 , 15 23 24 ->= 14 1 25 5 14 1 25 2 9 10 11 , 1 22 23 ->= 11 21 10 14 14 15 20 22 19 16 11 , 14 11 12 26 ->= 14 14 6 7 19 16 6 7 23 12 26 , 14 1 2 3 ->= 14 1 2 4 5 6 7 8 9 10 11 , 1 22 19 23 ->= 1 25 2 10 6 9 9 10 1 5 11 , 34 13 10 11 ->= 34 13 9 10 14 15 16 14 6 4 17 , 15 19 20 17 24 ->= 15 20 2 10 14 1 22 19 23 24 24 , 1 2 4 5 11 21 9 7 -> 1 2 4 2 4 22 20 25 22 16 15 , 1 22 19 ->= 11 21 10 14 14 15 20 22 19 16 15 , 14 11 12 28 ->= 14 14 6 7 19 16 6 7 23 12 28 , 14 1 2 7 ->= 14 1 2 4 5 6 7 8 9 10 15 , 1 22 19 19 ->= 1 25 2 10 6 9 9 10 1 5 15 , 15 19 20 17 18 ->= 15 20 2 10 14 1 22 19 23 24 18 , 1 2 4 5 11 21 9 9 -> 1 2 4 2 4 22 20 25 22 16 6 , 15 23 21 ->= 14 1 25 5 14 1 25 2 9 10 6 , 1 22 8 ->= 11 21 10 14 14 15 20 22 19 16 6 , 14 11 12 13 ->= 14 14 6 7 19 16 6 7 23 12 13 , 14 1 2 9 ->= 14 1 2 4 5 6 7 8 9 10 6 , 1 22 19 8 ->= 1 25 2 10 6 9 9 10 1 5 6 , 15 19 20 17 21 ->= 15 20 2 10 14 1 22 19 23 24 21 , 1 2 4 5 11 21 9 4 -> 1 2 4 2 4 22 20 25 22 16 1 , 1 22 20 ->= 11 21 10 14 14 15 20 22 19 16 1 , 14 11 12 29 ->= 14 14 6 7 19 16 6 7 23 12 29 , 14 1 2 4 ->= 14 1 2 4 5 6 7 8 9 10 1 , 1 22 19 20 ->= 1 25 2 10 6 9 9 10 1 5 1 , 15 19 20 17 35 ->= 15 20 2 10 14 1 22 19 23 24 35 , 14 11 12 30 ->= 14 14 6 7 19 16 6 7 23 12 30 , 15 19 20 17 12 ->= 15 20 2 10 14 1 22 19 23 24 12 , 1 2 4 5 11 21 9 10 -> 1 2 4 2 4 22 20 25 22 16 14 , 1 22 16 ->= 11 21 10 14 14 15 20 22 19 16 14 , 14 11 12 31 ->= 14 14 6 7 19 16 6 7 23 12 31 , 14 1 2 10 ->= 14 1 2 4 5 6 7 8 9 10 14 , 1 22 19 16 ->= 1 25 2 10 6 9 9 10 1 5 14 , 34 13 10 14 ->= 34 13 9 10 14 15 16 14 6 4 5 , 15 19 20 17 0 ->= 15 20 2 10 14 1 22 19 23 24 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 99-rule system { 0 1 2 3 ->= 0 1 2 4 5 6 7 8 9 10 11 , 12 13 10 11 ->= 12 13 9 10 14 15 16 14 6 4 17 , 18 19 20 17 21 ->= 18 20 2 10 14 1 22 19 23 24 21 , 0 1 2 4 ->= 0 1 2 4 5 6 7 8 9 10 1 , 12 13 10 14 ->= 12 13 9 10 14 15 16 14 6 4 5 , 19 23 24 ->= 16 1 25 5 14 1 25 2 9 10 11 , 20 22 23 ->= 23 21 10 14 14 15 20 22 19 16 11 , 16 11 12 26 ->= 16 14 6 7 19 16 6 7 23 12 26 , 16 1 2 3 ->= 16 1 2 4 5 6 7 8 9 10 11 , 27 13 10 11 ->= 27 13 9 10 14 15 16 14 6 4 17 , 20 22 19 ->= 23 21 10 14 14 15 20 22 19 16 15 , 16 11 12 28 ->= 16 14 6 7 19 16 6 7 23 12 28 , 16 1 2 7 ->= 16 1 2 4 5 6 7 8 9 10 15 , 19 23 21 ->= 16 1 25 5 14 1 25 2 9 10 6 , 16 11 12 13 ->= 16 14 6 7 19 16 6 7 23 12 13 , 16 1 2 9 ->= 16 1 2 4 5 6 7 8 9 10 6 , 19 19 20 17 21 ->= 19 20 2 10 14 1 22 19 23 24 21 , 16 11 12 29 ->= 16 14 6 7 19 16 6 7 23 12 29 , 16 1 2 4 ->= 16 1 2 4 5 6 7 8 9 10 1 , 16 11 12 30 ->= 16 14 6 7 19 16 6 7 23 12 30 , 20 22 16 ->= 23 21 10 14 14 15 20 22 19 16 14 , 16 11 12 31 ->= 16 14 6 7 19 16 6 7 23 12 31 , 16 1 2 10 ->= 16 1 2 4 5 6 7 8 9 10 14 , 20 22 19 16 ->= 20 25 2 10 6 9 9 10 1 5 14 , 27 13 10 14 ->= 27 13 9 10 14 15 16 14 6 4 5 , 4 22 23 ->= 3 21 10 14 14 15 20 22 19 16 11 , 10 11 12 26 ->= 10 14 6 7 19 16 6 7 23 12 26 , 10 1 2 3 ->= 10 1 2 4 5 6 7 8 9 10 11 , 32 13 10 11 ->= 32 13 9 10 14 15 16 14 6 4 17 , 10 11 12 28 ->= 10 14 6 7 19 16 6 7 23 12 28 , 10 1 2 7 ->= 10 1 2 4 5 6 7 8 9 10 15 , 7 23 21 ->= 10 1 25 5 14 1 25 2 9 10 6 , 10 11 12 13 ->= 10 14 6 7 19 16 6 7 23 12 13 , 10 1 2 9 ->= 10 1 2 4 5 6 7 8 9 10 6 , 4 22 20 ->= 3 21 10 14 14 15 20 22 19 16 1 , 10 11 12 29 ->= 10 14 6 7 19 16 6 7 23 12 29 , 10 1 2 4 ->= 10 1 2 4 5 6 7 8 9 10 1 , 10 11 12 30 ->= 10 14 6 7 19 16 6 7 23 12 30 , 10 11 12 31 ->= 10 14 6 7 19 16 6 7 23 12 31 , 10 1 2 10 ->= 10 1 2 4 5 6 7 8 9 10 14 , 32 13 10 14 ->= 32 13 9 10 14 15 16 14 6 4 5 , 25 22 23 ->= 17 21 10 14 14 15 20 22 19 16 11 , 5 11 12 26 ->= 5 14 6 7 19 16 6 7 23 12 26 , 5 1 2 3 ->= 5 1 2 4 5 6 7 8 9 10 11 , 33 13 10 11 ->= 33 13 9 10 14 15 16 14 6 4 17 , 5 11 12 28 ->= 5 14 6 7 19 16 6 7 23 12 28 , 5 1 2 7 ->= 5 1 2 4 5 6 7 8 9 10 15 , 22 23 21 ->= 5 1 25 5 14 1 25 2 9 10 6 , 5 11 12 13 ->= 5 14 6 7 19 16 6 7 23 12 13 , 5 1 2 9 ->= 5 1 2 4 5 6 7 8 9 10 6 , 5 11 12 29 ->= 5 14 6 7 19 16 6 7 23 12 29 , 5 1 2 4 ->= 5 1 2 4 5 6 7 8 9 10 1 , 5 11 12 30 ->= 5 14 6 7 19 16 6 7 23 12 30 , 25 22 16 ->= 17 21 10 14 14 15 20 22 19 16 14 , 5 11 12 31 ->= 5 14 6 7 19 16 6 7 23 12 31 , 5 1 2 10 ->= 5 1 2 4 5 6 7 8 9 10 14 , 33 13 10 14 ->= 33 13 9 10 14 15 16 14 6 4 5 , 31 1 2 3 ->= 31 1 2 4 5 6 7 8 9 10 11 , 29 22 19 23 ->= 29 25 2 10 6 9 9 10 1 5 11 , 30 13 10 11 ->= 30 13 9 10 14 15 16 14 6 4 17 , 28 19 20 17 21 ->= 28 20 2 10 14 1 22 19 23 24 21 , 31 1 2 4 ->= 31 1 2 4 5 6 7 8 9 10 1 , 30 13 10 14 ->= 30 13 9 10 14 15 16 14 6 4 5 , 1 2 4 5 11 21 9 3 -> 1 2 4 2 4 22 20 25 22 16 11 , 15 23 24 ->= 14 1 25 5 14 1 25 2 9 10 11 , 1 22 23 ->= 11 21 10 14 14 15 20 22 19 16 11 , 14 11 12 26 ->= 14 14 6 7 19 16 6 7 23 12 26 , 14 1 2 3 ->= 14 1 2 4 5 6 7 8 9 10 11 , 1 22 19 23 ->= 1 25 2 10 6 9 9 10 1 5 11 , 34 13 10 11 ->= 34 13 9 10 14 15 16 14 6 4 17 , 15 19 20 17 24 ->= 15 20 2 10 14 1 22 19 23 24 24 , 1 2 4 5 11 21 9 7 -> 1 2 4 2 4 22 20 25 22 16 15 , 1 22 19 ->= 11 21 10 14 14 15 20 22 19 16 15 , 14 11 12 28 ->= 14 14 6 7 19 16 6 7 23 12 28 , 14 1 2 7 ->= 14 1 2 4 5 6 7 8 9 10 15 , 1 22 19 19 ->= 1 25 2 10 6 9 9 10 1 5 15 , 15 19 20 17 18 ->= 15 20 2 10 14 1 22 19 23 24 18 , 1 2 4 5 11 21 9 9 -> 1 2 4 2 4 22 20 25 22 16 6 , 15 23 21 ->= 14 1 25 5 14 1 25 2 9 10 6 , 1 22 8 ->= 11 21 10 14 14 15 20 22 19 16 6 , 14 11 12 13 ->= 14 14 6 7 19 16 6 7 23 12 13 , 14 1 2 9 ->= 14 1 2 4 5 6 7 8 9 10 6 , 1 22 19 8 ->= 1 25 2 10 6 9 9 10 1 5 6 , 15 19 20 17 21 ->= 15 20 2 10 14 1 22 19 23 24 21 , 1 2 4 5 11 21 9 4 -> 1 2 4 2 4 22 20 25 22 16 1 , 1 22 20 ->= 11 21 10 14 14 15 20 22 19 16 1 , 14 11 12 29 ->= 14 14 6 7 19 16 6 7 23 12 29 , 14 1 2 4 ->= 14 1 2 4 5 6 7 8 9 10 1 , 1 22 19 20 ->= 1 25 2 10 6 9 9 10 1 5 1 , 15 19 20 17 35 ->= 15 20 2 10 14 1 22 19 23 24 35 , 14 11 12 30 ->= 14 14 6 7 19 16 6 7 23 12 30 , 15 19 20 17 12 ->= 15 20 2 10 14 1 22 19 23 24 12 , 1 2 4 5 11 21 9 10 -> 1 2 4 2 4 22 20 25 22 16 14 , 1 22 16 ->= 11 21 10 14 14 15 20 22 19 16 14 , 14 11 12 31 ->= 14 14 6 7 19 16 6 7 23 12 31 , 14 1 2 10 ->= 14 1 2 4 5 6 7 8 9 10 14 , 1 22 19 16 ->= 1 25 2 10 6 9 9 10 1 5 14 , 34 13 10 14 ->= 34 13 9 10 14 15 16 14 6 4 5 , 15 19 20 17 0 ->= 15 20 2 10 14 1 22 19 23 24 0 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 12->0, 13->1, 10->2, 11->3, 9->4, 14->5, 15->6, 16->7, 6->8, 4->9, 17->10, 18->11, 19->12, 20->13, 21->14, 2->15, 1->16, 22->17, 23->18, 24->19, 0->20, 5->21, 7->22, 8->23, 25->24, 26->25, 3->26, 27->27, 28->28, 29->29, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 98-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 10 14 ->= 11 13 15 2 5 16 17 12 18 19 14 , 20 16 15 9 ->= 20 16 15 9 21 8 22 23 4 2 16 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 21 , 12 18 19 ->= 7 16 24 21 5 16 24 15 4 2 3 , 13 17 18 ->= 18 14 2 5 5 6 13 17 12 7 3 , 7 3 0 25 ->= 7 5 8 22 12 7 8 22 18 0 25 , 7 16 15 26 ->= 7 16 15 9 21 8 22 23 4 2 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 13 17 12 ->= 18 14 2 5 5 6 13 17 12 7 6 , 7 3 0 28 ->= 7 5 8 22 12 7 8 22 18 0 28 , 7 16 15 22 ->= 7 16 15 9 21 8 22 23 4 2 6 , 12 18 14 ->= 7 16 