YES After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 92-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 5 2 4 0 0 3 2 0 -> 5 2 4 3 0 0 2 0 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 3 2 2 2 5 1 5 5 2 -> 3 2 5 2 1 2 5 5 2 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 0 4 1 2 3 5 4 0 1 3 -> 1 3 4 4 5 3 3 4 4 3 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 3 1 0 0 0 3 5 1 1 5 -> 1 3 1 1 4 5 3 4 1 4 , 4 1 3 0 5 0 5 1 3 5 -> 4 2 1 5 2 0 1 4 3 5 , 4 2 0 3 1 5 3 4 5 5 -> 4 1 3 3 4 4 4 3 4 2 , 0 2 1 1 1 2 3 3 2 3 5 -> 1 5 2 0 2 3 4 1 4 4 , 0 3 0 3 5 1 5 1 0 2 2 -> 0 2 3 1 2 0 0 5 3 5 1 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 3 5 1 1 0 1 3 0 2 -> 4 5 1 1 1 1 1 0 5 3 , 1 0 1 3 5 3 4 5 4 5 4 -> 2 4 3 4 0 0 1 5 2 1 , 1 2 4 2 2 5 5 5 5 3 4 -> 2 0 4 2 4 0 3 1 4 1 , 1 3 1 4 0 3 2 0 5 3 4 -> 1 3 2 4 1 0 1 4 5 1 , 1 3 5 5 1 5 4 1 3 5 4 -> 2 4 3 5 3 3 0 5 2 2 , 2 0 3 3 0 1 5 2 3 2 5 -> 5 3 0 3 4 1 5 0 1 3 , 2 0 4 3 0 5 0 0 4 4 5 -> 4 1 1 5 5 2 0 4 2 4 , 2 0 4 4 3 2 5 4 1 4 3 -> 3 3 1 5 4 3 0 1 4 2 , 2 1 3 4 1 1 2 5 0 3 2 -> 4 1 3 1 2 0 3 2 3 0 , 2 4 0 5 0 3 1 4 1 4 4 -> 1 5 1 3 0 3 3 3 2 3 , 2 5 2 3 5 3 1 3 1 3 2 -> 5 3 0 3 2 0 3 4 1 5 , 3 0 3 3 0 4 4 5 5 4 0 -> 2 1 4 4 4 0 0 5 1 2 , 3 0 4 5 0 2 1 5 4 5 2 -> 5 2 4 1 1 3 2 4 2 5 , 3 1 0 5 5 5 5 1 0 3 4 -> 0 1 5 4 1 3 5 5 0 4 , 3 1 1 1 0 0 1 5 2 2 1 -> 4 5 5 1 0 3 2 5 1 0 , 3 1 5 2 4 4 5 0 0 3 5 -> 5 2 1 4 2 1 1 2 5 0 , 3 2 2 3 5 2 1 1 3 0 5 -> 2 5 4 3 3 0 1 1 4 2 , 3 4 0 4 0 2 3 1 4 0 5 -> 0 1 3 3 1 5 5 3 5 1 , 3 4 2 3 5 4 3 4 5 4 1 -> 1 4 1 1 1 4 4 0 1 4 , 3 5 3 5 5 3 4 4 1 5 3 -> 1 5 1 5 1 2 4 4 5 0 , 3 5 5 3 1 2 0 5 2 0 1 -> 2 4 4 0 2 0 1 5 4 1 , 4 0 5 2 5 5 1 0 3 3 5 -> 3 4 1 0 2 1 4 2 1 2 , 4 1 2 4 1 4 0 4 1 5 5 -> 4 5 2 3 0 3 4 5 3 1 , 4 2 5 4 0 5 0 3 3 1 1 -> 4 3 0 2 4 4 0 3 3 0 , 4 4 2 4 1 2 0 4 5 2 5 -> 1 2 2 3 2 0 0 4 2 3 , 4 5 0 4 1 5 2 0 5 2 3 -> 3 4 5 3 5 5 3 5 2 2 , 4 5 0 4 2 3 0 4 3 1 5 -> 5 4 4 2 0 2 4 4 0 2 , 4 5 2 0 4 4 5 0 5 4 2 -> 1 4 0 2 2 1 2 4 2 1 , 4 5 2 3 0 2 0 3 5 2 2 -> 3 3 3 0 2 1 2 3 5 1 , 4 5 4 0 5 2 5 5 4 5 2 -> 2 2 0 5 0 3 4 2 3 1 , 5 0 1 5 5 5 4 3 0 3 1 -> 3 5 0 0 0 5 2 4 0 0 , 5 0 5 0 1 0 1 2 4 4 3 -> 5 5 5 0 4 3 4 0 3 5 , 5 1 2 5 4 0 3 0 2 3 0 -> 1 3 5 1 2 3 5 3 1 5 , 5 2 2 2 0 0 3 2 5 2 4 -> 2 2 3 2 2 3 0 1 5 5 , 5 2 3 3 2 3 0 1 3 0 2 -> 4 3 0 2 4 0 2 0 2 2 , 5 3 1 0 2 5 0 0 5 5 5 -> 1 2 4 4 3 3 4 0 5 3 , 5 4 3 4 1 2 4 2 5 1 1 -> 3 5 2 1 1 4 4 3 0 5 , 5 4 3 4 1 5 1 2 1 0 1 -> 5 5 5 5 4 3 0 3 1 3 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 1 2 1 1 5 2 0 4 3 2 3 4 -> 4 3 4 5 0 2 5 3 0 3 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 3 1 1 4 3 0 5 1 0 0 4 4 -> 5 1 2 0 2 2 2 1 2 1 , 4 0 4 3 2 3 1 1 2 0 5 3 -> 0 3 5 5 0 0 3 0 5 5 , 4 4 1 3 4 0 0 2 4 2 3 0 -> 0 0 0 3 1 5 5 3 1 3 , 5 2 4 4 2 5 4 3 3 2 4 4 -> 1 3 1 5 1 0 0 4 4 2 , 5 4 2 3 1 4 4 0 1 5 5 0 -> 2 3 2 5 4 1 5 4 0 4 , 5 4 4 1 4 2 3 4 1 2 3 3 -> 5 1 2 2 1 1 3 3 2 2 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 1 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 46-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 5 2 4 0 0 3 2 0 -> 5 2 4 3 0 0 2 0 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 3 2 2 2 5 1 5 5 2 -> 3 2 5 2 1 2 5 5 2 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 0 4 1 2 3 5 4 0 1 3 -> 1 3 4 4 5 3 3 4 4 3 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 3 1 0 0 0 3 5 1 1 5 -> 1 3 1 1 4 5 3 4 1 4 , 4 1 3 0 5 0 5 1 3 5 -> 4 2 1 5 2 0 1 4 3 5 , 4 2 0 3 1 5 3 4 5 5 -> 4 1 3 3 4 4 4 3 4 2 , 0 3 0 3 5 1 5 1 0 2 2 -> 0 2 3 1 2 0 0 5 3 5 1 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 2: 0 is interpreted by / \ | 1 1 | | 0 1 | \ / 1 is interpreted by / \ | 1 1 | | 0 1 | \ / 2 is interpreted by / \ | 1 1 | | 0 1 | \ / 3 is interpreted by / \ | 1 1 | | 0 1 | \ / 4 is interpreted by / \ | 1 0 | | 0 1 | \ / 5 is interpreted by / \ | 1 1 | | 0 1 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 42-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 5 2 4 0 0 3 2 0 -> 5 2 4 3 0 0 2 0 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 3 2 2 2 5 1 5 5 2 -> 3 2 5 2 1 2 5 5 2 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 3 0 3 5 1 5 1 0 2 2 -> 0 2 3 1 2 0 0 5 3 5 1 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } 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 1 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 | | 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 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 41-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 3 2 2 2 5 1 5 5 2 -> 3 2 5 2 1 2 5 5 2 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 3 0 3 5 1 5 1 0 2 2 -> 0 2 3 1 2 0 0 5 3 5 1 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 40-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 3 0 3 5 1 5 1 0 2 2 -> 0 2 3 1 2 0 0 5 3 5 1 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 39-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 1 3 3 4 1 5 3 4 4 -> 1 3 3 4 1 3 5 4 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 10: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 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 }, it remains to prove termination of the 38-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 2 2 4 5 0 2 5 4 0 1 4 4 -> 2 2 4 5 0 5 2 4 1 0 4 4 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 13: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 