YES After renaming modulo { b->0, q->1, p->2, 0->3, 1->4 }, it remains to prove termination of the 6-rule system { 0 1 0 -> 0 2 0 , 3 2 3 ->= 1 , 4 2 4 ->= 1 , 3 1 3 ->= 1 , 4 1 4 ->= 1 , 2 ->= 4 2 4 3 4 } 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 1 | | 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 | | 0 1 0 0 | | 0 0 0 0 | | 0 1 0 0 | \ / 4 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, 4->3, 3->4 }, it remains to prove termination of the 5-rule system { 0 1 0 -> 0 2 0 , 3 2 3 ->= 1 , 4 1 4 ->= 1 , 3 1 3 ->= 1 , 2 ->= 3 2 3 4 3 } 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, 0]->4, [0, 3]->5, [3, 2]->6, [2, 3]->7, [3, 0]->8, [0, 4]->9, [4, 1]->10, [1, 4]->11, [4, 0]->12, [3, 1]->13, [1, 3]->14, [3, 4]->15, [4, 3]->16, [1, 1]->17, [2, 1]->18, [1, 2]->19, [4, 2]->20, [2, 2]->21, [3, 3]->22, [4, 4]->23, [2, 4]->24 }, it remains to prove termination of the 125-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 9 10 11 12 ->= 1 2 , 5 13 14 8 ->= 1 2 , 3 4 ->= 5 6 7 15 16 8 , 0 1 2 1 -> 0 3 4 1 , 5 6 7 13 ->= 1 17 , 9 10 11 10 ->= 1 17 , 5 13 14 13 ->= 1 17 , 3 18 ->= 5 6 7 15 16 13 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 6 ->= 1 19 , 9 10 11 20 ->= 1 19 , 5 13 14 6 ->= 1 19 , 3 21 ->= 5 6 7 15 16 6 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 22 ->= 1 14 , 9 10 11 16 ->= 1 14 , 5 13 14 22 ->= 1 14 , 3 7 ->= 5 6 7 15 16 22 , 0 1 2 9 -> 0 3 4 9 , 5 6 7 15 ->= 1 11 , 9 10 11 23 ->= 1 11 , 5 13 14 15 ->= 1 11 , 3 24 ->= 5 6 7 15 16 15 , 2 1 2 0 -> 2 3 4 0 , 14 6 7 8 ->= 17 2 , 11 10 11 12 ->= 17 2 , 14 13 14 8 ->= 17 2 , 19 4 ->= 14 6 7 15 16 8 , 2 1 2 1 -> 2 3 4 1 , 14 6 7 13 ->= 17 17 , 11 10 11 10 ->= 17 17 , 14 13 14 13 ->= 17 17 , 19 18 ->= 14 6 7 15 16 13 , 2 1 2 3 -> 2 3 4 3 , 14 6 7 6 ->= 17 19 , 11 10 11 20 ->= 17 19 , 14 13 14 6 ->= 17 19 , 19 21 ->= 14 6 7 15 16 6 , 2 1 2 5 -> 2 3 4 5 , 14 6 7 22 ->= 17 14 , 11 10 11 16 ->= 17 14 , 14 13 14 22 ->= 17 14 , 19 7 ->= 14 6 7 15 16 22 , 2 1 2 9 -> 2 3 4 9 , 14 6 7 15 ->= 17 11 , 11 10 11 23 ->= 17 11 , 14 13 14 15 ->= 17 11 , 19 24 ->= 14 6 7 15 16 15 , 4 1 2 0 -> 4 3 4 0 , 7 6 7 8 ->= 18 2 , 24 10 11 12 ->= 18 2 , 7 13 14 8 ->= 18 2 , 21 4 ->= 7 6 7 15 16 8 , 4 1 2 1 -> 4 3 4 1 , 7 6 7 13 ->= 18 17 , 24 10 11 10 ->= 18 17 , 7 13 14 13 ->= 18 17 , 21 18 ->= 7 6 7 15 16 13 , 4 1 2 3 -> 4 3 4 3 , 7 6 7 6 ->= 18 19 , 24 10 11 20 ->= 18 19 , 7 13 14 6 ->= 18 19 , 21 21 ->= 7 6 7 15 16 6 , 4 1 2 5 -> 4 3 4 5 , 7 6 7 22 ->= 18 14 , 24 10 11 16 ->= 18 14 , 7 13 14 22 ->= 18 14 , 21 7 ->= 7 6 7 15 16 22 , 4 1 2 9 -> 4 3 4 9 , 7 6 7 15 ->= 18 11 , 24 10 11 23 ->= 18 11 , 7 13 14 15 ->= 18 11 , 21 24 ->= 7 6 7 15 16 15 , 8 1 2 0 -> 8 3 4 0 , 22 6 7 8 ->= 13 2 , 15 10 11 12 ->= 13 2 , 22 13 14 8 ->= 13 2 , 6 4 ->= 22 6 7 15 16 8 , 8 1 2 1 -> 8 3 4 1 , 22 6 7 13 ->= 13 17 , 15 10 11 10 ->= 13 17 , 22 13 14 13 ->= 13 17 , 6 18 ->= 22 6 7 15 16 13 , 8 1 2 3 -> 8 3 4 3 , 22 6 7 6 ->= 13 19 , 15 10 11 20 ->= 13 19 , 22 13 14 6 ->= 13 19 , 6 21 ->= 22 6 7 15 16 6 , 8 1 2 5 -> 8 3 4 5 , 22 6 7 22 ->= 13 14 , 15 10 11 16 ->= 13 14 , 22 13 14 22 ->= 13 14 , 6 7 ->= 22 6 7 15 16 22 , 8 1 2 9 -> 8 3 4 9 , 22 6 7 15 ->= 13 11 , 15 10 11 23 ->= 13 11 , 22 13 14 15 ->= 13 11 , 6 24 ->= 22 6 7 15 16 15 , 12 1 2 0 -> 12 3 4 0 , 16 6 7 8 ->= 10 2 , 23 10 11 12 ->= 10 2 , 16 13 14 8 ->= 10 2 , 20 4 ->= 16 6 7 15 16 8 , 12 1 2 1 -> 12 3 4 1 , 16 6 7 13 ->= 10 17 , 23 10 11 10 ->= 10 17 , 16 13 14 13 ->= 10 17 , 20 18 ->= 16 6 7 15 16 13 , 12 1 2 3 -> 12 3 4 3 , 16 6 7 6 ->= 10 19 , 23 10 11 20 ->= 10 19 , 16 13 14 6 ->= 10 19 , 20 21 ->= 16 6 7 15 16 6 , 12 1 2 5 -> 12 3 4 5 , 16 6 7 22 ->= 10 14 , 23 10 11 16 ->= 10 14 , 16 13 14 22 ->= 10 14 , 20 7 ->= 16 6 7 15 16 22 , 12 1 2 9 -> 12 3 4 9 , 16 6 7 15 ->= 10 11 , 23 10 11 23 ->= 10 11 , 16 13 14 15 ->= 10 11 , 20 24 ->= 16 6 7 15 16 15 } 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 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 1 | | 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 