24 21 5 16 24 15 4 2 8 , 7 3 0 1 ->= 7 5 8 22 12 7 8 22 18 0 1 , 7 16 15 4 ->= 7 16 15 9 21 8 22 23 4 2 8 , 12 12 13 10 14 ->= 12 13 15 2 5 16 17 12 18 19 14 , 7 3 0 29 ->= 7 5 8 22 12 7 8 22 18 0 29 , 7 16 15 9 ->= 7 16 15 9 21 8 22 23 4 2 16 , 7 3 0 30 ->= 7 5 8 22 12 7 8 22 18 0 30 , 13 17 7 ->= 18 14 2 5 5 6 13 17 12 7 5 , 7 3 0 31 ->= 7 5 8 22 12 7 8 22 18 0 31 , 7 16 15 2 ->= 7 16 15 9 21 8 22 23 4 2 5 , 13 17 12 7 ->= 13 24 15 2 8 4 4 2 16 21 5 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 21 , 9 17 18 ->= 26 14 2 5 5 6 13 17 12 7 3 , 2 3 0 25 ->= 2 5 8 22 12 7 8 22 18 0 25 , 2 16 15 26 ->= 2 16 15 9 21 8 22 23 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 2 3 0 28 ->= 2 5 8 22 12 7 8 22 18 0 28 , 2 16 15 22 ->= 2 16 15 9 21 8 22 23 4 2 6 , 22 18 14 ->= 2 16 24 21 5 16 24 15 4 2 8 , 2 3 0 1 ->= 2 5 8 22 12 7 8 22 18 0 1 , 2 16 15 4 ->= 2 16 15 9 21 8 22 23 4 2 8 , 9 17 13 ->= 26 14 2 5 5 6 13 17 12 7 16 , 2 3 0 29 ->= 2 5 8 22 12 7 8 22 18 0 29 , 2 16 15 9 ->= 2 16 15 9 21 8 22 23 4 2 16 , 2 3 0 30 ->= 2 5 8 22 12 7 8 22 18 0 30 , 2 3 0 31 ->= 2 5 8 22 12 7 8 22 18 0 31 , 2 16 15 2 ->= 2 16 15 9 21 8 22 23 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 21 , 24 17 18 ->= 10 14 2 5 5 6 13 17 12 7 3 , 21 3 0 25 ->= 21 5 8 22 12 7 8 22 18 0 25 , 21 16 15 26 ->= 21 16 15 9 21 8 22 23 4 2 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 21 3 0 28 ->= 21 5 8 22 12 7 8 22 18 0 28 , 21 16 15 22 ->= 21 16 15 9 21 8 22 23 4 2 6 , 17 18 14 ->= 21 16 24 21 5 16 24 15 4 2 8 , 21 3 0 1 ->= 21 5 8 22 12 7 8 22 18 0 1 , 21 16 15 4 ->= 21 16 15 9 21 8 22 23 4 2 8 , 21 3 0 29 ->= 21 5 8 22 12 7 8 22 18 0 29 , 21 16 15 9 ->= 21 16 15 9 21 8 22 23 4 2 16 , 21 3 0 30 ->= 21 5 8 22 12 7 8 22 18 0 30 , 24 17 7 ->= 10 14 2 5 5 6 13 17 12 7 5 , 21 3 0 31 ->= 21 5 8 22 12 7 8 22 18 0 31 , 21 16 15 2 ->= 21 16 15 9 21 8 22 23 4 2 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 21 , 31 16 15 26 ->= 31 16 15 9 21 8 22 23 4 2 3 , 29 17 12 18 ->= 29 24 15 2 8 4 4 2 16 21 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 28 12 13 10 14 ->= 28 13 15 2 5 16 17 12 18 19 14 , 31 16 15 9 ->= 31 16 15 9 21 8 22 23 4 2 16 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 21 , 16 15 9 21 3 14 4 26 -> 16 15 9 15 9 17 13 24 17 7 3 , 6 18 19 ->= 5 16 24 21 5 16 24 15 4 2 3 , 16 17 18 ->= 3 14 2 5 5 6 13 17 12 7 3 , 5 3 0 25 ->= 5 5 8 22 12 7 8 22 18 0 25 , 5 16 15 26 ->= 5 16 15 9 21 8 22 23 4 2 3 , 16 17 12 18 ->= 16 24 15 2 8 4 4 2 16 21 3 , 34 1 2 3 ->= 34 1 4 2 5 6 7 5 8 9 10 , 6 12 13 10 19 ->= 6 13 15 2 5 16 17 12 18 19 19 , 16 15 9 21 3 14 4 22 -> 16 15 9 15 9 17 13 24 17 7 6 , 16 17 12 ->= 3 14 2 5 5 6 13 17 12 7 6 , 5 3 0 28 ->= 5 5 8 22 12 7 8 22 18 0 28 , 5 16 15 22 ->= 5 16 15 9 21 8 22 23 4 2 6 , 16 17 12 12 ->= 16 24 15 2 8 4 4 2 16 21 6 , 6 12 13 10 11 ->= 6 13 15 2 5 16 17 12 18 19 11 , 16 15 9 21 3 14 4 4 -> 16 15 9 15 9 17 13 24 17 7 8 , 6 18 14 ->= 5 16 24 21 5 16 24 15 4 2 8 , 16 17 23 ->= 3 14 2 5 5 6 13 17 12 7 8 , 5 3 0 1 ->= 5 5 8 22 12 7 8 22 18 0 1 , 5 16 15 4 ->= 5 16 15 9 21 8 22 23 4 2 8 , 16 17 12 23 ->= 16 24 15 2 8 4 4 2 16 21 8 , 6 12 13 10 14 ->= 6 13 15 2 5 16 17 12 18 19 14 , 16 15 9 21 3 14 4 9 -> 16 15 9 15 9 17 13 24 17 7 16 , 16 17 13 ->= 3 14 2 5 5 6 13 17 12 7 16 , 5 3 0 29 ->= 5 5 8 22 12 7 8 22 18 0 29 , 5 16 15 9 ->= 5 16 15 9 21 8 22 23 4 2 16 , 16 17 12 13 ->= 16 24 15 2 8 4 4 2 16 21 16 , 6 12 13 10 35 ->= 6 13 15 2 5 16 17 12 18 19 35 , 5 3 0 30 ->= 5 5 8 22 12 7 8 22 18 0 30 , 6 12 13 10 0 ->= 6 13 15 2 5 16 17 12 18 19 0 , 16 15 9 21 3 14 4 2 -> 16 15 9 15 9 17 13 24 17 7 5 , 16 17 7 ->= 3 14 2 5 5 6 13 17 12 7 5 , 5 3 0 31 ->= 5 5 8 22 12 7 8 22 18 0 31 , 5 16 15 2 ->= 5 16 15 9 21 8 22 23 4 2 5 , 16 17 12 7 ->= 16 24 15 2 8 4 4 2 16 21 5 , 34 1 2 5 ->= 34 1 4 2 5 6 7 5 8 9 21 , 6 12 13 10 20 ->= 6 13 15 2 5 16 17 12 18 19 20 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 20->11, 16->12, 15->13, 21->14, 22->15, 23->16, 12->17, 18->18, 19->19, 24->20, 13->21, 17->22, 14->23, 25->24, 26->25, 27->26, 28->27, 29->28, 30->29, 31->30, 32->31, 33->32, 34->33, 11->34, 35->35 }, it remains to prove termination of the 97-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 7 12 13 15 ->= 7 12 13 9 14 8 15 16 4 2 6 , 17 18 23 ->= 7 12 20 14 5 12 20 13 4 2 8 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 17 17 21 10 23 ->= 17 21 13 2 5 12 22 17 18 19 23 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 30 12 13 25 ->= 30 12 13 9 14 8 15 16 4 2 3 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 27 17 21 10 23 ->= 27 21 13 2 5 12 22 17 18 19 23 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 6 17 21 10 19 ->= 6 21 13 2 5 12 22 17 18 19 19 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 6 17 21 10 34 ->= 6 21 13 2 5 12 22 17 18 19 34 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 6 17 21 10 23 ->= 6 21 13 2 5 12 22 17 18 19 23 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 12 22 17 21 ->= 12 20 13 2 8 4 4 2 12 14 12 , 6 17 21 10 35 ->= 6 21 13 2 5 12 22 17 18 19 35 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 6 17 21 10 0 ->= 6 21 13 2 5 12 22 17 18 19 0 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 , 6 17 21 10 11 ->= 6 21 13 2 5 12 22 17 18 19 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 96-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 7 12 13 15 ->= 7 12 13 9 14 8 15 16 4 2 6 , 17 18 23 ->= 7 12 20 14 5 12 20 13 4 2 8 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 30 12 13 25 ->= 30 12 13 9 14 8 15 16 4 2 3 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 27 17 21 10 23 ->= 27 21 13 2 5 12 22 17 18 19 23 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 6 17 21 10 19 ->= 6 21 13 2 5 12 22 17 18 19 19 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 6 17 21 10 34 ->= 6 21 13 2 5 12 22 17 18 19 34 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 6 17 21 10 23 ->= 6 21 13 2 5 12 22 17 18 19 23 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 12 22 17 21 ->= 12 20 13 2 8 4 4 2 12 14 12 , 6 17 21 10 35 ->= 6 21 13 2 5 12 22 17 18 19 35 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 6 17 21 10 0 ->= 6 21 13 2 5 12 22 17 18 19 0 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 , 6 17 21 10 11 ->= 6 21 13 2 5 12 22 17 18 19 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 95-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 7 12 13 15 ->= 7 12 13 9 14 8 15 16 4 2 6 , 17 18 23 ->= 7 12 20 14 5 12 20 13 4 2 8 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 27 17 21 10 23 ->= 27 21 13 2 5 12 22 17 18 19 23 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 6 17 21 10 19 ->= 6 21 13 2 5 12 22 17 18 19 19 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 6 17 21 10 34 ->= 6 21 13 2 5 12 22 17 18 19 34 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 6 17 21 10 23 ->= 6 21 13 2 5 12 22 17 18 19 23 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 12 22 17 21 ->= 12 20 13 2 8 4 4 2 12 14 12 , 6 17 21 10 35 ->= 6 21 13 2 5 12 22 