37-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 0 3 1 4 4 2 0 3 3 1 5 1 4 3 1 2 -> 0 3 1 4 4 2 3 0 3 1 5 1 4 3 1 2 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 17: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 36-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 1 3 1 4 1 0 0 5 0 3 4 4 0 1 4 3 -> 1 3 1 4 1 0 0 5 3 0 4 4 0 1 4 3 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 17: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 35-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 4 3 2 4 5 2 0 4 0 3 0 0 2 3 2 2 -> 4 3 2 4 5 2 0 4 3 0 0 0 2 3 2 2 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 17: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 34-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 2 3 1 4 3 3 3 0 1 3 4 0 2 5 1 2 2 1 -> 2 3 1 4 3 3 3 0 1 3 0 4 2 5 1 2 2 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 19: 0 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 33-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 2 3 5 2 4 2 3 2 2 2 4 5 4 1 5 1 0 1 -> 2 3 5 2 4 2 3 2 2 2 5 4 4 1 5 1 0 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 19: 0 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 is interpreted by / \ | 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 32-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 5 3 4 3 1 1 4 4 3 0 2 5 3 0 5 3 4 2 2 -> 5 3 4 3 1 1 4 4 3 2 0 5 3 0 5 3 4 2 2 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 20: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 31-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 2 5 3 1 2 0 1 5 4 2 1 2 5 3 3 2 1 4 4 4 5 2 -> 2 5 3 1 2 4 0 1 3 5 1 5 2 2 3 1 2 4 4 4 5 2 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 23: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 30-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 2 5 3 1 4 4 5 3 1 4 0 0 1 0 3 4 3 3 5 5 1 2 -> 2 5 3 1 4 4 5 3 1 4 0 0 1 0 4 3 3 3 5 5 1 2 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 23: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 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 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 29-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 0 3 2 3 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 -> 0 0 3 3 2 4 2 2 1 4 5 4 3 5 0 4 4 1 2 3 2 5 3 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 28-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 3 0 4 4 0 0 5 3 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 -> 3 0 4 4 0 0 3 5 3 2 3 0 4 1 2 5 4 2 0 4 2 1 0 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 24: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 }, it remains to prove termination of the 27-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 0 3 1 2 2 0 2 5 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 -> 0 3 1 2 2 0 5 2 4 2 3 1 5 0 2 5 2 1 2 5 3 0 5 3 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 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 }, it remains to prove termination of the 26-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 4 1 5 3 1 0 0 3 4 5 4 4 4 5 0 1 2 3 3 3 1 2 1 1 -> 4 1 5 3 1 0 0 3 5 4 4 4 4 5 0 1 2 3 3 3 1 2 1 1 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 25: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 }, it remains to prove termination of the 25-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 1 1 2 1 1 5 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 -> 1 1 2 1 5 1 4 3 2 4 1 4 5 2 1 1 1 4 0 5 0 2 3 5 0 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 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 }, it remains to prove termination of the 24-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 4 5 1 3 5 4 0 4 1 5 1 4 0 5 1 1 0 0 2 1 0 0 3 3 1 -> 4 5 1 3 5 4 0 4 1 1 5 4 0 5 1 1 0 0 2 1 0 0 3 3 1 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 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 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0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 }, it remains to prove termination of the 23-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 5 1 3 0 1 1 -> 5 3 5 4 1 4 4 2 1 5 2 5 1 1 1 4 4 2 4 1 5 3 0 1 1 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 26: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 }, it remains to prove termination of the 22-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 3 4 2 1 2 3 3 1 3 3 5 2 4 5 5 2 4 0 5 4 2 4 3 2 1 0 -> 3 2 4 3 4 3 2 1 1 3 5 2 2 3 0 1 4 5 2 5 4 3 5 4 2 0 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 27: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 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 }, it remains to prove termination of the 21-rule system { 0 1 2 2 0 3 2 4 -> 0 1 2 2 3 2 0 4 , 0 0 4 1 5 4 3 4 5 5 -> 0 0 4 1 5 3 4 4 5 5 , 2 3 2 5 5 1 2 0 3 2 -> 2 3 2 5 1 5 2 0 3 2 , 0 4 1 4 4 1 1 4 5 3 5 -> 0 4 1 4 4 1 5 1 4 3 5 , 0 4 5 3 3 2 2 4 5 5 1 -> 0 4 5 3 2 3 2 4 5 5 1 , 0 5 5 5 2 3 5 2 2 0 2 0 -> 0 5 2 5 2 5 3 5 2 0 2 0 , 5 4 5 3 4 3 1 2 4 0 5 2 5 -> 5 5 3 4 4 1 3 2 4 2 5 0 5 , 5 0 5 4 5 4 5 5 4 0 0 5 0 0 -> 5 0 5 4 5 4 5 5 0 4 0 5 0 0 , 2 0 3 0 5 4 1 0 5 1 2 0 2 4 1 1 -> 2 0 5 3 0 4 1 0 5 1 2 2 0 4 1 1 , 0 2 5 2 5 0 2 5 0 5 4 0 1 3 1 0 4 3 1 2 1 3 2 -> 0 2 5 2 5 0 2 5 5 0 4 1 0 3 1 0 4 3 1 1 2 3 2 , 1 2 5 4 3 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 -> 1 2 5 3 4 3 1 0 1 4 3 1 0 4 5 3 0 0 4 0 0 4 2 4 5 5 , 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 2 0 4 1 0 1 2 0 0 4 -> 5 1 2 2 3 5 1 1 2 4 1 2 2 1 3 4 0 2 4 1 0 1 2 0 0 4 , 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 5 4 0 4 5 1 5 5 -> 2 2 5 4 5 1 4 3 4 5 5 0 0 0 0 1 5 1 0 4 5 0 4 5 1 5 5 , 4 3 4 0 3 2 0 3 2 2 2 2 4 0 4 4 4 4 0 2 4 1 1 0 4 4 0 -> 4 3 4 0 0 2 3 2 3 2 2 4 2 4 4 4 0 1 0 4 4 2 0 4 1 4 0 , 5 1 2 4 5 2 5 1 4 3 1 1 5 1 0 5 1 3 0 4 5 5 5 4 5 1 0 0 -> 5 1 2 4 5 2 5 1 4 3 1 5 1 1 0 1 5 3 0 4 5 5 4 5 5 0 1 0 , 3 3 2 3 5 4 2 3 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 -> 3 2 3 3 5 4 3 2 3 1 0 3 3 4 5 3 1 5 1 5 3 2 1 3 5 1 2 5 3 , 4 1 5 5 3 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 -> 4 1 5 3 5 2 0 3 3 2 4 0 3 4 2 2 0 5 2 5 1 4 2 0 1 5 5 0 3 , 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 1 3 0 4 4 0 3 5 5 1 1 4 2 3 -> 4 5 4 3 2 0 2 2 4 0 0 1 5 4 4 3 1 0 4 4 0 3 5 5 1 1 4 2 3 , 0 1 0 3 4 2 1 0 4 0 2 5 4 5 1 5 5 0 3 4 1 0 2 4 5 4 3 1 3 4 -> 0 0 1 3 4 2 1 4 0 0 2 5 4 5 1 5 5 0 3 1 4 0 2 4 5 4 3 1 3 4 , 2 5 4 2 1 5 0 1 4 2 0 5 1 0 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 -> 2 5 4 2 1 5 0 1 4 2 0 5 0 1 1 3 2 4 1 2 4 0 5 5 4 3 5 5 0 1 , 4 0 5 2 0 2 0 4 5 3 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 -> 4 0 5 2 0 2 0 4 3 5 4 5 1 3 4 1 5 0 3 4 4 0 0 3 2 3 3 1 5 4 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 9: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 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 | \ / 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 1 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 | | 0 0 0 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, 4->1, 1->2, 5->3, 3->4, 2->5 }, it remains to prove termination of the 20-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 1 2 1 1 2 2 1 3 4 3 -> 0 1 2 1 1 2 3 2 1 4 3 , 0 1 3 4 4 5 5 1 3 3 2 -> 0 1 3 4 5 4 5 1 3 3 2 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 5 0 4 0 3 1 2 0 3 2 5 0 5 1 2 2 -> 5 0 3 4 0 1 2 0 3 2 5 5 0 1 2 2 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 5 0 1 2 0 2 5 0 0 1 -> 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 0 5 1 2 0 2 5 0 0 1 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 1 4 1 0 4 5 0 4 5 5 5 5 1 0 1 1 1 1 0 5 1 2 2 0 1 1 0 -> 1 4 1 0 0 5 4 5 4 5 5 1 5 1 1 1 0 2 0 1 1 5 0 1 2 1 0 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 }, it remains to prove termination of the 19-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 1 3 4 4 5 5 1 3 3 2 -> 0 1 3 4 5 4 5 1 3 3 2 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 5 0 4 0 3 1 2 0 3 2 5 0 5 1 2 2 -> 5 0 3 4 0 1 2 0 3 2 5 5 0 1 2 2 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 5 0 1 2 0 2 5 0 0 1 -> 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 0 5 1 2 0 2 5 0 0 1 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 1 4 1 0 4 5 0 4 5 5 5 5 1 0 1 1 1 1 0 5 1 2 2 0 1 1 0 -> 1 4 1 0 0 5 4 5 4 5 5 1 5 1 1 1 0 2 0 1 1 5 0 1 2 1 0 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 12: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 | | 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 }, it remains to prove termination of the 18-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 5 0 4 0 3 1 2 0 3 2 5 0 5 1 2 2 -> 5 0 3 4 0 1 2 0 3 2 5 5 0 1 2 2 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 5 0 1 2 0 2 5 0 0 1 -> 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 0 5 1 2 0 2 5 0 0 1 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 1 4 1 0 4 5 0 4 5 5 5 5 1 0 1 1 1 1 0 5 1 2 2 0 1 1 0 -> 1 4 1 0 0 5 4 5 4 5 5 1 5 1 1 1 0 2 0 1 1 5 0 1 2 1 0 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 17: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 17-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 5 0 1 2 0 2 5 0 0 1 -> 3 2 5 5 4 3 2 2 5 1 2 5 5 2 4 1 0 5 1 2 0 2 5 0 0 1 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 1 4 1 0 4 5 0 4 5 5 5 5 1 0 1 1 1 1 0 5 1 2 2 0 1 1 0 -> 1 4 1 0 0 5 4 5 4 5 5 1 5 1 1 1 0 2 0 1 1 5 0 1 2 1 0 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 27: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 16-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 1 4 1 0 4 5 0 4 5 5 5 5 1 0 1 1 1 1 0 5 1 2 2 0 1 1 0 -> 1 4 1 0 0 5 4 5 4 5 5 1 5 1 1 1 0 2 0 1 1 5 0 1 2 1 0 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 28: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 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 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 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 1 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 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 }, it remains to prove termination of the 15-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 2 3 3 4 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 -> 1 2 3 4 3 5 0 4 4 5 1 0 4 1 5 5 0 3 5 3 2 1 5 0 2 3 3 0 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 30: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 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 }, it remains to prove termination of the 14-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 2 4 0 1 1 0 4 3 3 2 2 1 5 4 -> 1 3 1 4 5 0 5 5 1 0 0 2 3 1 1 4 2 0 1 1 0 4 3 3 2 2 1 5 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 