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 1 | | 0 1 | \ / 21 is interpreted by / \ | 1 1 | | 0 1 | \ / 22 is interpreted by / \ | 1 0 | | 0 1 | \ / 23 is interpreted by / \ | 1 1 | | 0 1 | \ / 24 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, 13->9, 14->10, 15->11, 16->12, 17->13, 18->14, 19->15, 22->16, 9->17, 11->18, 10->19, 12->20 }, it remains to prove termination of the 88-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 5 9 10 8 ->= 1 2 , 3 4 ->= 5 6 7 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 5 6 7 9 ->= 1 13 , 5 9 10 9 ->= 1 13 , 3 14 ->= 5 6 7 11 12 9 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 6 ->= 1 15 , 5 9 10 6 ->= 1 15 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 16 ->= 1 10 , 5 9 10 16 ->= 1 10 , 3 7 ->= 5 6 7 11 12 16 , 0 1 2 17 -> 0 3 4 17 , 5 6 7 11 ->= 1 18 , 5 9 10 11 ->= 1 18 , 2 1 2 0 -> 2 3 4 0 , 10 6 7 8 ->= 13 2 , 10 9 10 8 ->= 13 2 , 15 4 ->= 10 6 7 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 10 6 7 9 ->= 13 13 , 18 19 18 19 ->= 13 13 , 10 9 10 9 ->= 13 13 , 15 14 ->= 10 6 7 11 12 9 , 2 1 2 3 -> 2 3 4 3 , 10 6 7 6 ->= 13 15 , 10 9 10 6 ->= 13 15 , 2 1 2 5 -> 2 3 4 5 , 10 6 7 16 ->= 13 10 , 18 19 18 12 ->= 13 10 , 10 9 10 16 ->= 13 10 , 15 7 ->= 10 6 7 11 12 16 , 2 1 2 17 -> 2 3 4 17 , 10 6 7 11 ->= 13 18 , 10 9 10 11 ->= 13 18 , 4 1 2 0 -> 4 3 4 0 , 7 6 7 8 ->= 14 2 , 7 9 10 8 ->= 14 2 , 4 1 2 1 -> 4 3 4 1 , 7 6 7 9 ->= 14 13 , 7 9 10 9 ->= 14 13 , 4 1 2 3 -> 4 3 4 3 , 7 6 7 6 ->= 14 15 , 7 9 10 6 ->= 14 15 , 4 1 2 5 -> 4 3 4 5 , 7 6 7 16 ->= 14 10 , 7 9 10 16 ->= 14 10 , 4 1 2 17 -> 4 3 4 17 , 7 6 7 11 ->= 14 18 , 7 9 10 11 ->= 14 18 , 8 1 2 0 -> 8 3 4 0 , 16 6 7 8 ->= 9 2 , 16 9 10 8 ->= 9 2 , 6 4 ->= 16 6 7 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 16 6 7 9 ->= 9 13 , 11 19 18 19 ->= 9 13 , 16 9 10 9 ->= 9 13 , 6 14 ->= 16 6 7 11 12 9 , 8 1 2 3 -> 8 3 4 3 , 16 6 7 6 ->= 9 15 , 16 9 10 6 ->= 9 15 , 8 1 2 5 -> 8 3 4 5 , 16 6 7 16 ->= 9 10 , 11 19 18 12 ->= 9 10 , 16 9 10 16 ->= 9 10 , 6 7 ->= 16 6 7 11 12 16 , 8 1 2 17 -> 8 3 4 17 , 16 6 7 11 ->= 9 18 , 16 9 10 11 ->= 9 18 , 20 1 2 0 -> 20 3 4 0 , 12 6 7 8 ->= 19 2 , 12 9 10 8 ->= 19 2 , 20 1 2 1 -> 20 3 4 1 , 12 6 7 9 ->= 19 13 , 12 9 10 9 ->= 19 13 , 20 1 2 3 -> 20 3 4 3 , 12 6 7 6 ->= 19 15 , 12 9 10 6 ->= 19 15 , 20 1 2 5 -> 20 3 4 5 , 12 6 7 16 ->= 19 10 , 12 9 10 16 ->= 19 10 , 20 1 2 17 -> 20 3 4 17 , 12 6 7 11 ->= 19 18 , 12 9 10 11 ->= 19 18 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 0 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 0 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 1 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 2 | | 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 | \ / 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, 14->13, 15->14, 16->15, 17->16, 18->17, 19->18, 20->19 }, it remains to prove termination of the 67-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 5 9 10 8 ->= 1 2 , 3 4 ->= 5 6 7 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 6 7 11 12 9 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 6 ->= 1 14 , 5 9 10 6 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 15 ->= 1 10 , 5 9 10 15 ->= 1 10 , 3 7 ->= 5 6 7 11 12 15 , 0 1 2 16 -> 0 3 4 16 , 5 6 7 11 ->= 1 17 , 5 9 10 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 10 6 7 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 10 6 7 11 12 9 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 7 ->= 10 6 7 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 7 6 7 8 ->= 13 2 , 7 9 10 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 7 6 7 6 ->= 13 14 , 7 9 10 6 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 7 6 7 15 ->= 13 10 , 7 9 10 15 ->= 13 10 , 4 1 2 16 -> 4 3 4 16 , 7 6 7 11 ->= 13 17 , 7 9 10 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 9 2 , 15 9 10 8 ->= 9 2 , 6 4 ->= 15 6 7 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 6 13 ->= 15 6 7 11 12 9 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 6 ->= 9 14 , 15 9 10 6 ->= 9 14 , 8 1 2 5 -> 