17 18 19 35 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 6 17 21 10 0 ->= 6 21 13 2 5 12 22 17 18 19 0 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 , 6 17 21 10 11 ->= 6 21 13 2 5 12 22 17 18 19 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 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 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 94-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 7 12 13 15 ->= 7 12 13 9 14 8 15 16 4 2 6 , 17 18 23 ->= 7 12 20 14 5 12 20 13 4 2 8 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 6 17 21 10 19 ->= 6 21 13 2 5 12 22 17 18 19 19 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 6 17 21 10 34 ->= 6 21 13 2 5 12 22 17 18 19 34 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 6 17 21 10 23 ->= 6 21 13 2 5 12 22 17 18 19 23 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 12 22 17 21 ->= 12 20 13 2 8 4 4 2 12 14 12 , 6 17 21 10 35 ->= 6 21 13 2 5 12 22 17 18 19 35 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 6 17 21 10 0 ->= 6 21 13 2 5 12 22 17 18 19 0 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 , 6 17 21 10 11 ->= 6 21 13 2 5 12 22 17 18 19 11 } 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 1 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 1 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 1 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 1 | | 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 35 is interpreted by / \ | 1 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, 30->30, 31->31, 32->32, 33->33, 34->34, 35->35 }, it remains to prove termination of the 93-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 17 18 23 ->= 7 12 20 14 5 12 20 13 4 2 8 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 6 17 21 10 19 ->= 6 21 13 2 5 12 22 17 18 19 19 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 6 17 21 10 34 ->= 6 21 13 2 5 12 22 17 18 19 34 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 6 17 21 10 23 ->= 6 21 13 2 5 12 22 17 18 19 23 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 12 22 17 21 ->= 12 20 13 2 8 4 4 2 12 14 12 , 6 17 21 10 35 ->= 6 21 13 2 5 12 22 17 18 19 35 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 6 17 21 10 0 ->= 6 21 13 2 5 12 22 17 18 19 0 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 , 6 17 21 10 11 ->= 6 21 13 2 5 12 22 17 18 19 11 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 33 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 34 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 35 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32, 33->33 }, it remains to prove termination of the 85-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 7 12 20 14 5 12 20 13 4 2 3 , 21 22 18 ->= 18 23 2 5 5 6 21 22 17 7 3 , 7 3 0 24 ->= 7 5 8 15 17 7 8 15 18 0 24 , 7 12 13 25 ->= 7 12 13 9 14 8 15 16 4 2 3 , 26 1 2 3 ->= 26 1 4 2 5 6 7 5 8 9 10 , 21 22 17 ->= 18 23 2 5 5 6 21 22 17 7 6 , 7 3 0 27 ->= 7 5 8 15 17 7 8 15 18 0 27 , 7 3 0 1 ->= 7 5 8 15 17 7 8 15 18 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 28 ->= 7 5 8 15 17 7 8 15 18 0 28 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 29 ->= 7 5 8 15 17 7 8 15 18 0 29 , 21 22 7 ->= 18 23 2 5 5 6 21 22 17 7 5 , 7 3 0 30 ->= 7 5 8 15 17 7 8 15 18 0 30 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 21 22 17 7 ->= 21 20 13 2 8 4 4 2 12 14 5 , 26 1 2 5 ->= 26 1 4 2 5 6 7 5 8 9 14 , 9 22 18 ->= 25 23 2 5 5 6 21 22 17 7 3 , 2 3 0 24 ->= 2 5 8 15 17 7 8 15 18 0 24 , 2 12 13 25 ->= 2 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 2 3 0 27 ->= 2 5 8 15 17 7 8 15 18 0 27 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 18 23 ->= 2 12 20 14 5 12 20 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 17 7 8 15 18 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 22 21 ->= 25 23 2 5 5 6 21 22 17 7 12 , 2 3 0 28 ->= 2 5 8 15 17 7 8 15 18 0 28 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 29 ->= 2 5 8 15 17 7 8 15 18 0 29 , 2 3 0 30 ->= 2 5 8 15 17 7 8 15 18 0 30 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 20 22 18 ->= 10 23 2 5 5 6 21 22 17 7 3 , 14 3 0 24 ->= 14 5 8 15 17 7 8 15 18 0 24 , 14 12 13 25 ->= 14 12 13 9 14 8 15 16 4 2 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 14 3 0 27 ->= 14 5 8 15 17 7 8 15 18 0 27 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 22 18 23 ->= 14 12 20 14 5 12 20 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 17 7 8 15 18 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 28 ->= 14 5 8 15 17 7 8 15 18 0 28 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 29 ->= 14 5 8 15 17 7 8 15 18 0 29 , 20 22 7 ->= 10 23 2 5 5 6 21 22 17 7 5 , 14 3 0 30 ->= 14 5 8 15 17 7 8 15 18 0 30 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 , 28 22 17 18 ->= 28 20 13 2 8 4 4 2 12 14 3 , 29 1 2 3 ->= 29 1 4 2 5 6 7 5 8 9 10 , 30 12 13 9 ->= 30 12 13 9 14 8 15 16 4 2 12 , 29 1 2 5 ->= 29 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 23 4 25 -> 12 13 9 13 9 22 21 20 22 7 3 , 6 18 19 ->= 5 12 20 14 5 12 20 13 4 2 3 , 12 22 18 ->= 3 23 2 5 5 6 21 22 17 7 3 , 5 3 0 24 ->= 5 5 8 15 17 7 8 15 18 0 24 , 5 12 13 25 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 22 17 18 ->= 12 20 13 2 8 4 4 2 12 14 3 , 33 1 2 3 ->= 33 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 23 4 15 -> 12 13 9 13 9 22 21 20 22 7 6 , 12 22 17 ->= 3 23 2 5 5 6 21 22 17 7 6 , 5 3 0 27 ->= 5 5 8 15 17 7 8 15 18 0 27 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 22 17 17 ->= 12 20 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 23 4 4 -> 12 13 9 13 9 22 21 20 22 7 8 , 6 18 23 ->= 5 12 20 14 5 12 20 13 4 2 8 , 12 22 16 ->= 3 23 2 5 5 6 21 22 17 7 8 , 5 3 0 1 ->= 5 5 8 15 17 7 8 15 18 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 22 17 16 ->= 12 20 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 23 4 9 -> 12 13 9 13 9 22 21 20 22 7 12 , 12 22 21 ->= 3 23 2 5 5 6 21 22 17 7 12 , 5 3 0 28 ->= 5 5 8 15 17 7 8 15 18 0 28 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 29 ->= 5 5 8 15 17 7 8 15 18 0 29 , 12 13 9 14 3 23 4 2 -> 12 13 9 13 9 22 21 20 22 7 5 , 12 22 7 ->= 3 23 2 5 5 6 21 22 17 7 5 , 5 3 0 30 ->= 5 5 8 15 17 7 8 15 18 0 30 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 22 17 7 ->= 12 20 13 2 8 4 4 2 12 14 5 , 33 1 2 5 ->= 33 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 1 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 1 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 0 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 1 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 1 | | 0 1 | \ / 27 is interpreted by / \ | 1 1 | | 0 1 | \ / 28 is interpreted by / \ | 1 1 | | 0 1 | \ / 29 is interpreted by / \ | 1 1 | | 0 1 | \ / 30 is interpreted by / \ | 1 1 | | 0 1 | \ / 31 is interpreted by / \ | 1 1 | | 0 1 | \ / 32 is interpreted by / \ | 1 1 | | 0 1 | \ / 33 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 21->17, 22->18, 18->19, 23->20, 17->21, 24->22, 25->23, 26->24, 27->25, 28->26, 29->27, 30->28, 