30: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / After renaming modulo { 0->0, 1->1, 2->2, 3->3, 4->4, 5->5 }, it remains to prove termination of the 13-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 5 3 1 5 2 3 0 2 1 5 0 3 2 0 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 -> 5 3 1 5 2 3 0 2 1 5 0 3 0 2 2 4 5 1 2 5 1 0 3 3 1 4 3 3 0 2 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 , 1 0 3 5 0 5 0 1 3 4 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 -> 1 0 3 5 0 5 0 1 4 3 1 3 2 4 1 2 3 0 4 1 1 0 0 4 5 4 4 2 3 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 31: 0 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 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 1 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 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 }, it remains to prove termination of the 11-rule system { 0 0 1 2 3 1 4 1 3 3 -> 0 0 1 2 3 4 1 1 3 3 , 5 4 5 3 3 2 5 0 4 5 -> 5 4 5 3 2 3 5 0 4 5 , 0 3 3 3 5 4 3 5 5 0 5 0 -> 0 3 5 3 5 3 4 3 5 0 5 0 , 3 1 3 4 1 4 2 5 1 0 3 5 3 -> 3 3 4 1 1 2 4 5 1 5 3 0 3 , 3 0 3 1 3 1 3 3 1 0 0 3 0 0 -> 3 0 3 1 3 1 3 3 0 1 0 3 0 0 , 0 5 3 5 3 0 5 3 0 3 1 0 2 4 2 0 1 4 2 5 2 4 5 -> 0 5 3 5 3 0 5 3 3 0 1 2 0 4 2 0 1 4 2 2 5 4 5 , 2 5 3 1 4 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 -> 2 5 3 4 1 4 2 0 2 1 4 2 0 1 3 4 0 0 1 0 0 1 5 1 3 3 , 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 3 1 0 1 3 2 3 3 -> 5 5 3 1 3 2 1 4 1 3 3 0 0 0 0 2 3 2 0 1 3 0 1 3 2 3 3 , 3 2 5 1 3 5 3 2 1 4 2 2 3 2 0 3 2 4 0 1 3 3 3 1 3 2 0 0 -> 3 2 5 1 3 5 3 2 1 4 2 3 2 2 0 2 3 4 0 1 3 3 1 3 3 0 2 0 , 4 4 5 4 3 1 5 4 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 -> 4 5 4 4 3 1 4 5 4 2 0 4 4 1 3 4 2 3 2 3 4 5 2 4 3 2 5 3 4 , 0 2 0 4 1 5 2 0 1 0 5 3 1 3 2 3 3 0 4 1 2 0 5 1 3 1 4 2 4 1 -> 0 0 2 4 1 5 2 1 0 0 5 3 1 3 2 3 3 0 4 2 1 0 5 1 3 1 4 2 4 1 } The system was filtered by the following matrix interpretation of type E_J with J = {1,...,2} and dimension 11: 0 is interpreted by / \ | 1 0 1 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 1 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 1 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 1 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 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 1 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | \ / 2 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 1 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 3 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 1 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 1 | | 0 1 0 0 0 0 0 0 0 0 0 | \ / 4 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 1 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | \ / 5 is interpreted by / \ | 1 0 0 0 0 0 0 0 0 0 0 | | 0 1 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 0 0 | | 0 0 0 0 0 0 0 0 0 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 { 5->0, 4->1, 3->2, 2->3, 0->4, 1->5 }, it remains to prove termination of the 10-rule system { 0 1 0 2 2 3 0 4 1 0 -> 0 1 0 2 3 2 0 4 1 0 , 4 2 2 2 0 1 2 0 0 4 0 4 -> 4 2 0 2 0 2 1 2 0 4 0 4 , 2 5 2 1 5 1 3 0 5 4 2 0 2 -> 2 2 1 5 5 3 1 0 5 0 2 4 2 , 2 4 2 5 2 5 2 2 5 4 4 2 4 4 -> 2 4 2 5 2 5 2 2 4 5 4 2 4 4 , 4 0 2 0 2 4 0 2 4 2 5 4 3 1 3 4 5 1 3 0 3 1 0 -> 4 0 2 0 2 4 0 2 2 4 5 3 4 1 3 4 5 1 3 3 0 1 0 , 3 0 2 5 1 1 3 4 3 5 1 3 4 5 2 1 4 4 5 4 4 5 0 5 2 2 -> 3 0 2 1 5 1 3 4 3 5 1 3 4 5 2 1 4 4 5 4 4 5 0 5 2 2 , 0 0 2 5 2 3 5 1 5 2 2 4 4 4 4 3 2 3 4 2 5 4 5 2 3 2 2 -> 0 0 2 5 2 3 5 1 5 2 2 4 4 4 4 3 2 3 4 5 2 4 5 2 3 2 2 , 2 3 0 5 2 0 2 3 5 1 3 3 2 3 4 2 3 1 4 5 2 2 2 5 2 3 4 4 -> 2 3 0 5 2 0 2 3 5 1 3 2 3 3 4 3 2 1 4 5 2 2 5 2 2 4 3 4 , 1 1 0 1 2 5 0 1 1 3 4 1 1 5 2 1 3 2 3 2 1 0 3 1 2 3 0 2 1 -> 1 0 1 1 2 5 1 0 1 3 4 1 1 5 2 1 3 2 3 2 1 0 3 1 2 3 0 2 1 , 4 3 4 1 5 0 3 4 5 4 0 2 5 2 3 2 2 4 1 5 3 4 0 5 2 5 1 3 1 5 -> 4 4 3 1 5 0 3 5 4 4 0 2 5 2 3 2 2 4 1 3 5 4 0 5 2 5 1 3 1 5 } The system was reversed. After renaming modulo { 0->0, 1->1, 4->2, 3->3, 2->4, 5->5 }, it remains to prove termination of the 10-rule system { 0 1 2 0 3 4 4 0 1 0 -> 0 1 2 0 4 3 4 0 1 0 , 2 0 2 0 0 4 1 0 4 4 4 2 -> 2 0 2 0 4 1 4 0 4 0 4 2 , 4 0 4 2 5 0 3 1 5 1 4 5 4 -> 4 2 4 0 5 0 1 3 5 5 1 4 4 , 2 2 4 2 2 5 4 4 5 4 5 4 2 4 -> 2 2 4 2 5 2 4 4 5 4 5 4 2 4 , 0 1 3 0 3 1 5 2 3 1 3 2 5 4 2 4 0 2 4 0 4 0 2 -> 0 1 0 3 3 1 5 2 3 1 2 3 5 2 4 4 0 2 4 0 4 0 2 , 4 4 5 0 5 2 2 5 2 2 1 4 5 2 3 1 5 3 2 3 1 1 5 4 0 3 -> 4 4 5 0 5 2 2 5 2 2 1 4 5 2 3 1 5 3 2 3 1 5 1 4 0 3 , 4 4 3 4 5 2 5 4 2 3 4 3 2 2 2 2 4 4 5 1 5 3 4 5 4 0 0 -> 4 4 3 4 5 2 4 5 2 3 4 3 2 2 2 2 4 4 5 1 5 3 4 5 4 0 0 , 2 2 3 4 5 4 4 4 5 2 1 3 4 2 3 4 3 3 1 5 3 4 0 4 5 0 3 4 -> 2 3 2 4 4 5 4 4 5 2 1 4 3 2 3 3 4 3 1 5 3 4 0 4 5 0 3 4 , 1 4 0 3 4 1 3 0 1 4 3 4 3 1 4 5 1 1 2 3 1 1 0 5 4 1 0 1 1 -> 1 4 0 3 4 1 3 0 1 4 3 4 3 1 4 5 1 1 2 3 1 0 1 5 4 1 1 0 1 , 5 1 3 1 5 4 5 0 2 3 5 1 2 4 4 3 4 5 4 0 2 5 2 3 0 5 1 2 3 2 -> 5 1 3 1 5 4 5 0 2 5 3 1 2 4 4 3 4 5 4 0 2 2 5 3 0 5 1 3 2 2 } Applying sparse 2-tiling [Hofbauer/Geser/Waldmann, FSCD 2019]. After renaming modulo { (0,0)->0, (0,1)->1, (1,2)->2, (2,0)->3, (0,3)->4, (3,4)->5, (4,4)->6, (4,0)->7, (1,0)->8, (0,4)->9, (4,3)->10, (0,2)->11, (0,5)->12, (0,7)->13, (3,0)->14, (5,0)->15, (6,0)->16, (4,1)->17, (4,2)->18, (1,4)->19, (2,1)->20, (2,2)->21, (2,3)->22, (2,4)->23, (2,5)->24, (2,7)->25, (3,2)->26, (5,2)->27, (6,2)->28, (3,1)->29, (1,5)->30, (5,1)->31, (4,5)->32, (5,4)->33, (1,3)->34, (3,5)->35, (5,5)->36, (4,7)->37, (6,4)->38, (3,3)->39, (5,3)->40, (1,1)->41, (3,7)->42, (1,7)->43, (6,1)->44, (6,5)->45 }, it remains to prove termination of the 490-rule system { 0 1 2 3 4 5 6 7 1 8 0 -> 0 1 2 3 9 10 5 7 1 8 0 , 0 1 2 3 4 5 6 7 1 8 1 -> 0 1 2 3 9 10 5 7 1 8 1 , 0 1 2 3 4 5 6 7 1 8 11 -> 0 1 2 3 9 10 5 7 1 8 11 , 0 1 2 3 4 5 6 7 1 8 4 -> 0 1 2 3 9 10 5 7 1 8 4 , 0 1 2 3 4 5 6 7 1 8 9 -> 0 1 2 3 9 10 5 7 1 8 9 , 0 1 2 3 4 5 6 7 1 8 12 -> 0 1 2 3 9 10 5 7 1 8 12 , 0 1 2 3 4 5 6 7 1 8 13 -> 0 1 2 3 9 10 5 7 1 8 13 , 8 1 2 3 4 5 6 7 1 8 0 -> 8 1 2 3 9 10 5 7 1 8 0 , 8 1 2 3 4 5 6 7 1 8 1 -> 8 1 2 3 9 10 5 7 1 8 1 , 8 1 2 3 4 5 6 7 1 8 11 -> 8 1 2 3 9 10 5 7 1 8 11 , 8 1 2 3 4 5 6 7 1 8 4 -> 8 1 2 3 9 10 5 7 1 8 4 , 8 1 2 3 4 5 6 7 1 8 9 -> 8 1 2 3 9 10 5 7 1 8 9 , 8 1 2 3 4 5 6 7 1 8 12 -> 8 1 2 3 9 10 5 7 1 8 12 , 8 1 2 3 4 5 6 7 1 8 13 -> 8 1 2 3 9 10 5 7 1 8 13 , 3 1 2 3 4 5 6 7 1 8 0 -> 3 1 2 3 9 10 5 7 1 8 0 , 3 1 2 3 4 5 6 7 1 8 1 -> 3 1 2 3 9 10 5 7 1 8 1 , 3 1 2 3 4 5 6 7 1 8 11 -> 3 1 2 3 9 10 5 7 1 8 11 , 3 1 2 3 4 5 6 7 1 8 4 -> 3 1 2 3 9 10 5 7 1 8 4 , 3 1 2 3 4 5 6 7 1 8 9 -> 3 1 2 3 9 10 5 7 1 8 9 , 3 1 2 3 4 5 6 7 1 8 12 -> 3 1 2 3 9 10 5 7 1 8 12 , 3 1 2 3 4 5 6 7 1 8 13 -> 3 1 2 3 9 10 5 7 1 8 13 , 14 1 2 3 4 5 6 7 1 8 0 -> 14 1 2 3 9 10 5 7 1 8 0 , 14 1 2 3 4 5 6 7 1 8 1 -> 14 1 2 3 9 10 5 7 1 8 1 , 14 1 2 3 4 5 6 7 1 8 11 -> 14 1 2 3 9 10 5 7 1 8 11 , 14 1 2 3 4 5 6 7 1 8 4 -> 14 1 2 3 9 10 5 7 1 8 4 , 14 1 2 3 4 5 6 7 1 8 9 -> 14 1 2 3 9 10 5 7 1 8 9 , 14 1 2 3 4 5 6 7 1 8 12 -> 14 1 2 3 9 10 5 7 1 8 12 , 14 1 2 3 4 5 6 7 1 8 13 -> 14 1 2 3 9 10 5 7 1 8 13 , 7 1 2 3 4 5 6 7 1 8 0 -> 7 1 2 3 9 10 5 7 1 8 0 , 7 1 2 3 4 5 6 7 1 8 1 -> 7 1 2 3 9 10 5 7 1 8 1 , 7 1 2 3 4 5 6 7 1 8 11 -> 7 1 2 3 9 10 5 7 1 8 11 , 7 1 2 3 4 5 6 7 1 8 4 -> 7 1 2 3 9 10 5 7 1 8 4 , 7 1 2 3 4 5 6 7 1 8 9 -> 7 1 2 3 9 10 5 7 1 8 9 , 7 1 2 3 4 5 6 7 1 8 12 -> 7 1 2 3 9 10 5 7 1 8 12 , 7 1 2 3 4 5 6 7 1 8 13 -> 7 1 2 3 9 10 5 7 1 8 13 , 15 1 2 3 4 5 6 7 1 8 0 -> 15 1 2 3 9 10 5 7 1 8 0 , 15 1 2 3 4 5 6 7 1 8 1 -> 15 1 2 3 9 10 5 7 1 8 1 , 15 1 2 3 4 5 6 7 1 8 11 -> 15 1 2 3 9 10 5 7 1 8 11 , 15 1 2 3 4 5 6 7 1 8 4 -> 15 1 2 3 9 10 5 7 1 8 4 , 15 1 2 3 4 5 6 7 1 8 9 -> 15 1 2 3 9 10 5 7 1 8 9 , 15 1 2 3 4 5 6 7 1 8 12 -> 15 1 2 3 9 10 5 7 1 8 12 , 15 1 2 3 4 5 6 7 1 8 13 -> 15 1 2 3 9 10 5 7 1 8 13 , 16 1 2 3 4 5 6 7 1 8 0 -> 16 1 2 3 9 10 5 7 1 8 0 , 16 1 2 3 4 5 6 7 1 8 1 -> 16 1 2 3 9 10 5 7 1 8 1 , 16 1 2 3 4 5 6 7 1 8 11 -> 16 1 2 3 9 10 5 7 1 8 11 , 16 1 2 3 4 5 6 7 1 8 4 -> 16 1 2 3 9 10 5 7 1 8 4 , 16 1 2 3 4 5 6 7 1 8 9 -> 16 1 2 3 9 10 5 7 1 8 9 , 16 1 2 3 4 5 6 7 1 8 12 -> 16 1 2 3 9 10 5 7 1 8 12 , 16 1 2 3 4 5 6 7 1 8 13 -> 16 1 2 3 9 10 5 7 1 8 13 , 11 3 11 3 0 9 17 8 9 6 6 18 3 -> 11 3 11 3 9 17 19 7 9 7 9 18 3 , 11 3 11 3 0 9 17 8 9 6 6 18 20 -> 11 3 11 3 9 17 19 7 9 7 9 18 20 , 11 3 11 3 0 9 17 8 9 6 6 18 21 -> 11 3 11 3 9 17 19 7 9 7 9 18 21 , 11 3 11 3 0 9 17 8 9 6 6 18 22 -> 11 3 11 3 9 17 19 7 9 7 9 18 22 , 11 3 11 3 0 9 17 8 9 6 6 18 23 -> 11 3 11 3 9 17 19 7 9 7 9 18 23 , 11 3 11 3 0 9 17 8 9 6 6 18 24 -> 11 3 11 3 9 17 19 7 9 7 9 18 24 , 11 3 11 3 0 9 17 8 9 6 6 18 25 -> 11 3 11 3 9 17 19 7 9 7 9 18 25 , 2 3 11 3 0 9 17 8 9 6 6 18 3 -> 2 3 11 3 9 17 19 7 9 7 9 18 3 , 2 3 11 3 0 9 17 8 9 6 6 18 20 -> 2 3 11 3 9 17 19 7 9 7 9 18 20 , 2 3 11 3 0 9 17 8 9 6 6 18 21 -> 2 3 11 3 9 17 19 7 9 7 9 18 21 , 2 3 11 3 0 9 17 8 9 6 6 18 22 -> 2 3 11 3 9 17 19 7 9 7 9 18 22 , 2 3 11 3 0 9 17 8 9 6 6 18 23 -> 2 3 11 3 9 17 19 7 9 7 9 18 23 , 2 3 11 3 0 9 17 8 9 6 6 18 24 -> 2 3 11 3 9 17 19 7 9 7 9 18 24 , 2 3 11 3 0 9 17 8 9 6 6 18 25 -> 2 3 11 3 9 17 19 7 9 7 9 18 25 , 21 3 11 3 0 9 17 8 9 6 6 18 3 -> 21 3 11 3 9 17 19 7 9 7 9 18 3 , 21 3 11 3 0 9 17 8 9 6 6 18 20 -> 21 3 11 3 9 17 19 7 9 7 9 18 20 , 21 3 11 3 0 9 17 8 9 6 6 18 21 -> 21 3 11 3 9 17 19 7 9 7 9 18 21 , 21 3 11 3 0 9 17 8 9 6 6 18 22 -> 21 3 11 3 9 17 19 7 9 7 9 18 22 , 21 3 11 3 0 9 17 8 9 6 6 18 23 -> 21 3 11 3 9 17 19 7 9 7 9 18 23 , 21 3 11 3 0 9 17 8 9 6 6 18 24 -> 21 3 11 3 9 17 19 7 9 7 9 18 24 , 21 3 11 3 0 9 17 8 9 6 6 18 25 -> 21 3 11 3 9 17 19 7 9 7 9 18 25 , 26 3 11 3 0 9 17 8 9 6 6 18 3 -> 26 3 11 3 9 17 19 7 9 7 9 18 3 , 26 3 11 3 0 9 17 8 9 6 6 18 20 -> 26 3 11 3 9 17 19 7 9 7 9 18 20 , 26 3 11 3 0 9 17 8 9 6 6 18 21 -> 26 3 11 3 9 17 19 7 9 7 9 18 21 , 26 3 11 3 0 9 17 8 9 6 6 18 22 -> 26 3 11 3 9 17 19 7 9 7 9 18 22 , 26 3 11 3 0 9 17 8 9 6 6 18 23 -> 26 3 11 3 9 17 19 7 9 7 9 18 23 , 26 3 11 3 0 9 17 8 9 6 6 18 24 -> 26 3 11 3 9 17 19 7 9 7 9 18 24 , 26 3 11 3 0 9 17 8 9 6 6 18 25 -> 26 3 11 3 9 17 19 7 9 7 9 18 25 , 18 3 11 3 0 9 17 8 9 6 6 18 3 -> 18 3 11 3 9 17 19 7 9 7 9 18 3 , 18 3 11 3 0 9 17 8 9 6 6 18 20 -> 18 3 11 3 9 17 19 7 9 7 9 18 20 , 18 3 11 3 0 9 17 8 9 6 6 18 21 -> 18 3 11 3 9 17 19 7 9 7 9 18 21 , 18 3 11 3 0 9 17 8 9 6 6 18 22 -> 18 3 11 3 9 17 19 7 9 7 9 18 22 , 18 3 11 3 0 9 17 8 9 6 6 18 23 -> 18 3 11 3 9 17 19 7 9 7 9 18 23 , 18 3 11 3 0 9 17 8 9 6 6 18 24 -> 18 3 11 3 9 17 19 7 9 7 9 18 24 , 18 3 11 3 0 9 17 8 9 6 6 18 25 -> 18 3 11 3 9 17 19 7 9 7 9 18 25 , 27 3 11 3 0 9 17 8 9 6 6 18 3 -> 27 3 11 3 9 17 19 7 9 7 9 18 3 , 27 3 11 3 0 9 17 8 9 6 6 18 20 -> 27 3 11 3 9 17 19 7 9 7 9 18 20 , 27 3 11 3 0 9 17 8 9 6 6 18 21 -> 27 3 11 3 9 17 19 7 9 7 9 18 21 , 27 3 11 3 0 9 17 8 9 6 6 18 22 -> 27 3 11 3 9 17 19 7 9 7 9 18 22 , 27 3 11 