8 3 4 5 , 15 6 7 15 ->= 9 10 , 11 18 17 12 ->= 9 10 , 15 9 10 15 ->= 9 10 , 6 7 ->= 15 6 7 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 6 7 11 ->= 9 17 , 15 9 10 11 ->= 9 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 12 9 10 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 6 ->= 18 14 , 12 9 10 6 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 6 7 15 ->= 18 10 , 12 9 10 15 ->= 18 10 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 , 12 9 10 11 ->= 18 17 } 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 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 1 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 9->6, 10->7, 8->8, 6->9, 7->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19 }, it remains to prove termination of the 66-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 9 10 9 ->= 1 14 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 3 10 ->= 5 9 10 11 12 15 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 9 10 8 ->= 13 2 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 9 10 9 ->= 13 14 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 9 10 11 ->= 13 17 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 65-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 3 10 ->= 5 9 10 11 12 15 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 9 10 8 ->= 13 2 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 9 10 9 ->= 13 14 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 9 10 11 ->= 13 17 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 0 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 11 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 | | 0 1 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 }, it remains to prove termination of the 64-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 9 10 8 ->= 13 2 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 9 10 9 ->= 13 14 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 9 10 11 ->= 13 17 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 63-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 9 10 9 ->= 13 14 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 9 10 11 ->= 13 17 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 62-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 9 10 11 ->= 13 17 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 61-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 9 4 ->= 15 9 10 11 12 8 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 0 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 5 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 9 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 | | 0 1 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 }, it remains to prove termination of the 60-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 9 10 8 ->= 18 2 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 59-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 9 10 9 ->= 18 14 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 58-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 9 10 11 ->= 18 17 , 12 6 7 11 ->= 18 17 } 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 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 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 | \ / 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 }, it remains to prove termination of the 57-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 9 10 8 ->= 6 2 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 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 | \ / 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 }, it remains to prove termination of the 56-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 9 10 9 ->= 6 14 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 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 | \ / 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 }, it remains to prove termination of the 55-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 9 10 15 ->= 1 7 