20->29, 31->30, 32->31, 33->32 }, it remains to prove termination of the 83-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 19 20 2 5 5 6 17 18 21 7 3 , 7 3 0 22 ->= 7 5 8 15 21 7 8 15 19 0 22 , 7 12 13 23 ->= 7 12 13 9 14 8 15 16 4 2 3 , 24 1 2 3 ->= 24 1 4 2 5 6 7 5 8 9 10 , 17 18 21 ->= 19 20 2 5 5 6 17 18 21 7 6 , 7 3 0 25 ->= 7 5 8 15 21 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 21 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 21 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 21 7 8 15 19 0 27 , 17 18 7 ->= 19 20 2 5 5 6 17 18 21 7 5 , 7 3 0 28 ->= 7 5 8 15 21 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 17 18 21 7 ->= 17 29 13 2 8 4 4 2 12 14 5 , 24 1 2 5 ->= 24 1 4 2 5 6 7 5 8 9 14 , 9 18 19 ->= 23 20 2 5 5 6 17 18 21 7 3 , 2 3 0 22 ->= 2 5 8 15 21 7 8 15 19 0 22 , 2 12 13 23 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 21 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 19 20 ->= 2 12 29 14 5 12 29 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 21 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 18 17 ->= 23 20 2 5 5 6 17 18 21 7 12 , 2 3 0 26 ->= 2 5 8 15 21 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 21 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 21 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 29 18 19 ->= 10 20 2 5 5 6 17 18 21 7 3 , 14 3 0 22 ->= 14 5 8 15 21 7 8 15 19 0 22 , 14 12 13 23 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 21 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 18 19 20 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 21 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 21 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 21 7 8 15 19 0 27 , 29 18 7 ->= 10 20 2 5 5 6 17 18 21 7 5 , 14 3 0 28 ->= 14 5 8 15 21 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 18 21 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 20 4 23 -> 12 13 9 13 9 18 17 29 18 7 3 , 12 18 19 ->= 3 20 2 5 5 6 17 18 21 7 3 , 5 3 0 22 ->= 5 5 8 15 21 7 8 15 19 0 22 , 5 12 13 23 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 18 21 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 20 4 15 -> 12 13 9 13 9 18 17 29 18 7 6 , 12 18 21 ->= 3 20 2 5 5 6 17 18 21 7 6 , 5 3 0 25 ->= 5 5 8 15 21 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 18 21 21 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 20 4 4 -> 12 13 9 13 9 18 17 29 18 7 8 , 6 19 20 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 18 16 ->= 3 20 2 5 5 6 17 18 21 7 8 , 5 3 0 1 ->= 5 5 8 15 21 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 18 21 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 20 4 9 -> 12 13 9 13 9 18 17 29 18 7 12 , 12 18 17 ->= 3 20 2 5 5 6 17 18 21 7 12 , 5 3 0 26 ->= 5 5 8 15 21 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 21 7 8 15 19 0 27 , 12 13 9 14 3 20 4 2 -> 12 13 9 13 9 18 17 29 18 7 5 , 12 18 7 ->= 3 20 2 5 5 6 17 18 21 7 5 , 5 3 0 28 ->= 5 5 8 15 21 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 18 21 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 82-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 17 18 19 ->= 19 20 2 5 5 6 17 18 21 7 3 , 7 3 0 22 ->= 7 5 8 15 21 7 8 15 19 0 22 , 7 12 13 23 ->= 7 12 13 9 14 8 15 16 4 2 3 , 24 1 2 3 ->= 24 1 4 2 5 6 7 5 8 9 10 , 17 18 21 ->= 19 20 2 5 5 6 17 18 21 7 6 , 7 3 0 25 ->= 7 5 8 15 21 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 21 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 21 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 21 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 21 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 17 18 21 7 ->= 17 29 13 2 8 4 4 2 12 14 5 , 24 1 2 5 ->= 24 1 4 2 5 6 7 5 8 9 14 , 9 18 19 ->= 23 20 2 5 5 6 17 18 21 7 3 , 2 3 0 22 ->= 2 5 8 15 21 7 8 15 19 0 22 , 2 12 13 23 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 21 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 19 20 ->= 2 12 29 14 5 12 29 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 21 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 18 17 ->= 23 20 2 5 5 6 17 18 21 7 12 , 2 3 0 26 ->= 2 5 8 15 21 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 21 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 21 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 29 18 19 ->= 10 20 2 5 5 6 17 18 21 7 3 , 14 3 0 22 ->= 14 5 8 15 21 7 8 15 19 0 22 , 14 12 13 23 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 21 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 18 19 20 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 21 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 21 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 21 7 8 15 19 0 27 , 29 18 7 ->= 10 20 2 5 5 6 17 18 21 7 5 , 14 3 0 28 ->= 14 5 8 15 21 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 18 21 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 20 4 23 -> 12 13 9 13 9 18 17 29 18 7 3 , 12 18 19 ->= 3 20 2 5 5 6 17 18 21 7 3 , 5 3 0 22 ->= 5 5 8 15 21 7 8 15 19 0 22 , 5 12 13 23 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 18 21 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 20 4 15 -> 12 13 9 13 9 18 17 29 18 7 6 , 12 18 21 ->= 3 20 2 5 5 6 17 18 21 7 6 , 5 3 0 25 ->= 5 5 8 15 21 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 18 21 21 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 20 4 4 -> 12 13 9 13 9 18 17 29 18 7 8 , 6 19 20 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 18 16 ->= 3 20 2 5 5 6 17 18 21 7 8 , 5 3 0 1 ->= 5 5 8 15 21 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 18 21 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 20 4 9 -> 12 13 9 13 9 18 17 29 18 7 12 , 12 18 17 ->= 3 20 2 5 5 6 17 18 21 7 12 , 5 3 0 26 ->= 5 5 8 15 21 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 21 7 8 15 19 0 27 , 12 13 9 14 3 20 4 2 -> 12 13 9 13 9 18 17 29 18 7 5 , 12 18 7 ->= 3 20 2 5 5 6 17 18 21 7 5 , 5 3 0 28 ->= 5 5 8 15 21 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 18 21 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 22->17, 21->18, 19->19, 23->20, 24->21, 17->22, 18->23, 20->24, 25->25, 26->26, 27->27, 28->28, 29->29, 30->30, 31->31, 32->32 }, it remains to prove termination of the 81-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 9 23 19 ->= 20 24 2 5 5 6 22 23 18 7 3 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 19 24 ->= 2 12 29 14 5 12 29 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 29 23 19 ->= 10 24 2 5 5 6 22 23 18 7 3 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 23 19 24 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 23 18 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 80-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 15 19 24 ->= 2 12 29 14 5 12 29 13 4 2 8 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 29 23 19 ->= 10 24 2 5 5 6 22 23 18 7 3 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 23 19 24 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 23 18 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 