3 0 9 17 8 9 6 6 18 23 -> 27 3 11 3 9 17 19 7 9 7 9 18 23 , 27 3 11 3 0 9 17 8 9 6 6 18 24 -> 27 3 11 3 9 17 19 7 9 7 9 18 24 , 27 3 11 3 0 9 17 8 9 6 6 18 25 -> 27 3 11 3 9 17 19 7 9 7 9 18 25 , 28 3 11 3 0 9 17 8 9 6 6 18 3 -> 28 3 11 3 9 17 19 7 9 7 9 18 3 , 28 3 11 3 0 9 17 8 9 6 6 18 20 -> 28 3 11 3 9 17 19 7 9 7 9 18 20 , 28 3 11 3 0 9 17 8 9 6 6 18 21 -> 28 3 11 3 9 17 19 7 9 7 9 18 21 , 28 3 11 3 0 9 17 8 9 6 6 18 22 -> 28 3 11 3 9 17 19 7 9 7 9 18 22 , 28 3 11 3 0 9 17 8 9 6 6 18 23 -> 28 3 11 3 9 17 19 7 9 7 9 18 23 , 28 3 11 3 0 9 17 8 9 6 6 18 24 -> 28 3 11 3 9 17 19 7 9 7 9 18 24 , 28 3 11 3 0 9 17 8 9 6 6 18 25 -> 28 3 11 3 9 17 19 7 9 7 9 18 25 , 9 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 7 , 9 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 17 , 9 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 18 , 9 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 10 , 9 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 6 , 9 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 32 , 9 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 9 18 23 7 12 15 1 34 35 36 31 19 6 37 , 19 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 7 , 19 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 17 , 19 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 18 , 19 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 10 , 19 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 6 , 19 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 32 , 19 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 19 18 23 7 12 15 1 34 35 36 31 19 6 37 , 23 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 7 , 23 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 17 , 23 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 18 , 23 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 10 , 23 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 6 , 23 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 32 , 23 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 23 18 23 7 12 15 1 34 35 36 31 19 6 37 , 5 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 7 , 5 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 17 , 5 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 18 , 5 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 10 , 5 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 6 , 5 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 32 , 5 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 5 18 23 7 12 15 1 34 35 36 31 19 6 37 , 6 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 7 , 6 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 17 , 6 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 18 , 6 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 10 , 6 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 6 , 6 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 32 , 6 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 6 18 23 7 12 15 1 34 35 36 31 19 6 37 , 33 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 7 , 33 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 17 , 33 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 18 , 33 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 10 , 33 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 6 , 33 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 32 , 33 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 33 18 23 7 12 15 1 34 35 36 31 19 6 37 , 38 7 9 18 24 15 4 29 30 31 19 32 33 7 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 7 , 38 7 9 18 24 15 4 29 30 31 19 32 33 17 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 17 , 38 7 9 18 24 15 4 29 30 31 19 32 33 18 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 18 , 38 7 9 18 24 15 4 29 30 31 19 32 33 10 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 10 , 38 7 9 18 24 15 4 29 30 31 19 32 33 6 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 6 , 38 7 9 18 24 15 4 29 30 31 19 32 33 32 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 32 , 38 7 9 18 24 15 4 29 30 31 19 32 33 37 -> 38 18 23 7 12 15 1 34 35 36 31 19 6 37 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 11 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 11 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 2 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 2 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 21 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 21 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 26 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 26 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 18 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 18 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 27 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 27 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 7 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 7 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 17 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 17 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 18 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 18 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 10 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 10 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 6 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 6 