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 | \ / 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 }, it remains to prove termination of the 54-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 9 10 15 ->= 13 7 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 | \ / 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 }, it remains to prove termination of the 53-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 9 10 15 ->= 18 7 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 | \ / 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 }, it remains to prove termination of the 52-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 15 9 10 15 ->= 6 7 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } 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 1 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 1 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 | \ / 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 }, it remains to prove termination of the 51-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 3 13 ->= 5 9 10 11 12 6 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 14 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 15 ->= 1 7 , 0 1 2 16 -> 0 3 4 16 , 5 9 10 11 ->= 1 17 , 5 6 7 11 ->= 1 17 , 2 1 2 0 -> 2 3 4 0 , 14 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 14 13 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 14 10 ->= 7 9 10 11 12 15 , 2 1 2 16 -> 2 3 4 16 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 13 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 13 14 , 4 1 2 5 -> 4 3 4 5 , 10 6 7 15 ->= 13 7 , 4 1 2 16 -> 4 3 4 16 , 10 6 7 11 ->= 13 17 , 8 1 2 0 -> 8 3 4 0 , 15 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 13 ->= 15 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 15 6 7 9 ->= 6 14 , 8 1 2 5 -> 8 3 4 5 , 11 18 17 12 ->= 6 7 , 15 6 7 15 ->= 6 7 , 9 10 ->= 15 9 10 11 12 15 , 8 1 2 16 -> 8 3 4 16 , 15 9 10 11 ->= 6 17 , 15 6 7 11 ->= 6 17 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 14 , 19 1 2 5 -> 19 3 4 5 , 12 6 7 15 ->= 18 7 , 19 1 2 16 -> 19 3 4 16 , 12 6 7 11 ->= 18 17 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 3: 0 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 | | 0 1 0 | | 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 11 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 1 0 | \ / 14 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 | | 0 1 0 | | 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 | | 0 1 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, 14->13, 15->14, 16->15, 17->16, 13->17, 18->18, 19->19 }, it remains to prove termination of the 50-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 13 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 14 ->= 1 7 , 0 1 2 15 -> 0 3 4 15 , 5 9 10 11 ->= 1 16 , 5 6 7 11 ->= 1 16 , 2 1 2 0 -> 2 3 4 0 , 13 4 ->= 7 9 10 11 12 8 , 2 1 2 1 -> 2 3 4 1 , 13 17 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 13 10 ->= 7 9 10 11 12 14 , 2 1 2 15 -> 2 3 4 15 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 17 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 17 13 , 4 1 2 5 -> 4 3 4 5 , 10 6 7 14 ->= 17 7 , 4 1 2 15 -> 4 3 4 15 , 10 6 7 11 ->= 17 16 , 8 1 2 0 -> 8 3 4 0 , 14 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 17 ->= 14 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 14 6 7 9 ->= 6 13 , 8 1 2 5 -> 8 3 4 5 , 11 18 16 12 ->= 6 7 , 14 6 7 14 ->= 6 7 , 9 10 ->= 14 9 10 11 12 14 , 8 1 2 15 -> 8 3 4 15 , 14 9 10 11 ->= 6 16 , 14 6 7 11 ->= 6 16 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 13 , 19 1 2 5 -> 19 3 4 5 , 12 6 7 14 ->= 18 7 , 19 1 2 15 -> 19 3 4 15 , 12 6 7 11 ->= 18 16 } 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 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 0 | | 0 1 | \ / 3 is interpreted by / \ | 1 0 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / 6 is interpreted by / \ | 1 0 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 0 | | 0 1 | \ / 15 is interpreted