1 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 79-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 29 23 19 ->= 10 24 2 5 5 6 22 23 18 7 3 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 23 19 24 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 23 18 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 78-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 23 19 24 ->= 14 12 29 14 5 12 29 13 4 2 8 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 23 18 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 6: 0 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 1 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 1 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 1 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 1 | | 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 | | 0 1 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | | 0 0 0 0 0 0 | \ / 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 77-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 26 23 18 19 ->= 26 29 13 2 8 4 4 2 12 14 3 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 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 1 | | 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 1 0 0 0 | \ / 23 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 | \ / 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 76-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 12 13 4 ->= 7 12 13 9 14 8 15 16 4 2 8 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 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 1 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 1 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 1 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 1 | | 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 75-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 7 12 13 2 ->= 7 12 13 9 14 8 15 16 4 2 5 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 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 1 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 1 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 1 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 1 | | 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 74-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 3 0 25 ->= 2 5 8 15 18 7 8 15 19 0 25 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 | | 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 1 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 1 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 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 1 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 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 | \ / 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 73-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 3 0 1 ->= 2 5 8 15 18 7 8 15 19 0 1 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 | | 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 1 0 0 0 | \ / 2 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 | \ / 3 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 | \ / 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 72-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 3 0 26 ->= 2 5 8 15 18 7 8 15 19 0 26 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 | | 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 1 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 1 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 71-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 27 ->= 2 5 8 15 18 7 8 15 19 0 27 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 | | 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 1 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 1 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 70-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 31 1 2 5 ->= 31 1 4 2 5 6 7 5 8 9 14 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 69-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 27 1 2 5 ->= 27 1 4 2 5 6 7 5 8 9 14 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 68-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 30 1 2 5 ->= 30 1 4 2 5 6 7 5 8 9 14 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 67-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 14 12 13 2 ->= 14 12 13 9 14 8 15 16 4 2 5 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 66-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 0 1 2 5 ->= 0 1 4 2 5 6 7 5 8 9 14 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 65-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 12 13 15 ->= 14 12 13 9 14 8 15 16 4 2 6 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 64-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 12 13 4 ->= 14 12 13 9 14 8 15 16 4 2 8 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 63-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 21 1 2 5 ->= 21 1 4 2 5 6 7 5 8 9 14 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 62-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 12 13 20 ->= 14 12 13 9 14 8 15 16 4 2 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 0 0 1 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 61-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 3 0 28 ->= 2 5 8 15 18 7 8 15 19 0 28 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } 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 1 | | 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 1 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 1 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 60-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 , 32 1 2 5 ->= 32 1 4 2 5 6 7 5 8 9 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 1 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 29 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 30 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 59-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 3 0 17 ->= 2 5 8 15 18 7 8 15 19 0 17 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 } 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 1 | | 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 1 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 32 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 30->30, 31->31, 32->32 }, it remains to prove termination of the 58-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 32 1 2 3 ->= 32 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 } 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 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 | \ / 32 is interpreted by / \ | 1 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, 30->30, 32->31 }, it remains to prove termination of the 57-rule system { 0 1 2 3 ->= 0 1 4 2 5 6 7 5 8 9 10 , 11 12 13 9 ->= 11 12 13 9 14 8 15 16 4 2 12 , 7 3 0 17 ->= 7 5 8 15 18 7 8 15 19 0 17 , 7 12 13 20 ->= 7 12 13 9 14 8 15 16 4 2 3 , 21 1 2 3 ->= 21 1 4 2 5 6 7 5 8 9 10 , 22 23 18 ->= 19 24 2 5 5 6 22 23 18 7 6 , 7 3 0 25 ->= 7 5 8 15 18 7 8 15 19 0 25 , 7 3 0 1 ->= 7 5 8 15 18 7 8 15 19 0 1 , 7 3 0 26 ->= 7 5 8 15 18 7 8 15 19 0 26 , 7 12 13 9 ->= 7 12 13 9 14 8 15 16 4 2 12 , 7 3 0 27 ->= 7 5 8 15 18 7 8 15 19 0 27 , 7 3 0 28 ->= 7 5 8 15 18 7 8 15 19 0 28 , 22 23 18 7 ->= 22 29 13 2 8 4 4 2 12 14 5 , 2 12 13 20 ->= 2 12 13 9 14 8 15 16 4 2 3 , 30 1 2 3 ->= 30 1 4 2 5 6 7 5 8 9 10 , 2 12 13 15 ->= 2 12 13 9 14 8 15 16 4 2 6 , 2 12 13 4 ->= 2 12 13 9 14 8 15 16 4 2 8 , 9 23 22 ->= 20 24 2 5 5 6 22 23 18 7 12 , 2 12 13 9 ->= 2 12 13 9 14 8 15 16 4 2 12 , 2 12 13 2 ->= 2 12 13 9 14 8 15 16 4 2 5 , 14 3 0 17 ->= 14 5 8 15 18 7 8 15 19 0 17 , 14 3 0 25 ->= 14 5 8 15 18 7 8 15 19 0 25 , 14 3 0 1 ->= 14 5 8 15 18 7 8 15 19 0 1 , 14 3 0 26 ->= 14 5 8 15 18 7 8 15 19 0 26 , 14 12 13 9 ->= 14 12 13 9 14 8 15 16 4 2 12 , 14 3 0 27 ->= 14 5 8 15 18 7 8 15 19 0 27 , 29 23 7 ->= 10 24 2 5 5 6 22 23 18 7 5 , 14 3 0 28 ->= 14 5 8 15 18 7 8 15 19 0 28 , 27 1 2 3 ->= 27 1 4 2 5 6 7 5 8 9 10 , 28 12 13 9 ->= 28 12 13 9 14 8 15 16 4 2 12 , 12 13 9 14 3 24 4 20 -> 12 13 9 13 9 23 22 29 23 7 3 , 12 23 19 ->= 3 24 2 5 5 6 22 23 18 7 3 , 5 3 0 17 ->= 5 5 8 15 18 7 8 15 19 0 17 , 5 12 13 20 ->= 5 12 13 9 14 8 15 16 4 2 3 , 12 23 18 19 ->= 12 29 13 2 8 4 4 2 12 14 3 , 31 1 2 3 ->= 31 1 4 2 5 6 7 5 8 9 10 , 12 13 9 14 3 24 4 15 -> 12 13 9 13 9 23 22 29 23 7 6 , 12 23 18 ->= 3 24 2 5 5 6 22 23 18 7 6 , 5 3 0 25 ->= 5 5 8 15 18 7 8 15 19 0 25 , 5 12 13 15 ->= 5 12 13 9 14 8 15 16 4 2 6 , 12 23 18 18 ->= 12 29 13 2 8 4 4 2 12 14 6 , 12 13 9 14 3 24 4 4 -> 12 13 9 13 9 23 22 29 23 7 8 , 6 19 24 ->= 5 12 29 14 5 12 29 13 4 2 8 , 12 23 16 ->= 3 24 2 5 5 6 22 23 18 7 8 , 5 3 0 1 ->= 5 5 8 15 18 7 8 15 19 0 1 , 5 12 13 4 ->= 5 12 13 9 14 8 15 16 4 2 8 , 12 23 18 16 ->= 12 29 13 2 8 4 4 2 12 14 8 , 12 13 9 14 3 24 4 9 -> 12 13 9 13 9 23 22 29 23 7 12 , 12 23 22 ->= 3 24 2 5 5 6 22 23 18 7 12 , 5 3 0 26 ->= 5 5 8 15 18 7 8 15 19 0 26 , 5 12 13 9 ->= 5 12 13 9 14 8 15 16 4 2 12 , 5 3 0 27 ->= 5 5 8 15 18 7 8 15 19 0 27 , 12 13 9 14 3 24 4 2 -> 12 13 9 13 9 23 22 29 23 7 5 , 12 23 7 ->= 3 24 2 5 5 6 22 23 18 7 5 , 5 3 0 28 ->= 5 5 8 15 18 7 8 15 19 0 28 , 5 12 13 2 ->= 5 12 13 9 14 8 15 16 4 2 5 , 12 23 18 7 ->= 12 29 13 2 8 4 4 2 12 14 5 } 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 11->0, 12->1, 13->2, 9->3, 14->4, 8->5, 15->6, 16->7, 4->8, 2->9, 7->10, 3->11, 0->12, 17->13, 5->14, 18->15, 19->16, 20->17, 21->18, 1->19, 6->20, 10->21, 22->22, 23->23, 24->24, 25->25, 26->26, 27->27, 28->28, 29->29, 30->30, 31->31 }, it remains to prove termination of the 56-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 9 11 ->= 18 19 8 9 14 20 10 14 5 3 21 , 22 23 15 ->= 16 24 9 14 14 20 22 23 15 10 20 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 19 ->= 10 14 5 6 15 10 5 6 16 12 19 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 27 ->= 10 14 5 6 15 10 5 6 16 12 27 , 10 11 12 28 ->= 10 14 5 6 15 10 5 6 16 12 28 , 22 23 15 10 ->= 22 29 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 30 19 9 11 ->= 30 19 8 9 14 20 10 14 5 3 21 , 9 1 2 6 ->= 9 1 2 3 4 5 6 7 8 9 20 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 23 22 ->= 17 24 9 14 14 20 22 23 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 4 11 12 19 ->= 4 14 5 6 15 10 5 6 16 12 19 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 27 ->= 4 14 5 6 15 10 5 6 16 12 27 , 29 23 10 ->= 21 24 9 14 14 20 22 23 15 10 14 , 4 11 12 28 ->= 4 14 5 6 15 10 5 6 16 12 28 , 27 19 9 11 ->= 27 19 8 9 14 20 10 14 5 3 21 , 28 1 2 3 ->= 28 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 24 8 17 -> 1 2 3 2 3 23 22 29 23 10 11 , 1 23 16 ->= 11 24 9 14 14 20 22 23 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 23 15 16 ->= 1 29 2 9 5 8 8 9 1 4 11 , 31 19 9 11 ->= 31 19 8 9 14 20 10 14 5 3 21 , 1 2 3 4 11 24 8 6 -> 1 2 3 2 3 23 22 29 23 10 20 , 1 23 15 ->= 11 24 9 14 14 20 22 23 15 10 20 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 20 , 1 23 15 15 ->= 1 29 2 9 5 8 8 9 1 4 20 , 1 2 3 4 11 24 8 8 -> 1 2 3 2 3 23 22 29 23 10 5 , 20 16 24 ->= 14 1 29 4 14 1 29 2 8 9 5 , 1 23 7 ->= 11 24 9 14 14 20 22 23 15 10 5 , 14 11 12 19 ->= 14 14 5 6 15 10 5 6 16 12 19 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 23 15 7 ->= 1 29 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 24 8 3 -> 1 2 3 2 3 23 22 29 23 10 1 , 1 23 22 ->= 11 24 9 14 14 20 22 23 15 10 1 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 27 ->= 14 14 5 6 15 10 5 6 16 12 27 , 1 2 3 4 11 24 8 9 -> 1 2 3 2 3 23 22 29 23 10 14 , 1 23 10 ->= 11 24 9 14 14 20 22 23 15 10 14 , 14 11 12 28 ->= 14 14 5 6 15 10 5 6 16 12 28 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 23 15 10 ->= 1 29 2 9 5 8 8 9 1 4 14 } 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 1 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 1 | | 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 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 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 1 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 | \ / 30 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 31 is interpreted by / \ | 1 0 0 0 0 | | 0 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, 23->19, 24->20, 20->21, 25->22, 19->23, 26->24, 27->25, 28->26, 29->27, 30->28, 21->29, 31->30 }, it remains to prove termination of the 55-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 28 23 9 11 ->= 28 23 8 9 14 21 10 14 5 3 29 , 9 1 2 6 ->= 9 1 2 3 4 5 6 7 8 9 21 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 29 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 25 23 9 11 ->= 25 23 8 9 14 21 10 14 5 3 29 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 30 23 9 11 ->= 30 23 8 9 14 21 10 14 5 3 29 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 | | 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 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, 30->30 }, it remains to prove termination of the 54-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 28 23 9 11 ->= 28 23 8 9 14 21 10 14 5 3 29 , 9 1 2 6 ->= 9 1 2 3 4 5 6 7 8 9 21 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 29 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 30 23 9 11 ->= 30 23 8 9 14 21 10 14 5 3 29 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 | | 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 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 1 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 1 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 | \ / 30 is interpreted by / \ | 1 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, 29->28, 30->29 }, it remains to prove termination of the 53-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 9 1 2 6 ->= 9 1 2 3 4 5 6 7 8 9 21 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 29 23 9 11 ->= 29 23 8 9 14 21 10 14 5 3 28 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 | | 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 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 1 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 1 