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 32 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 32 , 28 21 23 18 21 24 33 6 32 33 32 33 18 23 37 -> 28 21 23 18 24 27 23 6 32 33 32 33 18 23 37 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 0 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 0 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 8 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 8 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 3 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 3 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 14 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 14 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 7 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 7 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 15 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 15 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 3 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 3 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 20 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 20 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 21 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 21 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 22 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 22 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 23 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 23 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 24 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 24 , 16 1 34 14 4 29 30 27 22 29 34 26 24 33 18 23 7 11 23 7 9 7 11 25 -> 16 1 8 4 39 29 30 27 22 29 2 22 35 27 23 6 7 11 23 7 9 7 11 25 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 9 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 19 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 23 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 5 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 6 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 33 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 14 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 14 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 29 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 29 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 26 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 26 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 39 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 39 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 5 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 5 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 35 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 35 , 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 41 30 33 7 4 42 -> 38 6 32 15 12 27 21 24 27 21 20 19 32 27 22 29 30 40 26 22 29 30 31 19 7 4 42 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 9 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 9 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 19 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 19 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 23 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 23 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 5 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 5 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 6 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 6 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 33 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 33 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 0 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 1 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 11 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 4 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 9 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 12 , 38 6 10 5 32 27 24 33 18 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 -> 38 6 10 5 32 27 23 32 27 22 5 10 26 21 21 21 23 6 32 31 30 40 5 32 33 7 0 13 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 7 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 7 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 17 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 17 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 18 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 18 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 10 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 10 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 6 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 6 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 32 -> 11 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 32 , 11 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 37 -> 11 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30 40 5 7 9 32 15 4 5 32 , 2 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 37 -> 2 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 37 , 21 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 7 -> 21 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 7 , 21 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 17 -> 21 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 17 , 21 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 18 -> 21 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 18 , 