by / \ | 1 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 | \ / 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 }, it remains to prove termination of the 49-rule system { 0 1 2 0 -> 0 3 4 0 , 5 6 7 8 ->= 1 2 , 3 4 ->= 5 9 10 11 12 8 , 0 1 2 1 -> 0 3 4 1 , 0 1 2 3 -> 0 3 4 3 , 5 6 7 9 ->= 1 13 , 0 1 2 5 -> 0 3 4 5 , 5 6 7 14 ->= 1 7 , 0 1 2 15 -> 0 3 4 15 , 5 9 10 11 ->= 1 16 , 5 6 7 11 ->= 1 16 , 2 1 2 0 -> 2 3 4 0 , 2 1 2 1 -> 2 3 4 1 , 13 17 ->= 7 9 10 11 12 6 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 13 10 ->= 7 9 10 11 12 14 , 2 1 2 15 -> 2 3 4 15 , 4 1 2 0 -> 4 3 4 0 , 10 6 7 8 ->= 17 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 10 6 7 9 ->= 17 13 , 4 1 2 5 -> 4 3 4 5 , 10 6 7 14 ->= 17 7 , 4 1 2 15 -> 4 3 4 15 , 10 6 7 11 ->= 17 16 , 8 1 2 0 -> 8 3 4 0 , 14 6 7 8 ->= 6 2 , 8 1 2 1 -> 8 3 4 1 , 9 17 ->= 14 9 10 11 12 6 , 8 1 2 3 -> 8 3 4 3 , 14 6 7 9 ->= 6 13 , 8 1 2 5 -> 8 3 4 5 , 11 18 16 12 ->= 6 7 , 14 6 7 14 ->= 6 7 , 9 10 ->= 14 9 10 11 12 14 , 8 1 2 15 -> 8 3 4 15 , 14 9 10 11 ->= 6 16 , 14 6 7 11 ->= 6 16 , 19 1 2 0 -> 19 3 4 0 , 12 6 7 8 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 12 6 7 9 ->= 18 13 , 19 1 2 5 -> 19 3 4 5 , 12 6 7 14 ->= 18 7 , 19 1 2 15 -> 19 3 4 15 , 12 6 7 11 ->= 18 16 } 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 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 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 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 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 | | 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 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 | \ / 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 1 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 | | 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 | \ / 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 1 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 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 2 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 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 | \ / 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 1 0 0 0 0 0 0 1 | | 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 1 0 0 0 0 0 0 0 | | 0 0 0 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 1 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 9->6, 10->7, 11->8, 12->9, 8->10, 15->11, 16->12, 13->13, 17->14, 7->15, 6->16, 14->17, 18->18, 19->19 }, it remains to prove termination of the 45-rule system { 0 1 2 0 -> 0 3 4 0 , 3 4 ->= 5 6 7 8 9 10 , 0 1 2 1 -> 0 3 4 1 , 0 1 2 3 -> 0 3 4 3 , 0 1 2 5 -> 0 3 4 5 , 0 1 2 11 -> 0 3 4 11 , 5 6 7 8 ->= 1 12 , 2 1 2 0 -> 2 3 4 0 , 2 1 2 1 -> 2 3 4 1 , 13 14 ->= 15 6 7 8 9 16 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 13 7 ->= 15 6 7 8 9 17 , 2 1 2 11 -> 2 3 4 11 , 4 1 2 0 -> 4 3 4 0 , 7 16 15 10 ->= 14 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 7 16 15 6 ->= 14 13 , 4 1 2 5 -> 4 3 4 5 , 7 16 15 17 ->= 14 15 , 4 1 2 11 -> 4 3 4 11 , 7 16 15 8 ->= 14 12 , 10 1 2 0 -> 10 3 4 0 , 17 16 15 10 ->= 16 2 , 10 1 2 1 -> 10 3 4 1 , 6 14 ->= 17 6 7 8 9 16 , 10 1 2 3 -> 10 3 4 3 , 17 16 15 6 ->= 16 13 , 10 1 2 5 -> 10 3 4 5 , 8 18 12 9 ->= 16 15 , 17 16 15 17 ->= 16 15 , 6 7 ->= 17 6 7 8 9 17 , 10 1 2 11 -> 10 3 4 11 , 17 6 7 8 ->= 16 12 , 17 16 15 8 ->= 16 12 , 19 1 2 0 -> 19 3 4 0 , 9 16 15 10 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 9 16 15 6 ->= 18 13 , 19 1 2 5 -> 19 3 4 5 , 9 16 15 17 ->= 18 15 , 19 1 2 11 -> 19 3 4 11 , 9 16 15 8 ->= 18 12 } 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 1 | | 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 1 | | 0 1 | \ / 8 is interpreted by / \ | 1 0 | | 0 1 | \ / 9 is interpreted by / \ | 1 0 | | 0 1 | \ / 10 is interpreted by / \ | 1 0 | | 0 1 | \ / 11 is interpreted by / \ | 1 0 | | 0 1 | \ / 12 is interpreted by / \ | 1 0 | | 0 1 | \ / 13 is interpreted by / \ | 1 0 | | 0 1 | \ / 14 is interpreted by / \ | 1 1 | | 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 | \ / 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 }, it remains to prove termination of the 44-rule system { 0 1 2 0 -> 0 3 4 0 , 3 4 ->= 5 6 7 8 9 10 , 0 1 2 1 -> 0 3 4 1 , 0 1 2 3 -> 0 3 4 3 , 0 1 2 5 -> 0 3 4 5 , 0 1 2 11 -> 0 3 4 11 , 5 6 7 8 ->= 1 12 , 2 1 2 0 -> 2 3 4 0 , 2 1 2 1 -> 2 3 4 1 , 13 14 ->= 15 6 7 8 9 16 , 2 1 2 3 -> 2 3 4 3 , 2 1 2 5 -> 2 3 4 5 , 13 7 ->= 15 6 7 8 9 17 , 2 1 2 11 -> 2 3 4 11 , 4 1 2 0 -> 4 3 4 0 , 7 16 15 10 ->= 14 2 , 4 1 2 1 -> 4 3 4 1 , 4 1 2 3 -> 4 3 4 3 , 7 16 15 6 ->= 14 13 , 4 1 2 5 -> 4 3 4 5 , 7 16 15 17 ->= 14 15 , 4 1 2 11 -> 4 3 4 11 , 7 16 15 8 ->= 14 12 , 10 1 2 0 -> 10 3 4 0 , 17 16 15 10 ->= 16 2 , 10 1 2 1 -> 10 3 4 1 , 6 14 ->= 17 6 7 8 9 16 , 10 1 2 3 -> 10 3 4 3 , 17 16 15 6 ->= 16 13 , 10 1 2 5 -> 10 3 4 5 , 8 18 12 9 ->= 16 15 , 17 16 15 17 ->= 16 15 , 6 7 ->= 17 6 7 8 9 17 , 10 1 2 11 -> 10 3 4 11 , 17 16 15 8 ->= 16 12 , 19 1 2 0 -> 19 3 4 0 , 9 16 15 10 ->= 18 2 , 19 1 2 1 -> 19 3 4 1 , 19 1 2 3 -> 19 3 4 3 , 9 16 15 6 ->= 18 13 , 19 1 2 5 -> 19 3 4 5 , 9 16 15 17 ->= 18 15 , 19 1 2 11 -> 19 3 4 11 , 9 16 15 8 ->= 18 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 1 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / After renaming modulo { 3->0, 4->1, 5->2, 6->3, 7->4, 8->5, 9->6, 10->7, 0->8, 1->9, 2->10, 11->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19 }, it remains to prove termination of the 43-rule system { 0 1 ->= 2 3 4 5 6 7 , 8 9 10 9 -> 8 0 1 9 , 8 9 10 0 -> 8 0 1 0 , 8 9 10 2 -> 8 0 1 2 , 8 9 10 11 -> 8 0 1 11 , 2 3 4 5 ->= 9 12 , 10 9 10 8 -> 10 0 1 8 , 10 9 10 9 -> 10 0 1 9 , 13 14 ->= 15 3 4 5 6 16 , 10 9 10 0 -> 10 0 1 0 , 10 9 10 2 -> 10 0 1 2 , 13 4 ->= 15 3 4 5 6 17 , 10 9 10 11 -> 10 0 1 11 , 1 9 10 8 -> 1 0 1 8 , 4 16 15 7 ->= 14 10 , 1 9 10 9 -> 1 0 1 9 , 1 9 10 0 -> 1 0 1 0 , 4 16 15 3 ->= 14 13 , 1 9 10 2 -> 1 0 1 2 , 4 16 15 17 ->= 14 15 , 1 9 10 11 -> 1 0 1 11 , 4 16 15 5 ->= 14 12 , 7 9 10 8 -> 7 0 1 8 , 17 16 15 7 ->= 16 10 , 7 9 10 9 -> 7 0 1 9 , 3 14 ->= 17 3 4 5 6 16 , 7 9 10 0 -> 7 0 1 0 , 17 16 15 3 ->= 16 13 , 7 9 10 2 -> 7 0 1 2 , 5 18 12 6 ->= 16 15 , 17 16 15 17 ->= 16 15 , 3 4 ->= 17 3 4 5 6 17 , 7 9 10 11 -> 7 0 1 11 , 17 16 15 5 ->= 16 12 , 19 9 10 8 -> 19 0 1 8 , 6 16 15 7 ->= 18 10 , 19 9 10 9 -> 19 0 1 9 , 19 9 10 0 -> 19 0 1 0 , 6 16 15 3 ->= 18 13 , 19 9 10 2 -> 19 0 1 2 , 6 16 15 17 ->= 18 15 , 19 9 10 11 -> 19 0 1 11 , 6 16 15 5 ->= 18 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16, 11->17, 18->18, 19->19 }, it remains to prove termination of the 42-rule system { 0 1 ->= 2 3 4 5 6 7 , 8 9 10 9 -> 8 0 1 9 , 8 9 10 0 -> 8 0 1 0 , 8 9 10 2 -> 8 0 1 2 , 2 3 4 5 ->= 9 11 , 10 9 10 8 -> 10 0 1 8 , 10 9 10 9 -> 10 0 1 9 , 12 13 ->= 14 3 4 5 6 15 , 10 9 10 0 -> 10 0 1 0 , 10 9 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 10 9 10 17 -> 10 0 1 17 , 1 9 10 8 -> 1 0 1 8 , 4 15 14 7 ->= 13 10 , 1 9 10 9 -> 1 0 1 9 , 1 9 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 9 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 1 9 10 17 -> 1 0 1 17 , 4 15 14 5 ->= 13 11 , 7 9 10 8 -> 7 0 1 8 , 16 15 14 7 ->= 15 10 , 7 9 10 9 -> 7 0 1 9 , 3 13 ->= 16 3 4 5 6 15 , 7 9 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 9 10 2 -> 7 0 1 2 , 5 18 11 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 7 9 10 17 -> 7 0 1 17 , 16 15 14 5 ->= 15 11 , 19 9 10 8 -> 19 0 1 8 , 6 15 14 7 ->= 18 10 , 19 9 10 9 -> 19 0 1 9 , 19 9 10 0 -> 19 0 1 0 , 6 15 14 3 ->= 18 12 , 19 9 10 2 -> 19 0 1 2 , 6 15 14 16 ->= 18 14 , 19 9 10 17 -> 19 0 1 17 , 6 15 14 5 ->= 18 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 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 41-rule system { 0 1 ->= 2 3 4 5 6 7 , 8 9 10 9 -> 8 0 1 9 , 8 9 10 0 -> 8 0 1 0 , 8 9 10 2 -> 8 0 1 2 , 2 3 4 5 ->= 9 11 , 10 9 10 8 -> 10 0 1 8 , 10 9 10 9 -> 10 0 1 9 , 12 13 ->= 14 3 4 5 6 15 , 10 9 10 0 -> 10 0 1 0 , 10 9 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 10 9 10 17 -> 10 0 1 17 , 1 9 10 8 -> 1 0 1 8 , 4 15 14 7 ->= 13 10 , 1 9 10 9 -> 