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 }, it remains to prove termination of the 52-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 9 1 2 6 ->= 9 1 2 3 4 5 6 7 8 9 21 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 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 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 | \ / 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 }, it remains to prove termination of the 51-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 9 1 2 8 ->= 9 1 2 3 4 5 6 7 8 9 5 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 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 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 | \ / 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 }, it remains to prove termination of the 50-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 9 1 2 9 ->= 9 1 2 3 4 5 6 7 8 9 14 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 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 | \ / 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 }, it remains to prove termination of the 49-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 14 1 2 9 ->= 14 1 2 3 4 5 6 7 8 9 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 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 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 1 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 1 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 | \ / 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 }, it remains to prove termination of the 48-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 14 1 2 6 ->= 14 1 2 3 4 5 6 7 8 9 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 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 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 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 1 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 1 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 | \ / 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 }, it remains to prove termination of the 47-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 14 1 2 8 ->= 14 1 2 3 4 5 6 7 8 9 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 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 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 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 1 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 1 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 | \ / 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 }, it remains to prove termination of the 46-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 14 11 12 26 ->= 14 14 5 6 15 10 5 6 16 12 26 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 2 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 45-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 11 12 24 ->= 14 14 5 6 15 10 5 6 16 12 24 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 2 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 44-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 11 12 13 ->= 14 14 5 6 15 10 5 6 16 12 13 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 8: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 | | 0 0 0 1 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 43-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 14 11 12 25 ->= 14 14 5 6 15 10 5 6 16 12 25 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 2 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 42-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 14 11 12 22 ->= 14 14 5 6 15 10 5 6 16 12 22 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 2 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 41-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 14 11 12 23 ->= 14 14 5 6 15 10 5 6 16 12 23 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 1 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 2 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 40-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 , 1 19 15 10 ->= 1 27 2 9 5 8 8 9 1 4 14 } 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 1 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 1 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 1 | | 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 1 0 0 | | 0 0 0 0 0 | \ / 19 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 | \ / 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 | \ / 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 }, it remains to prove termination of the 39-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 , 1 19 10 ->= 11 20 9 14 14 21 18 19 15 10 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 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 }, it remains to prove termination of the 38-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 2 3 4 11 20 8 6 -> 1 2 3 2 3 19 18 27 19 10 21 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 37-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 19 15 16 ->= 1 27 2 9 5 8 8 9 1 4 11 , 1 19 15 ->= 11 20 9 14 14 21 18 19 15 10 21 , 1 19 15 15 ->= 1 27 2 9 5 8 8 9 1 4 21 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 19 15 7 ->= 1 27 2 9 5 8 8 9 1 4 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 1 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 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 }, it remains to prove termination of the 33-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 13 ->= 4 14 5 6 15 10 5 6 16 12 13 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 1 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 | \ / 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 }, it remains to prove termination of the 32-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 22 ->= 4 14 5 6 15 10 5 6 16 12 22 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 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 | \ / 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 }, it remains to prove termination of the 31-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 23 ->= 4 14 5 6 15 10 5 6 16 12 23 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 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 | \ / 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 }, it remains to prove termination of the 30-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 11 12 24 ->= 4 14 5 6 15 10 5 6 16 12 24 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 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, 24->24, 25->25, 26->26, 27->27, 28->28 }, it remains to prove termination of the 29-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 4 11 12 25 ->= 4 14 5 6 15 10 5 6 16 12 25 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 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 | \ / 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, 24->24, 25->25, 26->26, 27->27, 28->28 }, it remains to prove termination of the 28-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 