21 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 10 -> 21 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 10 , 21 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 6 -> 21 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 6 , 21 21 22 5 32 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28 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 18 -> 28 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 18 , 28 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 10 -> 28 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 10 , 28 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 6 -> 28 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 6 , 28 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 32 -> 28 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 32 , 28 21 22 5 32 33 6 6 32 27 20 34 5 18 22 5 10 39 29 30 40 5 7 9 32 15 4 5 37 -> 28 22 26 23 6 32 33 6 32 27 20 19 10 26 22 39 5 10 29 30 40 5 7 9 32 15 4 5 37 , 1 19 7 4 5 17 34 14 1 19 10 5 10 29 19 32 31 41 2 22 29 41 8 12 33 17 8 1 41 8 -> 1 19 7 4 5 17 34 14 1 19 10 5 10 29 19 32 31 41 2 22 29 8 1 30 33 17 41 8 1 8 , 1 19 7 4 5 17 34 14 1 19 10 5 10 29 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32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 3 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 3 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 20 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 20 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 21 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 21 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 22 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 22 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 23 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 23 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 24 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 24 , 32 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 25 -> 32 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 25 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 3 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 3 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 20 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 20 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 21 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 21 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 22 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 22 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 23 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 23 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 24 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 24 , 36 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 25 -> 36 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 25 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 3 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 3 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 20 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 20 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 21 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 21 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 22 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 22 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 23 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 23 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 24 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 24 , 45 31 34 29 30 33 32 15 11 22 35 31 2 23 6 10 5 32 33 7 11 24 27 22 14 12 31 2 22 26 25 -> 45 31 34 29 30 33 32 15 11 24 40 29 2 23 6 10 5 32 33 7 11 21 24 40 14 12 31 34 26 21 25 } 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 1 | | 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 1 | | 0 1 | \ / 7 is interpreted by / \ | 1 0 | | 0 1 | \ / 8 is interpreted by / \ | 1 1 | | 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 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 1 | | 0 1 | \ / 19 is interpreted by / \ | 1 0 | | 0 1 | \ / 20 is interpreted by / \ | 1 0 | | 0 1 | \ / 21 is interpreted by / \ | 1 1 | | 0 1 | \ / 22 is interpreted by / \ | 1 1 | | 0 1 | \ / 23 is interpreted by / \ | 1 0 | | 0 1 | \ / 24 is interpreted by / \ | 1 1 | | 0 1 | \ / 25 is interpreted by / \ | 1 0 | | 0 1 | \ / 26 is interpreted by / \ | 1 1 | | 0 1 | \ / 27 is interpreted by / \ | 1 1 | | 0 1 | \ / 28 is interpreted by / \ | 1 0 | | 0 1 | \ / 29 is interpreted by / \ | 1 1 | | 0 1 | \ / 30 is interpreted by / \ | 1 1 | | 0 1 | \ / 31 is interpreted by / \ | 1 1 | | 0 1 | \ / 32 is interpreted by / \ | 1 1 | | 0 1 | \ / 33 is interpreted by / \ | 1 1 | | 0 1 | \ / 34 is interpreted by / \ | 1 1 | | 0 1 | \ / 35 is interpreted by / \ | 1 1 | | 0 1 | \ / 36 is interpreted by / \ | 1 0 | | 0 1 | \ / 37 is interpreted by / \ | 1 0 | | 0 1 | \ / 38 is interpreted by / \ | 1 0 | | 0 1 | \ / 39 is interpreted by / \ | 1 0 | | 0 1 | \ / 40 is interpreted by / \ | 1 0 | | 0 1 | \ / 41 is interpreted by / \ | 1 1 | | 0 1 | \ / 42 is interpreted by / \ | 1 0 | | 0 1 | \ / 43 is interpreted by / \ | 1 0 | | 0 1 | \ / 44 is interpreted by / \ | 1 0 | | 0 1 | \ / 45 is interpreted by / \ | 1 0 | | 0 1 | \ / After renaming modulo { }, it remains to prove termination of the 0-rule system { } The system is trivially terminating.