1 0 1 9 , 1 9 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 9 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 1 9 10 17 -> 1 0 1 17 , 4 15 14 5 ->= 13 11 , 7 9 10 8 -> 7 0 1 8 , 16 15 14 7 ->= 15 10 , 7 9 10 9 -> 7 0 1 9 , 3 13 ->= 16 3 4 5 6 15 , 7 9 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 9 10 2 -> 7 0 1 2 , 5 18 11 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 7 9 10 17 -> 7 0 1 17 , 16 15 14 5 ->= 15 11 , 6 15 14 7 ->= 18 10 , 19 9 10 9 -> 19 0 1 9 , 19 9 10 0 -> 19 0 1 0 , 6 15 14 3 ->= 18 12 , 19 9 10 2 -> 19 0 1 2 , 6 15 14 16 ->= 18 14 , 19 9 10 17 -> 19 0 1 17 , 6 15 14 5 ->= 18 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 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 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 }, it remains to prove termination of the 40-rule system { 0 1 ->= 2 3 4 5 6 7 , 8 9 10 9 -> 8 0 1 9 , 8 9 10 0 -> 8 0 1 0 , 8 9 10 2 -> 8 0 1 2 , 2 3 4 5 ->= 9 11 , 10 9 10 8 -> 10 0 1 8 , 10 9 10 9 -> 10 0 1 9 , 12 13 ->= 14 3 4 5 6 15 , 10 9 10 0 -> 10 0 1 0 , 10 9 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 10 9 10 17 -> 10 0 1 17 , 1 9 10 8 -> 1 0 1 8 , 4 15 14 7 ->= 13 10 , 1 9 10 9 -> 1 0 1 9 , 1 9 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 9 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 1 9 10 17 -> 1 0 1 17 , 4 15 14 5 ->= 13 11 , 7 9 10 8 -> 7 0 1 8 , 16 15 14 7 ->= 15 10 , 7 9 10 9 -> 7 0 1 9 , 3 13 ->= 16 3 4 5 6 15 , 7 9 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 9 10 2 -> 7 0 1 2 , 5 18 11 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 7 9 10 17 -> 7 0 1 17 , 16 15 14 5 ->= 15 11 , 6 15 14 7 ->= 18 10 , 19 9 10 9 -> 19 0 1 9 , 19 9 10 0 -> 19 0 1 0 , 6 15 14 3 ->= 18 12 , 19 9 10 2 -> 19 0 1 2 , 6 15 14 16 ->= 18 14 , 6 15 14 5 ->= 18 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 1 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 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 1 0 | | 0 0 0 0 0 | | 0 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 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 9->8, 11->9, 10->10, 8->11, 12->12, 13->13, 14->14, 15->15, 16->16, 17->17, 18->18, 19->19 }, it remains to prove termination of the 37-rule system { 0 1 ->= 2 3 4 5 6 7 , 2 3 4 5 ->= 8 9 , 10 8 10 11 -> 10 0 1 11 , 10 8 10 8 -> 10 0 1 8 , 12 13 ->= 14 3 4 5 6 15 , 10 8 10 0 -> 10 0 1 0 , 10 8 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 10 8 10 17 -> 10 0 1 17 , 1 8 10 11 -> 1 0 1 11 , 4 15 14 7 ->= 13 10 , 1 8 10 8 -> 1 0 1 8 , 1 8 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 8 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 1 8 10 17 -> 1 0 1 17 , 4 15 14 5 ->= 13 9 , 7 8 10 11 -> 7 0 1 11 , 16 15 14 7 ->= 15 10 , 7 8 10 8 -> 7 0 1 8 , 3 13 ->= 16 3 4 5 6 15 , 7 8 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 8 10 2 -> 7 0 1 2 , 5 18 9 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 7 8 10 17 -> 7 0 1 17 , 16 15 14 5 ->= 15 9 , 6 15 14 7 ->= 18 10 , 19 8 10 8 -> 19 0 1 8 , 19 8 10 0 -> 19 0 1 0 , 6 15 14 3 ->= 18 12 , 19 8 10 2 -> 19 0 1 2 , 6 15 14 16 ->= 18 14 , 6 15 14 5 ->= 18 9 } 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 1 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 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 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 18 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 19 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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 }, it remains to prove termination of the 34-rule system { 0 1 ->= 2 3 4 5 6 7 , 2 3 4 5 ->= 8 9 , 10 8 10 11 -> 10 0 1 11 , 10 8 10 8 -> 10 0 1 8 , 12 13 ->= 14 3 4 5 6 15 , 10 8 10 0 -> 10 0 1 0 , 10 8 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 10 8 10 17 -> 10 0 1 17 , 1 8 10 11 -> 1 0 1 11 , 4 15 14 7 ->= 13 10 , 1 8 10 8 -> 1 0 1 8 , 1 8 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 8 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 1 8 10 17 -> 1 0 1 17 , 4 15 14 5 ->= 13 9 , 7 