4 11 12 26 ->= 4 14 5 6 15 10 5 6 16 12 26 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } 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 1 | | 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 1 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, 24->24, 25->25, 26->26, 27->27, 28->28 }, it remains to prove termination of the 27-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 19 7 ->= 11 20 9 14 14 21 18 19 15 10 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 1 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 | | 0 1 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 }, it remains to prove termination of the 26-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 9 -> 1 2 3 2 3 19 18 27 19 10 14 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 25-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 1 2 3 4 11 20 8 8 -> 1 2 3 2 3 19 18 27 19 10 5 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 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 }, it remains to prove termination of the 24-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 10 1 2 17 ->= 10 1 2 3 4 5 6 7 8 9 11 , 18 19 15 ->= 16 20 9 14 14 21 18 19 15 10 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 10 11 12 26 ->= 10 14 5 6 15 10 5 6 16 12 26 , 18 19 15 10 ->= 18 27 2 9 5 8 8 9 1 4 14 , 9 1 2 17 ->= 9 1 2 3 4 5 6 7 8 9 11 , 3 19 18 ->= 17 20 9 14 14 21 18 19 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 27 19 10 ->= 28 20 9 14 14 21 18 19 15 10 14 , 26 1 2 3 ->= 26 1 2 3 4 5 6 7 8 9 1 , 1 2 3 4 11 20 8 17 -> 1 2 3 2 3 19 18 27 19 10 11 , 1 19 16 ->= 11 20 9 14 14 21 18 19 15 10 11 , 14 1 2 17 ->= 14 1 2 3 4 5 6 7 8 9 11 , 21 16 20 ->= 14 1 27 4 14 1 27 2 8 9 5 , 1 2 3 4 11 20 8 3 -> 1 2 3 2 3 19 18 27 19 10 1 , 1 19 18 ->= 11 20 9 14 14 21 18 19 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 7: 0 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 1 0 1 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 1 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 3 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 1 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 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 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / 28 is interpreted by / \ | 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 10->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 18->17, 19->18, 20->19, 21->20, 22->21, 23->22, 24->23, 25->24, 26->25, 27->26, 17->27, 28->28 }, it remains to prove termination of the 20-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 17 18 15 ->= 16 19 9 14 14 20 17 18 15 10 20 , 10 11 12 21 ->= 10 14 5 6 15 10 5 6 16 12 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 17 18 15 10 ->= 17 26 2 9 5 8 8 9 1 4 14 , 3 18 17 ->= 27 19 9 14 14 20 17 18 15 10 1 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 26 18 10 ->= 28 19 9 14 14 20 17 18 15 10 14 , 25 1 2 3 ->= 25 1 2 3 4 5 6 7 8 9 1 , 1 18 16 ->= 11 19 9 14 14 20 17 18 15 10 11 , 20 16 19 ->= 14 1 26 4 14 1 26 2 8 9 5 , 1 2 3 4 11 19 8 3 -> 1 2 3 2 3 18 17 26 18 10 1 , 1 18 17 ->= 11 19 9 14 14 20 17 18 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 0 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 1 | | 0 1 | \ / 13 is interpreted by / \ | 1 1 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 0 | | 0 1 | \ / 16 is interpreted by / \ | 1 0 | | 0 1 | \ / 17 is interpreted by / \ | 1 0 | | 0 1 | \ / 18 is interpreted by / \ | 1 0 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 1 | | 0 1 | \ / 22 is interpreted by / \ | 1 1 | | 0 1 | \ / 23 is interpreted by / \ | 1 1 | | 0 1 | \ / 24 is interpreted by / \ | 1 1 | | 0 1 | \ / 25 is interpreted by / \ | 1 1 | | 0 1 | \ / 26 is interpreted by / \ | 1 0 | | 0 1 | \ / 27 is interpreted by / \ | 1 0 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 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, 28->27 }, it remains to prove termination of the 19-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 13 ->= 10 14 5 6 15 10 5 6 16 12 13 , 17 18 15 ->= 16 19 9 14 14 20 17 18 15 10 20 , 10 11 12 21 ->= 10 14 5 6 15 10 5 6 16 12 21 , 10 11 12 22 ->= 10 14 5 6 15 10 5 6 16 12 22 , 10 11 12 23 ->= 10 14 5 6 15 10 5 6 16 12 23 , 10 1 2 3 ->= 10 1 2 3 4 5 6 7 8 9 1 , 10 11 12 24 ->= 10 14 5 6 15 10 5 6 16 12 24 , 10 11 12 25 ->= 10 14 5 6 15 10 5 6 16 12 25 , 17 18 15 10 ->= 17 26 2 9 5 8 8 9 1 4 14 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 26 18 10 ->= 27 19 9 14 14 20 17 18 15 10 14 , 25 1 2 3 ->= 25 1 2 3 4 5 6 7 8 9 1 , 1 18 16 ->= 11 19 9 14 14 20 17 18 15 10 11 , 20 16 19 ->= 14 1 26 4 14 1 26 2 8 9 5 , 1 2 3 4 11 19 8 3 -> 1 2 3 2 3 18 17 26 18 10 1 , 1 18 17 ->= 11 19 9 14 14 20 17 18 15 10 1 , 14 1 2 3 ->= 14 1 2 3 4 5 6 7 8 9 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 4: 0 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 1 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 11 is interpreted by / \ | 2 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 2 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 2 0 | \ / 18 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 1 0 0 1 | | 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 22 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 23 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 24 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 25 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 26 is interpreted by / \ | 1 0 0 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 0 0 0 | \ / 27 is interpreted by / \ | 1 0 0 0 | | 0 1 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, 17->10, 18->11, 15->12, 16->13, 19->14, 14->15, 20->16, 10->17, 26->18, 27->19, 25->20, 11->21 }, it remains to prove termination of the 12-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 ->= 13 14 9 15 15 16 10 11 12 17 16 , 17 1 2 3 ->= 17 1 2 3 4 5 6 7 8 9 1 , 10 11 12 17 ->= 10 18 2 9 5 8 8 9 1 4 15 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 18 11 17 ->= 19 14 9 15 15 16 10 11 12 17 15 , 20 1 2 3 ->= 20 1 2 3 4 5 6 7 8 9 1 , 1 11 13 ->= 21 14 9 15 15 16 10 11 12 17 21 , 16 13 14 ->= 15 1 18 4 15 1 18 2 8 9 5 , 1 2 3 4 21 14 8 3 -> 1 2 3 2 3 11 10 18 11 17 1 , 15 1 2 3 ->= 15 1 2 3 4 5 6 7 8 9 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 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 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 20 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 21 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 11-rule system { 0 1 2 3 ->= 0 1 2 3 4 5 6 7 8 9 1 , 10 11 12 ->= 13 14 9 15 15 16 10 11 12 17 16 , 17 1 2 3 ->= 17 1 2 3 4 5 6 7 8 9 1 , 10 11 12 17 ->= 10 18 2 9 5 8 8 9 1 4 15 , 9 1 2 3 ->= 9 1 2 3 4 5 6 7 8 9 1 , 4 1 2 3 ->= 4 1 2 3 4 5 6 7 8 9 1 , 18 11 17 ->= 19 14 9 15 15 16 10 11 12 17 15 , 20 1 2 3 ->= 20 1 2 3 4 5 6 7 8 9 1 , 1 11 13 ->= 21 14 9 15 15 16 10 11 12 17 21 , 16 13 14 ->= 15 1 18 4 15 1 18 2 8 9 5 , 15 1 2 3 ->= 15 1 2 3 4 5 6 7 8 9 1 } The system is trivially terminating.