8 10 11 -> 7 0 1 11 , 16 15 14 7 ->= 15 10 , 7 8 10 8 -> 7 0 1 8 , 3 13 ->= 16 3 4 5 6 15 , 7 8 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 8 10 2 -> 7 0 1 2 , 5 18 9 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 7 8 10 17 -> 7 0 1 17 , 16 15 14 5 ->= 15 9 , 6 15 14 7 ->= 18 10 , 6 15 14 3 ->= 18 12 , 6 15 14 16 ->= 18 14 , 6 15 14 5 ->= 18 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 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 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 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / 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 }, it remains to prove termination of the 31-rule system { 0 1 ->= 2 3 4 5 6 7 , 2 3 4 5 ->= 8 9 , 10 8 10 11 -> 10 0 1 11 , 10 8 10 8 -> 10 0 1 8 , 12 13 ->= 14 3 4 5 6 15 , 10 8 10 0 -> 10 0 1 0 , 10 8 10 2 -> 10 0 1 2 , 12 4 ->= 14 3 4 5 6 16 , 1 8 10 11 -> 1 0 1 11 , 4 15 14 7 ->= 13 10 , 1 8 10 8 -> 1 0 1 8 , 1 8 10 0 -> 1 0 1 0 , 4 15 14 3 ->= 13 12 , 1 8 10 2 -> 1 0 1 2 , 4 15 14 16 ->= 13 14 , 4 15 14 5 ->= 13 9 , 7 8 10 11 -> 7 0 1 11 , 16 15 14 7 ->= 15 10 , 7 8 10 8 -> 7 0 1 8 , 3 13 ->= 16 3 4 5 6 15 , 7 8 10 0 -> 7 0 1 0 , 16 15 14 3 ->= 15 12 , 7 8 10 2 -> 7 0 1 2 , 5 17 9 6 ->= 15 14 , 16 15 14 16 ->= 15 14 , 3 4 ->= 16 3 4 5 6 16 , 16 15 14 5 ->= 15 9 , 6 15 14 7 ->= 17 10 , 6 15 14 3 ->= 17 12 , 6 15 14 16 ->= 17 14 , 6 15 14 5 ->= 17 9 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 5: 0 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 6 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 7 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 8 is interpreted by / \ | 1 0 0 1 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 1 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 12 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 13 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 14 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 15 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 16 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 17 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 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, 12->11, 13->12, 14->13, 15->14, 16->15, 17->16 }, it remains to prove termination of the 28-rule system { 0 1 ->= 2 3 4 5 6 7 , 2 3 4 5 ->= 8 9 , 10 8 10 8 -> 10 0 1 8 , 11 12 ->= 13 3 4 5 6 14 , 10 8 10 0 -> 10 0 1 0 , 10 8 10 2 -> 10 0 1 2 , 11 4 ->= 13 3 4 5 6 15 , 4 14 13 7 ->= 12 10 , 1 8 10 8 -> 1 0 1 8 , 1 8 10 0 -> 1 0 1 0 , 4 14 13 3 ->= 12 11 , 1 8 10 2 -> 1 0 1 2 , 4 14 13 15 ->= 12 13 , 4 14 13 5 ->= 12 9 , 15 14 13 7 ->= 14 10 , 7 8 10 8 -> 7 0 1 8 , 3 12 ->= 15 3 4 5 6 14 , 7 8 10 0 -> 7 0 1 0 , 15 14 13 3 ->= 14 11 , 7 8 10 2 -> 7 0 1 2 , 5 16 9 6 ->= 14 13 , 15 14 13 15 ->= 14 13 , 3 4 ->= 15 3 4 5 6 15 , 15 14 13 5 ->= 14 9 , 6 14 13 7 ->= 16 10 , 6 14 13 3 ->= 16 11 , 6 14 13 15 ->= 16 13 , 6 14 13 5 ->= 16 9 } 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 1 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 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 1 0 | | 0 0 0 0 0 | | 0 1 0 0 0 | \ / 9 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | \ / 10 is interpreted by / \ | 1 0 1 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 1 | | 0 0 0 0 0 | \ / 11 is interpreted by / \ | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 0 0 0 | | 0 0 0 0 0 | | 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5, 6->6, 7->7, 8->8, 9->9, 11->10, 12->11, 13->12, 14->13, 15->14, 10->15, 16->16 }, it remains to prove termination of the 19-rule system { 0 1 ->= 2 3 4 5 6 7 , 2 3 4 5 ->= 8 9 , 10 11 ->= 12 3 4 5 6 13 , 10 4 ->= 12 3 4 5 6 14 , 4 13 12 7 ->= 11 15 , 4 13 12 3 ->= 11 10 , 4 13 12 14 ->= 11 12 , 4 13 12 5 ->= 11 9 , 14 13 12 7 ->= 13 15 , 3 11 ->= 14 3 4 5 6 13 , 14 13 12 3 ->= 13 10 , 5 16 9 6 ->= 13 12 , 14 13 12 14 ->= 13 12 , 3 4 ->= 14 3 4 5 6 14 , 14 13 12 5 ->= 13 9 , 6 13 12 7 ->= 16 15 , 6 13 12 3 ->= 16 10 , 6 13 12 14 ->= 16 12 , 6 13 12 5 ->= 16 9 } The system is trivially terminating.